UP Sidlangan's CEEM 2014

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The thing is, you can’t just go around reviewing blindly.

It’s best to invest in a program or material/s that already

gathers together information which will more likely be on

the exam than something that you randomly dug up from your high school notes. There’s no way to feel completely

secure on an exam with such a wide coverage, so just review what you can, and be confident in what you know. – FATIMA SUCALDITO, INTARMED UPCAT 2011 TOPNOTCHER

TABLE OF CONTENTS MATHEMATICS

2

SCIENCE

15

READING COMPREHENSION

28

LANGUAGE PROFICIENCY

58

POINTERS

69

ANSWER KEY

77

upsidlangan

THE COLLEGE ENTRANCE EXAM MODULE IS DIVIDED INTO FOUR SECTIONS MATHEMATICS SCIENCE READING COMPREHENSION LANGUAGE PROFICIENCY

1

MATHEMATICS

COLLEGE ENTRANCE EXAM MODULE

MATHEMATICS GENERAL DIRECTIONS ONE Solve each problem carefully and decide which the

best answer among the given choices is.

TWO Appropriately

blacken the circle your answer

corresponds to after the appropriate item number on your answer sheet. CORRECT METHOD OF SHADING THE BUBBLE A

B

WRONG METHODS OF SHADING THE BUBBLE

D

A

B

C

D

A

B

C

D

A

B

C

D

THREE Calculators are not allowed.

MATHEMATICS

2

upsidlangan 1.

What is 462 more than the product of 24 and 76? a.

2172

b. 2286

2.

c.

2362

d. 2387

3 of the class went to the canteen to eat. A third of the 5 remaining people in the room were doing school work while another

At lunch time,

third were chatting. The rest were sleeping. If there were 6 students sleeping, how many students does the class have? a.

40

b. 38 3.

c.

42

d. 45

In a school field trip, the ratio of students to teachers is 5:2. If the ratio of boys to girls among the students is 3:2 and there were 420 people who joined the field trip, how many boy students were there? a.

170

b. 180 4.

c.

190

d. 200

A fourth of a cake was set aside. Then a third of the remaining cake was

eaten. If there are 8 slices of cake left, how many slices of cake were there originally? a.

12

b. 14 5.

c.

16

d. 18

Matt could build a house in 24 days, while Stan could build the same

house in 12 days. If they worked together to build one house, how many days would it take for the house to be finished? a.

6

b. 7

3

MATHEMATICS

c.

8

d. 9

COLLEGE ENTRANCE EXAM MODULE 6.

What is the equation of a line passing through the points (4,6) and (2,7)? a.

7.

1

đ?‘Śđ?‘Ś = đ?‘Ľđ?‘Ľ + 8 2 1

b. đ?‘Śđ?‘Ś = đ?‘Ľđ?‘Ľ + 7 2

c.

1

đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ + 8 2 1

d. đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ + 7 2

Three colors are to be mixed to create a new color. If the ratio of the red, yellow and blue paint is 2: 3: 5 respectively. If 6 litres of paint were used

in total, what is the difference (in liters) between the amounts of red and blue paints used? a.

1.2

b. 1.4 8.

1.6

The scores of a student in his exams are 82, 77, 86, and 89. What should be his score in the last exam to get an average of 85? a.

89

b. 90 9.

c.

d. 1.8

c.

91

d. 92

A bus travelled 400 km in 8 hours. If a car travelled the same distance in 10 hours, how much faster was the bus than the car? a.

5 km/h

b. 10 km/h

c.

15 km/h

d. 20 km/h

10. A fruit vendor earned X pesos in a month. He used a fourth of his earnings to restock his supplies, and a third of the remaining money for personal purposes. How much of his earnings are left? a.

X/5

b. X/4

c.

X/3

d. X/4

MATHEMATICS

4

upsidlangan 11. Jake bought a bag for 850 pesos. If he was able to sell the bag for 935 pesos, how much, in percent, was his profit? a.

5%

b. 10%

c.

15%

d. 20%

12. A water tank has two pipes connected to it. One fills the tank with water, while the other empties it. If the first pipe could fill the tank in an hour, and the second pipe could empty a full water tank in an hour and a half.

How long would it take for the water tank to be full if both pipes are opened? a.

2 hours

b. 2 and ½ hours

c.

3 hours

d. 3 and ½ hours

13. In a school, 60% of the students are 16 years old and above. If there are

96 students who are below 16 years old, how many students does the school have? a.

58

b. 40

c.

240

d. 156

14. John had an average of 42 on his first three exams. After another two

exams, his average was 37. What should be his score in the next exam to achieve a total average of 41 in all of his exams? a.

43

b. 44

c.

45

d. 46

15. Sofia is 4 years younger than Mike. Ten years ago, Sofia’s age was only half of Mike’s. What is Mike’s age now? a.

16

b. 18

5

MATHEMATICS

c.

20

d. 22

COLLEGE ENTRANCE EXAM MODULE 16. A wheel’s radius is 6. If it travels a distance of 144π, how many revolutions does the wheel make? a.

12

c.

b. 13

14

d. 15

17. A 4ft. ladder is set against a wall. If the top of the ladder is 3 ft. away

from the ground, how far is the bottom end of the ladder from the wall? a.

7 ft

b. √7 ft

18. If đ?‘Žđ?‘Ž = a.

3

đ?‘?đ?‘?+2 2

= đ?‘?đ?‘? − 4, what is đ?‘Žđ?‘Ž?

b. 4

c.

6 ft

c.

5

d. √6 ft

d. 6

19. What is the equation of the line that passes through (2,4) and is perpendicular to the lineđ?‘Śđ?‘Ś = (2/3)đ?‘Ľđ?‘Ľ − 5? a.

2

đ?‘Śđ?‘Ś = đ?‘Ľđ?‘Ľ + 7 3

2

b. đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ − 7 3

c.

3

đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ − 7 2 3

d. đ?‘Śđ?‘Ś = − + 7 2

20. James joined a marathon and ran at a speed of 5 km/h. Jimmy joined the same marathon running at a speed of 3 km/h. If the marathon was a

20-kilometrerun, how much longer did it take Jimmy to finish the

marathon than James? a.

1 and

2

hours 3 1 b. 1 and hours 3

1 2 and hours 3 2 d. 2 and hours 3 c.

MATHEMATICS

6

upsidlangan 21. The sum of three numbers is 242. The difference between the smallest

number and the largest number is 12 while the difference between the middle and largest number is 7. What is the value of the middle number? a.

75

b. 80

c.

85

d. 87

22. What is the solution set (đ?‘Ľđ?‘Ľ, đ?‘Śđ?‘Ś) in systems of equations: 3đ?‘Ľđ?‘Ľ + 4đ?‘Śđ?‘Ś = 10 and2đ?‘Ľđ?‘Ľ − đ?‘Śđ?‘Ś = 3 ?

a.

(1, 2)

b. (2, 1)

c.

(-2, 1)

d. (-1, 2)

23. What is the slope of the line passing through (−4, 6) and (2,3)? a.

b.

− 1 2

1 2

c.

2

d. -2

24. Manny bought a television for Php 5000. It had a 20% discount. What was the television’s original price? a.

Php 5750

b. Php 6000

c.

Php 6250

d. Php 6500

25. Eddy can clean the house in 1 hour and 15 minutes. If Joe helps him,

they can clean the house in half an hour. How long will it take for Joe to clean the house alone?

a. b.

7

3 5 4 5

5

hour

c.

hour

d. 1 hour

MATHEMATICS

6

hour

COLLEGE ENTRANCE EXAM MODULE 26. What is tan θ?

a.

11

7

ᶿ 4

b. c. d.

7

11 4

11 4 7 7

4

27. If the radius of the circle is 7 cm, what is the area of the shaded region?

a.

146.14 cm²

c.

153.86 cm²

b. 300 cm²

d. 446.14 cm²

28. The sunlight hits a building at an angle of 60⁰, what is the length of the shadow if the building is 25 meters tall? a.

12.5

c.

b.

25

d.

√3

25√3

25√3 2

29. An isosceles triangle has an area of 48 cm² and a base with length 12 cm. What is the triangle’s perimeter?

a.

30 cm

b. 32 cm

c.

34 cm

d. 36 cm

MATHEMATICS

8

upsidlangan 30. Point B (4, 6) is the midpoint of line segment AC. If point A has coordinates (0, 7), find the coordinates of point C. a.

(8, 5)

b. (7, 5)

c.

(7, 4)

d. (8, 4)

31. AB has length 6. If C is the midpoint of AB, find the area of the shaded region is region. a.

36Ď€

c.

30Ď€

b. 33Ď€

A

C

B

d. 27Ď€

32. If 2������ �� + ������ 12 = ������ 48, what is ��? a.

36

b. 4

c.

2

d. 24

33. The graph of y = 2x² − 2x + c passes through the point (3, 4). What is the value of c? a.

8

b. -8 34. 2(3x 2 )3 is equal to: a.

6x 5 b. 6x 6

9

MATHEMATICS

c.

21

d. -21

c.

54x 5 d. 54x 6

COLLEGE ENTRANCE EXAM MODULE 35. If the length of the side of each of the small squares is 2 cm, what is the area of the shaded region?

a.

36 cm²

c.

26 cm²

b. 18 cm² d. 28 cm²

36. If the length of the side of a square is halved, what is the effect on the area A? a.

A/2

b. 2A

37. (x 4 y 2 )3 = a.

x4 y5 b. x 7 y 2

38. What is the value of x? a.

66

c.

22

c.

A/4

d. 4A

c.

x7 y6 d. x12 y 6 X+66

b. 33 3X

d. 11 e.

39. [(420÷6 )- 6 × 8] + [3 - 4(7 × 2 - 21) - (4 × 3 -6)²] = a.

17

b. -39

c.

-49

d. 22

MATHEMATICS

10

upsidlangan 40. What is the sum of the first five prime numbers? a.

18

c.

b. 28

39

d. 53

41. The product of 3.25 and 0.4 added to the quotient of 1.96 divided by 0.28 is a.

9.1

c.

b. 5.7

6.65

d. 8.3

42. It takes 21 days for 4 workers to finish a job. How many days will it take for 7 workers to finish the same job? a.

10

c.

b. 12

14

d. 16

43. Train A leaves the station at a speed of 40 km/h. Two hours later, train B leaves the same station at a speed of 60 km/h. Relative to the time train

A left the station, after how many hours will train B overtake train A? a.

5 hours

c.

b. 5.5 hours

6 hours

d. 6.5 hours

c.

44. Which of these dimensions cannot form a triangle? a.

3, 4, 6

c.

b. 11, 4, 8

d. 2, 7, 3

45. Which side has the shortest length? a.

AB

b. BC

c. AC d. cannot be determined

11

MATHEMATICS

3, 9, 8 A

80° C

55° B

COLLEGE ENTRANCE EXAM MODULE 46. What is the value of a.

2

6! ? 3!

b. 6

c.

18

d. 120

47. There are 12 green marbles, 8 yellow marbles and 16 blue marbles in a bag. If one marble is picked at random, what is the probability that it is not a blue marble? a.

1 3

48. What is196 a.

2744

b. 3� 2?

2 9

b. 4268

c.

4

c.

1138

9

d.

5 9

d. 3572

49. A car travelled west for 4 kilometres, then north for 6 kilometres. The car

travelled another 6 kilometres to the west, then another 9 kilometres to the north. How far is the car from its starting point?

a.

25 km

c.

b. 5√13 km

3√13 km

d. 39 km

50. George has 15 bills of P20, P50, and P100 denominations in his wallet. If

there are 3 more P20 bills than P50 bills, and he has a total of P610 pesos, how many P50 peso bills does he have? a.

6

b. 5

c.

8

d. 7

51. The volume of a cube is 512 m³. What is the surface area of the cube? a.

64 m²

b. 256 m²

c.

384 m²

d. 128 m²

MATHEMATICS

12

upsidlangan 52. A triangle has vertices,(0, 4), (3, −2)and (5, 7). This triangle is a.

Equilateral

c.

b. Isosceles

scalene

d. not enough information

53. If the three circles have the same radius A = 4 m, what is the area of the shaded region?

A

a.

96 m²

c.

b. 48 m²

24 m²

d. 192 m²

54. Max deposited Php 20,000 in a bank with a simple interest of 3% per year. How much will his money be after 3 years? a.

Php 22,000

c.

b. Php 21,800

Php 22,800

d. Php 23,000

55. A cone and a square pyramid have the same height and volume. If the base of the pyramid has an area of 49 m², what is the radius of the base

of the cone?

56.

a.

7Ď€

x+2

=

a.

�� – 2

x2 −4

b.

13

1

đ?‘Ľđ?‘Ľ+2

MATHEMATICS

b. 7√đ?œ‹đ?œ‹

c.

c.

7ďż˝ √đ?œ‹đ?œ‹ 1

x−2

d. đ?‘Ľđ?‘Ľ + 2

d. √7đ?œ‹đ?œ‹

COLLEGE ENTRANCE EXAM MODULE 57. What is the sum of the first 50 multiples of 3? a.

3750

b. 3675

c.

3725

d. 3825

58. The sum of the geometric progression 3, 12, 48,... is 4095. How many terms does the progression have? a.

5

c.

b. 6

7

d. 8

59. A cylinder is to be wrapped. If it has a radius of 6 cm and a height of 4 cm, how much wrapper will be used? a.

84π cm²

b. 120π cm²

60. Convert a.

25π to degrees. 4

1080⁰

b. 1125⁰

c.

72π cm²

c.

1170⁰

d. 100π cm²

d. 1215⁰

MATHEMATICS

14

upsidlangan

SCIENCE GENERAL DIRECTIONS ONE Read each problem carefully and decide which the

best answer among the given choices is.

TWO Appropriately

blacken the circle your answer

corresponds to after the appropriate item number on your answer sheet. CORRECT METHOD OF SHADING THE BUBBLE A

B

WRONG METHODS OF SHADING THE BUBBLE

D

THREE Calculators are not allowed.

15

SCIENCE

A

B

C

D

A

B

C

D

A

B

C

D

COLLEGE ENTRANCE EXAM MODULE 1.

The Mohs scale of mineral hardness was created in 1812 by the German

geologist Friedrich Mohs in order to characterize the scratch resistance of various minerals through the ability of a harder material to scratch a

softer material. According to Mohs hardness scale, which of the following minerals cannot be scratched by Topaz? a. 2.

b. Corundum

Shield

b. Composite

d. Fluorite

c.

Cinder

d. Caldera

Who proposed the Continental Drift Theory in the early 1900’s? Harry Hess

b. Albert Einstein

c.

Alfred Wegener

d. Alexandre Brongniart

In vertebrate organisms, oxygen and carbon dioxide are transported throughout the body by binding to a. b. c. d.

5.

Gypsum

eruptions between 140,000 and 5,380 BP. What kind of volcano is it?

a. 4.

c.

Taal Volcano lies in the middle of Taal Lake and was formed by explosive

a. 3.

Talc

water molecules in the blood hemoglobin in white blood cells hemoglobin in red blood cells lymph in white blood cells

The ability of embryonic cells to retain the potential to develop into any part of the organism is referred to as a. cell fate b. pattern formation

c. polarity d. totipotency

SCIENCE

16

upsidlangan 6.

Most cells in the human body contain proto-oncogenes that can be stimulated to become cancerous (oncogenes) through mutations. The normal function of proto-oncogenes in human cells is to a. b. c. d.

7.

repair damaged regions of DNA produce antibodies against invading pathogens control normal cell growth and division splice introns from mRNA during RNA processing

The evolutionary history of a species, or groups of related species, is referred to as a. phylogeny b. speciation

8.

c. the fossil record d. paleontology

Which of the following is a large family of RNA molecules that is responsible for conveying genetic information from DNA to the

ribosome, where they specify the amino acid sequence of the protein

products of gene expression? a. 9.

tRNA

b. cRNA

c.

mRNA

Peter figured in a car accident. After that, he lost his ability to talk. What part of the nervous system has most likely been affected? a.

Cerebrum

b. medulla oblongata

c.

cerebellum

d. spinal cord

10. Which of the following does not describe a mineral? a.

Crystalline structure

c.

Organic substance in solid form

b. Exist naturally

d. Composed of one or more elements

17

d. rRNA

SCIENCE

COLLEGE ENTRANCE EXAM MODULE 11. An atom’s mass is largely determined by the mass of its __________. a.

nucleus

b. protons

c.

electrons

d. neutrons

12. Noble gases have no electronegativity values because ________________. a.

they form very few compounds since they are gases

c.

they are radioactive

b. they are rare

d. they have stable electronic configurations

13. In his periodic table, Mendeleev left blank spaces for undiscovered elements. How did he predict the properties of these elements? a.

He studied the new elements produced by radioactive decay.

c.

He studied the stars’ spectra that contained them.

b. He determined their properties such as freezing point, valence and density.

d. He noted periodic trends of known elements surrounding the undiscovered ones.

14. Salts are known to be crystal lattice-forming compounds. What type of bond is responsible for forming the lattice? a.

hydrogen

b. covalent

c.

ionic

d. polar

15. An idea that is proven correct every time it is tested is called a a.

theory

b. hypothesis

c.

scientific method

d. scientific law

SCIENCE

18

upsidlangan 16. The property of matter that is dependent on altitude is _________. a.

mass

b. weight

c.

density

d. volume

17. Which of the following is likely to be a Noble Gas? a.

a very toxic and reactive green gas

c.

an unreactive colourless gas

b.

pale yellow reactive gas

d. low boiling liquid forming an unreactive gas 18. The chemical reaction below can be classified as a ________ reaction? Zn+(s) + HCl(aq) ------ > ZnCl2 (aq) + H2 g() a.

synthesis

b. decomposition

c.

single-replacement

d. double-replacement

19. Which of the following is not an evidence of a chemical reaction? a.

A liquid water freezes into an ice cube.

c.

A piece of copper raised the temperature of an acid upon addition.

b. An iron nail changed into a rusty orange color.

d. Gas bubbles produced when an antacid tablet was placed in water.

20. The relationship between the temperature and volume of a gas is explained by Charles’ Law. Which graph represents this relationship?

a.

19

SCIENCE

b.

COLLEGE ENTRANCE EXAM MODULE

c.

d.

21. How much 3.0 M NaCl solution will you need to prepare 150 mL of 1.5 M NaCl solution? a.

300 mL

b. 30 mL

c.

75 mL

d. 13 mL

22. From the reaction below, how many moles of butane gas (C4H10) is needed to produce 14 moles of carbon dioxide (CO2)?

C4H10 + a.

13 2

O2 ------ > 4CO2 + 5H2O

12 moles

b. 3.5 moles

c.

56 moles

d. 0 moles

23. Absorption of heat energy is NOT involved in _______. a.

vaporization

b. sublimation

c.

condensation

d. melting

24. The predicted high temperature for New Delhi on a given day is 41oC. Is

this temperature higher or lower than the predicted daytime high of 103oF for the same day in Phoenix, Arizona? a.

Higher

b. Lower

SCIENCE

20

upsidlangan 25. A chunk of coal is weighed twice while suspended from a spring scale.

When the coal is suspended in air, the scale registers 156g; when the

coal is suspended underwater at 20oC, the scale registers 59g. What is the density of the coal? The density of water at 20oC is 0.9982 g cm-3. a.

c.

2.7 g cm-3

1.3 g cm-3

d. 1.6 g cm-3

b. 4.6 g cm-3

26. In the sample of sulfur weighing 4.07g, how many moles of sulfur are present? a.

0.127 mol S

c.

b. b. 0.234 mol S

0.154 mol S

d. 0.138 mol S

27. A 0.455g sample of magnesium is allowed to burn in 2.315g of oxygen

gas. The sole product is magnesium oxide. After the reaction, no magnesium remains and the mass of unreacted oxygen is 2.015g. What mass of magnesium oxide is produced? a. 1.555 g

b. 1.254 g

c.

1.879 g

d. 1.755 g

28. Potassium-40 is one of the few naturally occurring radioactive isotopes

of elements of low atomic number. Its percent natural abundance among K isotopes is 0.012%. How many K-40 atoms are present in

225mL of whole milk containing 1.65 mg K/mL? a.

6.6 x 1015 atoms K-40

b. 9.6 x 1017 atoms K-40

c.

6.9 x 1017 atoms K-40

d. 6.9 x 1015 atoms K-40

29. What is the mass in kilogram of 1 litre kerosene which has a specific gravity of 0.6? a.

21

0.3

SCIENCE

b. 300

c.

600

d. 0.6

COLLEGE ENTRANCE EXAM MODULE 30. A small can weighs 1.16 N in air and has a volume of 1 x 10-5 m3. How much will it weigh when completely submerged in water? a.

0.014 N

b. 10.4 N

c.

1.06 N

d. 3.4 N

31. Which of the following is false? a.

Magnets always have two poles.

c.

A coil which carries a current becomes a magnet.

b. Moving electrons in atoms cause magnetic fields. d. Force of repulsion/attraction is directly proportional to the distance between two poles.

32. An object is located 15.0 cm. in front of a concave mirror whose focal length is 5.0 cm. At what distance will the image form? a.

3.8 cm

b. 7.5 cm

c.

0.1 cm

d. 0.3 cm

33. When equal amounts of red and green lights are combined, what color of light is produced?

a.

yellow

b. magenta

c.

cyan

d. white

34. Which concept would distinguish a colloid from a suspension? a. particles scatter light

b. particles remain suspended even after long standing c. exhibits more than one phase

d. particles are large enough to be visible

SCIENCE

22

upsidlangan For the next three questions:

A girl is riding a bicycle while eating her favorite strawberry-flavored ice cream. Too busy enjoying her food, the girl fails to notice a bump on a road. The 0.02 kg ice cream slips from her hand. The ice cream is held 0.67 m above the road and is thrown upwards at 0.20 meters per second. 35. How long will it take before the ice cream hits the ground? a. 0.36 seconds b. 0.39 seconds

c. 0.35 seconds d. 0.58 seconds

36. At what speed will the ice cream hit the ground? a. 3.6 meters per second b. 3.9 meters per second

c. 3.0 meters per second d. 3.5 meters per second

37. If the ice cream hits the ground without bouncing back, what is the impulse on the ice cream? a. 0.205 kg-mps b. 0.073 kg-mps

c. 0.124 kg-mps d. zero

For the next two questions: Superman is on his way to meet with Lois Lane when he sees the girl in the previous problem. Superman is at a distance of 30 meters and a height of 50 meters away from the little girl and her ice cream. 38. Calculate the minimum constant velocity Superman must travel if he was to catch the ice cream at 0.1 meters above the ground. a. 10.583 km/s b. 10.347 km/s

c. 10.674 km/s d. 10.358 km/s

39. What is true about the ice cream and Superman if Superman stops moving at the moment he catches ice cream? a. Both Superman and the ice cream will have zero momentum. b. Both Superman and the ice cream will experience zero impulse.

23

SCIENCE

COLLEGE ENTRANCE EXAM MODULE c.

Superman will experience a zero impulse and the ice cream will have zero momentum. d. Superman will have a nonzero momentum and the ice cream will experience a nonzero impulse.

For the next two questions, refer to the phase diagram of water shown below. Lf = 334 kJ/kg Lv = 2260 kJ/kg Specific heat = 4.184J/g°C

40. Given 3kg of water, how much heat is produced at region 4? a. 753.33 kJ

b. 0 kJ

c.

717.02 kJ

d. 6780 kJ

41. In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in

0.320 kg of water. Assuming that all the heater’s power goes into the

water, how much time is required to raise the temperature of water from 20oC to 80oC? a. 6.7 min

b. 5.3 min

c.

4.8 min

d. 6.1 min

SCIENCE

24

upsidlangan 42. What sort of intermolecular forces exist in a crystal of ice? a. Dipole forces

c.

b. London forces

Hydrogen bonds

d. Polar covalent bonds

43. True or False. If the acceleration is zero, the particle cannot be moving. a. True

b. False

44. True or False. A projectile launched at an angle đ?‘žđ?‘ž with initial velocity đ?‘Łđ?‘Łđ?‘œđ?‘œ has zero acceleration at the top of its trajectory. a. True

b. False

45. True or False. A force which is always perpendicular to the velocity of a particle does no work on the particle. a. True

b. False

46. On a velocity vs. time graph, the motion of a car travelling along a straight road with uniform acceleration of 2m/s 2 would appear as a. horizontal straight line

b. straight line sloping upward to the right

c. straight line sloping downward to the right

d. curved line whose slope increases with time 47. A stationary 0.300[kg] picture frame hangs from a nail by a single string, as shown in the figure on the right. What is the tension in the string? a.

1.47 N

b. 1.52 N

25

SCIENCE

c.

3.05 N

d. 5.69 N

COLLEGE ENTRANCE EXAM MODULE 48. Which of the following statements is/are true? I.

The dot product of two vectors is a scalar and will be equal to zero if the vectors are perpendicular. II. U·V = |U| |V| cos θ, where 0° ≤ θ ≤ 180°, and θ is the angle when the two vectors are placed tail-to-tail. III. One of the applications of the cross product is the projection of the vector onto a line. a. I only

b. II only

c.

I and II only

d. I and III only

49. A 20.0 kg box initially at rest has a net force of 30.0 N in the direction of its displacement. What is its speed after it moved 10.0 m? a. 3.87 m/s b. b.5.48 m/s

c. 10.0 m/s d. 30.0 m/s

50. A particle moving in one dimension has the following position vs time

plot. At point C, what can you say about the particle’s velocity vx and acceleration ax?

a. vx < 0 and ax > 0 b. vx > 0 and ax > 0

c.

vx = 0 and ax = 0

d. vx = 0 and ax > 0

51. A box with weight 55 N is on a rough horizontal surface. An external force F is applied horizontally to the box. A normal force and a friction force are also present, denoted by N and f. When force F equals 2.0 N, the box is in motion at constant velocity. When force F equals 2.6 N, the acceleration of the box is closest to: a. 0.15 m/s2 b. 0.11 m/s2

c.

0.18 m/s2

d. 0.16 m/s2

SCIENCE

26

upsidlangan 52. A 5.0-[kg] box is at rest on a ramp inclined at an angle of 15◦. The coefficients of static and kinetic friction are μs = 0.60 and μk = 0.20, respectively. If you push the box downward along the ramp, what is the minimum amount of force that you must apply on the box for the box to start moving? a. 3.2 N

b. 9.5 N

c.

16 N

d. 28 N

53. A stone is thrown upward from a roof at the same time as an identical stone is dropped from there. The two stones _________. a.

reach the ground at the same time

c.

have the same acceleration when they reach the ground

b. have the same velocity when they reach the ground d. none of the above

For the next seven questions: During basketball practice, Midorima Shintaro, the best shooter of ‘The Generation of Miracles’, tries to make a shot 100 meters from the basket. He releases the ball at an angle of 45 degrees from the horizontal. 54. At what initial velocity must Midorima release the ball for him to make the shot? The basket and the ball are at equal heights right before the ball is released. a. 31.3 meters per second b. 29.8 meters per second

c. 30.7 meters per second d. 32.4 meters per second

55. How long is the air time of the ball? a. 5.1 seconds b. 4.5 seconds

c. 3.9 seconds d. 3.8 seconds

56. What is the maximum height of the ball above the basket? a. 24.9 meters b. 20.7 meters

27

SCIENCE

c. 23.5 meters d. 22.4 meters

COLLEGE ENTRANCE EXAM MODULE 57. A bird is flying near the basketball court. At the time Midorima releases the ball, the bird is just above the basket and is flying horizontally towards Midorima at a constant speed of 8 meters per second. Calculate the instantaneous horizontal velocity of the ball when the bird catches it. a. b. c. d.

24.5 meters per second 22.1 meters per second 21.6 meters per second 21.3 meters per second

58. The bird catches the ball t seconds after flying over the basket. What is the value of t? a. 4.0 seconds b. 3.3 seconds

c. 3.6 seconds d. 2.9 seconds

59. How high is the bird above the basket? a. 17.9 meters b. 19.4 meters

c. 17.6 meters d. 19.6 meters

60. A metal ball is thrown vertically upwards from the roof at the same time a rubber ball of equal mass is dropped from there. The two balls _______. a. b. c. d.

will hit the ground with the same velocity will hit the ground with the same momentum will hit the ground with the same impulse none of the above

SCIENCE

28

upsidlangan

READING COMPREHENSION GENERAL DIRECTIONS ONE Read each problem carefully and decide which the

best answer among the given choices is.

TWO Appropriately

blacken the circle your answer

corresponds to after the appropriate item number on your answer sheet. CORRECT METHOD OF SHADING THE BUBBLE A

29

B

READING COMPREHENSION

D

WRONG METHODS OF SHADING THE BUBBLE A

B

C

D

A

B

C

D

A

B

C

D

COLLEGE ENTRANCE EXAM MODULE Woodrow Wilson won his first office in 1910 when he

was elected governor of New Jersey. Two years later he was elected president in one of the most rapid political rises in

our history. For a while Wilson had practiced law but found it both boring and unprofitable; then he became a political

scientist and finally president of Princeton University. He did

an outstanding job at Princeton, but when he was asked by the Democratic boss of New Jersey, Jim Smith, to run for governor, Wilson readily accepted because his position at Princeton was becoming untenable.

Until 1910, Wilson seemed to be a conservative

Democrat in the Grover Cleveland tradition. He had denounced Bryan in 1896 and had voted for the National

Democratic candidate who supported gold. In fact, when the Democratic machine first pushed Wilson's nomination

in 1912, the young New Jersey progressives wanted no part of him. Wilson later assured them that he would champion the progressive cause, and so they decided to work for his

election. It is easy to accuse Wilson of political expediency, but it is entirely possible that by 1912 he had changed his

views as had countless other Americans. While governor of

New Jersey, he carried out his election pledges by enacting an impressive list of reforms.

Wilson secured the Democratic nomination on the

forty-sixth ballot. In the general campaign, Wilson emerged

as the middle-of-the-road candidate - between the

conservative William H. Taft and the more radical Theodore

Roosevelt. Wilson called his program the New Freedom, which he said was the restoration of free competition as it

had existed before the growth of the trusts. In contrast, Theodore Roosevelt was advocating a New Nationalism,

which seemed to call for massive federal intervention in the

economic life of the nation. Wilson felt that the trusts should READING COMPREHENSION

30

upsidlangan be destroyed, but he made a distinction between a trust and legitimately successful big business. Theodore Roosevelt,

on the other hand, accepted the trusts as inevitable but said that the government should regulate them by establishing a new regulatory agency. 1.

The author's main purpose in writing this passage is to a.

argue that Wilson is one of the great U.S. presidents

c.

explain Wilson's concept of the New Freedom

e.

suggest reasons that Wilson's presidency may have started World

b. survey the difference between Wilson, Taft, and Roosevelt d. discuss some major events of Wilson's career

2.

War I

The author implies which of the following about the New Jersey progressives? a.

They did not support Wilson after he was governor.

c.

They were more interested in political expediency than in political

b. They were not conservative Democrats. causes or reforms.

d. Along with Wilson, they were supporters of Bryan in 1896. e.

3.

They particularly admired Wilson's experience as president of Princeton University.

The passage supports which of the following conclusions about the progress of Wilson's political career? a.

Few politicians have progressed so rapidly toward the attainment of

higher office.

b. Failures late in his career caused him to be regarded as a president who regressed instead of progressed.

31

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE c.

Wilson encountered little opposition after he determined to seek the presidency.

d. The League of Nations marked the end of Wilson's reputation as a e. 4.

strong leader.

Wilson's political allies were Bryan and Taft.

In the statement "Wilson readily accepted because his position at

Princeton was becoming untenable" (line 7), the meaning of "untenable" is probably which of the following? a.

unlikely to last for years

c.

difficult to maintain or continue

e.

something he did not have a tenacious desire to continue

b. filled with considerably less tension d. filled with achievement that would appeal to voters

5.

According to the passage, which of the following was probably true about the presidential campaign of 1912? a.

Woodrow Wilson won the election by an overwhelming majority.

b. The inexperience of Theodore Roosevelt accounted for his radical c.

position.

Wilson was unable to attract two-thirds of the votes but won anyway.

d. There were three nominated candidates for the presidency. e. 6.

Wilson's New Freedom did not represent Democratic interests.

John was a compassionate, sensitive, and gentle man. His twin brother James however, was merciless, unfeeling, and cruel. The relationship between the two sentences is best described as a.

cause and effect

b. contrast

c.

repetition

d. statement and example READING COMPREHENSION

32

upsidlangan 7.

The nonfiction novel Midnight in the Garden of Good and Evil, by John Berendt was very popular. It was on the New York Times bestseller list for over 90 weeks. How are the two sentences related? a.

The second sentence explains why the book is popular.

c.

The first sentence explains the meaning of the second.

b. The first sentence contradicts the second.

d. The second sentence provides evidence for the first. 8.

Two of the most common causes of homelessness are the lack of homes and of income with which to rent or acquire them.Two million jobs are lost in industry every year and 50% of the people laid off end up in jobs that pay low wages. How are the two sentences related? a.

The first sentence contradicts the second.

c.

The second sentence illustrates the point made by the first sentence.

b. The second sentence presents an event and the first sentence its consequences.

d. The first sentence explains the meaning of the second.

During the 1890's in America, child labor was common

in the garment trade. Textile

manufacturers squeezed

workers into small, cramped, poorly ventilated workplaces

known as sweatshops. Factory labor had a devastating

effect on children's lives. For example, children who worked six-day weeks in a candy factory refused gifts of candy. The

legs of a 7-year-old girl were paralyzed and deformed because she worked "day after day with little legs crossed, pulling out bastings from garments."

33

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE 9.

The purpose of the passage is to present a.

a personal observation

b. a solution to the problem

c.

factual information

d. opposing scientific theories

Research shows that young children who are read to on

a regular basis will grow up to be better readers. When

children sit in their parent's lap and listen to stories, they are

learning about the pleasures of reading and the patterns of language. When you see children turning the pages of a

book, looking at the pictures, and telling the story, often from memory, they are engaged in what is called emergent

literacy. Parents can foster this early language and literacy development by talking with their children, telling them

stories, reading to them every day, and surrounding them with books.

10. The writer's main point is that a.

parents should read to their children every day

c.

pretend reading is one of the first steps towards learning to read

b. children must learn the alphabet before they can learn to read d. parents should buy their children lots of books 11. Emergent literacy is best defined as a.

the practice of pretend reading

c.

patterns of language

b. reading to children every day

d. early language and reading development

READING COMPREHENSION

34

upsidlangan They sound more like people everyday Discover, May 2000 Male chimps tend to be a tight bunch. They sit close and

groom each other, hunt together, and close ranks periodically to patrol their boundaries silently. Sometimes

they even sneak outside their territory to beat up or kill

males from neighboring groups. The compelling force behind all this male bonding, primatologists concluded,

must be kinship. After all, males always stay in the group where they're born, while females leave when they are sexually mature.

Now, thanks to molecular genetics, we know otherwise.

Over the past nine years, in Uganda's Kibale National Park,

researchers from Harvard University and the University of Michigan have scavenged hair left by nesting and self-

grooming chimpanzees. Embedded in those samples are

cells that provide a DNA blueprint of each chimp. When the researchers compared the chimps' kinship to their behavior, they found that males who sit together and groom each

other are not closely related. More significant still: Those who hunt and patrol borders together aren't closely related either.

Kinship doesn't underlie male cooperation, in other

words. Chimpanzees get to know each other and keep track of the political intrigue that goes with making, breaking, and

manipulating relationships. Although kinship is important, chimps often rely on the fragile ties of friendship.

12. According to the researchers from Harvard University and the University of Michigan, what is the force that makes Chimpanzees stick together?

a.

kinship

b. fear

35

c.

love

d. hate

READING COMPREHENSION

e.

friendship

COLLEGE ENTRANCE EXAM MODULE 13. Which of the following made the researchers debunk the old beliefs in male chimpanzees' cooperation? a.

Female chimpanzees leave when sexually mature.

c.

Male chimpanzees exhibit violent behaviour towards those not of

b. Males stay in groups when they are born. their own group.

d. Members of chimpanzee groups may not be related to each other.

e.

Male chimpanzees tend to protect their own members.

14. Which of the following best expresses the main idea of the selection? a.

Chimpanzees behave like people.

c.

Even among chimpanzees, blood is thicker than water.

b. Friendship, not kinship, is the strongest between male chimpanzees.

d. Researchers have explained the force that binds chimpanzees e.

together.

none of the above The degree in which the essence and aim of politics is

power over man, politics is evil; for it is to this degree that it degrades man to a means for other men. It is to be found

on the political scene. For here the animus dominandii is not a mere admixture to prevailing aims of a different kind but

the very essence of intention, the very lifeblood of the action, the constitutive principle of politics as a distinct

sphere of human activity. Politics is a struggle for power

over men, and whatever its ultimate aim may be, power is

its immediate goal and the modes of acquiring, maintaining, and demonstrating it determine the techniques of political action.

The evil that corrupts political action is the same evil

that corrupts all action, but the corruption of political action READING COMPREHENSION

36

upsidlangan is indeed the paradigm and prototype of all possible

corruption. The distinction between innocence and guilt, morality and immorality, goodness and evil, but lies in the degree alone in which two types of action deviate from the

ethical norm. Nor is the distinction of a normative character at all. To hold differently, as the school of the dual standard does, is to confound the moral obligations of man and his actual behavior with respect to these obligations. There is

not one kind of ethical precept applying to political action

and another one for the private sphere, but one and the

same ethical standard applies to both, observed and observable, however, by either with unequal compliance. 15. According to the selection, politics is evil because _________? a.

it provides opportunities for corruption

c.

it makes the politician go against the acceptable norms of civil

b. it degrades man to a level where he becomes the tool of other men behaviour

d. it destroys the character and disregards morality

e.

politicians disregard the welfare of others in their pursuit of wealth and power

16. The selection tells us that the goal of every evil politician is _______? a.

acquisition of wealth

c.

destruction of enemies

e.

capturing the most powerful position

b. expansion of political base

d. acquisition of power

17. The second paragraph tells us that _______.

37

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE a.

Corruption in politics is different from corruption in private life.

c.

Different ethical standards apply to corruption in politics and in the

b. Politics attracts the most corrupt. private sphere.

d. The political acts of a person differ from his private ones.

e.

The evil that corrupts political action is the evil that corrupts all action.

Traditionally a good father provided for his family and

acted as disciplinarian—but he could be a pretty remote character. Today many men actively share parenthood with

their wives and consider child rearing as important as their careers.

But a father is not simply a "second mother"—like Mom,

another nurturer and comforting presence. Good fathers

have more arousing and playful relationship with their children. Research suggests that fathers are more likely than

mothers to teach physical competence, adventurousness, new skills and confidence in asserting opinions.

Henry Biller, co-author of The Father Factor, says that

children with effective fathers get along better with their

peers and display more social confidence. They are more comfortable in new situations, adapt to change more easily and score higher on intelligence tests.

18. Based on the selection, which statement best expresses the role of fathers today? a.

A father should be a disciplinarian, first and foremost.

b. A father is neither a friend nor a brother to his children, but someone c.

who should command their respect and obedience.

A father must be a good provider. He should put his career over and above his other functions in the family.

READING COMPREHENSION

38

upsidlangan d. A father must equally share with the mother the task of bringing up their children. He is a disciplinarian, a provider, a friend, a teacher,

f.

and a model to his children.

none of the above

19. Children with effective fathers tend to be ______ than those without effective fathers. a.

more adaptable

c.

better able to get along with their peers

e.

all of the above

b. more socially confident

d. more comfortable in unfamiliar situations

20. Which of the following is the best title for the selection? a.

Father, A Friend to His Children

c.

The Family's Disciplinarian

e.

The Ideal Father

b. The Role of Effective Fathers Today

d. The Importance of a Father

Isang pag-aaral tungkol sa pagsasanay ng mga marino

ang isinagawa ng World Maritime University (WMU) sa Malmo, Sweden at ng Seafarers International Research

Centre (SIRC) ng University of Wales sa Cardiff, United Kingdom. Inirekomenda nito ang paghihigpit sa pagbibigay

ng akreditasyon sa mga pribadong paaralan sa Pilipinas na may kursong pangmaritima at pagsasanay sa mga nais maging marino.

Kinumpirma ng pag-aaral na ito ang dati nang

masamang reputasyon ng mga eskwelahan sa maritima ng bansa dahil sa kakulangan at hindi maayos na superbisyon

39

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE ng pamahalaan. Sinabi nilang hindi lang kumplikado ang “patung-patong na istraktura sa superbisyon at pagkontrol ng

pangmaritimang

edukasyon

at

pagsanay

kundi

naaapakan pa ng awtoridad ang ilang ahensya nito sa ibang larangan."

Pinuna rin ng nasabing pag-aaral na pinondohan ng

European Commission na pera lamang ang habol ng maraming paaralang maritima sa Pilipinas. Wala silang

sapat na kagamitan at pasilidad, at kulang din sa karanasan ang pagsakay sa barko ang kanilang mga guro.

21. Ano ang inirekomenda ng isang pag-aaral ng World Maritime University at Seafarers International Research Centre? a.

pagsuspinde sa mga paaralang maritima sa Pilipinas

b. paghihigpit sa akreditasyon ng mga paaralang may mga kursong c.

pangmaritima

pagpapatigil sa mga kursong maritiima sa Pilipinas

d. pagpapabuti sa mga kursong pangmaritima sa mga paaralan sa e.

Pilipinas

pagmumulta ng mga paaralang maritima sa Pilipinas

22. Ano ang epekto ng kulang at hindi maayos na superbisyon ng pamahalaan sa mga paaralang maritima? a.

masamang reputasyon ng mga paaralang maritima sa bansa

c.

pagbawas sa dami ng mga nag-aaral ng kursong maritime

e.

pagkalugi ng mga paaralang maritima sa bansa

b. pandaraya ng mga paaralang maritima

d. pagbagsak ng mga nag-aaral ng mga kursong maritima sa mga eksaminasyon na ibinibigay sa ibang bansa

READING COMPREHENSION

40

upsidlangan 23. Ayon sa pag-aaral, ano ang talagang habol ng mga paaralang maritima sa Pilipinas? a.

kasanayan ng mga mag-aaral

c.

pera lamang ng mga mag-aaral

e.

kaunlaran ng Pilipinas

b. mabigyan ang mga mag-aaral ng karanasan sa pagsakay ng barko

d. kasikatan sa larangan ng edukasyon

Isa sa mga pangunahing problema ang sunog sa

masikip ng lungsod katulad ng Maynila. Bagaman may Bureau of Fire Protection (BFP) na tagaapula ng sunog, hindi makakapayapa

ng

kalooban

ang

nagdudumilat

na

katotohanang kulang ito sa tao, pondo at kagamitan—at kung

gayon,

kapasidad

upang

magresponde

nang

mabilisan at sa paraang epektibo tuwing magkakasunog sa anumang lugar.

Nakapagpapalala sa sitwasyon ang hindi mapigil na

pagdami sa lungsod ng mga tinaguriang firetrap, mga

gusali at bahay na hindi tumutugon sa mga pamantayan at walang

permiso

mula

sa

mga

kinauukulang

tagapagpatupad ng kaligtasan. Idagdag pa rito ang mga

bumberong magnanakaw na pumapatay lang ng sunog kapag may suhol at mangingilabot ka sa isiping isang

tinderbox ang Maynila na pwedeng sumabog anumang oras.

24. Ano ang paksa ng seleksyon? a.

Problema sa sunog ng Maynila

c.

Kasikipan ng Maynila

b. Kahinaan ng BFP

41

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE d. Mga Bumberong magnanakaw e.

Mga problema ng Maynila

25. Ano ang pangunahing ideya ng seleksyon? a.

Walang kapasidad ang BFP na patayin ang malaking sunog sa Maynila

b. Nakapagpapalala sa problema sa sunog ang paglaki ng populasyon c.

ng Maynila

Maraming dahilan kung bakit malala na ang problema sa sunog ng Maynila

d. Hindi tumutugon sa mga pamantayan ang mga gusali sa Maynila

e.

Walang kakayahan ang Maynila na lutasin ang maraming problema nito

26. Bakit mahirap pagtiwalaan ang mga bumbero ng Maynila? a.

Kulang sila sa karanasan at kasanayan.

c.

Abala sila sa pagpatay ng maraming sunog.

e.

Tamad at kulang sila sa kasanayan.

b. Mabagal silang dumating kapag may sunog. d. Magnanakaw o tiwali ang marami sa kanila.

Maliliit na negosyo ang bumubuo sa ekonomiyang tago

o di-pormal na sektor ng ekonomiya. Ito ang mga

negosyong hindi nagbabayad ng buwis, lumilihis sa batas, walang tiyak na oras ang trabaho, at walang kredito sa bangko. Kabilang dito ang mga tindahang sari-sari, mga

naglalakong tindero, mga tsuper ng dyip at taksi, mga katulong, mga gurong nagtitinda ng damit, mga klerk na

nagbebenta ng appliances, at mga tindero ng tiket ng

sweepstakes. Kasama ang mga negosyong midyum ang laki, binubuo nila ang 90 porsyento ng mga negosyo sa Pilipinas.

READING COMPREHENSION

42

upsidlangan Kadalasan, isa lamang ang may-ari ng negosyong

kabilang sa ekonomiyang tago. Dalawang-katlo o 66

porsyento ang mga negosyong ganito ang binubuo ng

iisang tao lamang. Nasa bahay lamang ang kanilang negosyo at wala silang sariling talyer o pagawaan.

Pagtitinda ang kadalasang ginagawa ng 70 porsyento ng mga negosyong ito.

27. Bakit tinatawag ng ekonomiyang tago ang sektor na kinabibilangan ng mga tindero sa kalye at nga naglalako ng taho? a.

dahil hindi sila nagpapakita sa mga awtoridad

c.

dahil wala silang permanenteng lugar

e.

dahil hindi sila nagbabayad ng buwis at lihis sa batas ang kanilang

b. dahil lihim ang kanilang pangnenegosyo

d. dahil nakalagay ang kanilang negosyo sa tagong lugar pagnenegosyo

28. Ano ang bumubuo ng siyam sa sampung negosyo sa Pilipinas? a.

mga negosyong kabilang sa ekonomiyang tago

c.

mga negosyong kabilang sa sektor na pormal

e.

mga negosyong isang milyon o higit pa ang puhunan

b. mga negosyong maliit o midyum ang laki

d. mga negosyong pag-aari ng iisang tao lamang

29. Alin sa mga sumusunod na gawain ang bumubuo ng pinakamalaking bahagi ng ekonomiyang tago? a.

pagtitinda

b. pagmamaneho

43

READING COMPREHENSION

c.

pagkukumpuni

d. pagkakatulong

COLLEGE ENTRANCE EXAM MODULE Dreams By Langston Hughes Hold fast to dreams For if dreams die

Life is a broken-winged bird That cannot fly.

Hold fast to dreams

For when dreams go Life is a barren field Frozen with snow.

30. What figure of speech did the author use in the first stanza? a.

Simile

b. Hyperbole

c.

Metaphor

d. Irony

31. The author is a South African Negro during the Apartheid Policy when

most blacks were treated as inferior. To what could he be alluding to in the last two lines of the poem? a.

White People

b. Slaves

c. Snow

d. Ice

32. What effect does the poem have upon other Negroes? a.

It made them sadder.

c.

It increased their anger towards Whites.

b. It made them feel downtrodden.

d. It increased their determination.

READING COMPREHENSION

44

upsidlangan 33. Which statement is not a correct inference based on the poem? a.

Blacks and Whites enjoy equal rights.

c.

Blacks also have dreams of a better life.

b. Blacks are treated inferior over Whites.

d. Whites enjoy more rights over Blacks.

What is the happy life? Self-sufficiency and abiding

tranquillity. This is the gift of greatness of soul, the gift of constancy which perseveres in a course judged right. How

can these attitudes be attained? By surveying truth in its

entirety, by safeguarding in every action order, measure, decorum, a will that is without malice and benign, focused undeviatingly upon reason, once amiable and admirable.

The wise man’s soul should have the quality of a God’s. What can a man desire if he possesses everything that is

honorable? If the dishonorable can contribute to the

optimum state, then the happy life will be comprised of elements other than honorable. And what could be meaner or stupider than to weave the good of the rational soul out of irrational strands?

-Seneca

34. What constitutes a happy life? a.

Attainment of everything that one desires

c.

Self-sufficiency and tranquillity

b. Being at peace with everyone

d. none of the above

35. How can one attain a happy life, according to Seneca? a.

45

By being hypocritical

READING COMPREHENSION

c.

Both a and b

COLLEGE ENTRANCE EXAM MODULE b. By getting what one wants no matter what the cost

d. none of the above

36. What is an indication that a man’s soul is already like that of a God’s? a.

He is at peace with others.

c.

He attains everything he desires without limitation.

b. He desires everything.

d. He discerns truth, focuses upon reason, has a will that is without malice.

37. Which of the following statements is NOT true based on the selection? a.

Self-sufficiency does not bring happiness.

c.

Man should aim to have a soul like that of a God’s.

b. Greatness of soul is attainable.

d. Man should not desire that which is dishonorable. Kabataan: Pag-asa ng Bayan Mula sa Likha IV nina Samonte, et al.

“ Ang kabataan ang pag-asa ng bayan.”Ito ang sinabi ni

Dr. Jose Rizal, ang ating pambansang bayani. Malaki ang

pagtitiwala niya sa angking talino at kakayahan ng mga kabataan. Naniniwala siya na mahahango ang bansang Pilipinas sa tiyak na kasawian kung sila, ang mga kabataan, ang magkakaroon ng tunay na pag-ibig sa bayan. Maraming

maitutulong

ang

mga

kabataan

sa

pagpapaunlad ng bansa. Maaaring simulan nila ang pagmamalasakit sa kani-kanilang mga pamayanan. Sa mga

proyektong inilulunsad ng pamahalaan, may mga gawaing pangkabataan katulad ng pagpapaganda ng kapaligiran at paglilinis ng mga sari-sariling bakuran. Makatutulong din

READING COMPREHENSION

46

upsidlangan ang mga kabataan sa pagpapanatili ng katahimikan at

kapayapaan sa mga pamayanan. Ngunit, bakit tila yata ang mga kabataang ito ang bibigo sa dakilang pangarap ng

yumaong bayani? Bakit tila nais nilang sikilin ang

damdaming makabayang siyang sandata sa pagtatanggol sa Inang Bayan?

38. Alin sa mga sumusunod ang HINDI nagpapakita ng pagmamalasakit sa pamayanan?

a.

Pakikiisa sa mga proyekto ng pamayanan.

c.

Paglilinis ng mga sari-sariling bakuran.

b. Pagpapanatili ng kapayapaan at katahimikan.

d. Pakikiisa sa kapwa kabataang may masamang bisyo. 39. Paano maiaahon ng kabataan ang bansang Pilipinas sa tiyak na kasawian? a.

Sa pamamagitan ng pagkakaroon ng tunay na pag-ibig sa bayan

c.

Parehong tama ang a at b

b. Sa pamamagitan ng pagtugon sa kani-kaniyang kagustuhan lamang

d. Walang tamang sagot

40. Ano ang nadarama ng may-akda sa kabataan na kanyang ipinahiwatig sa huling dalawang pangungusap ng talata? a.

Tuwa sapagkat tunay na pag-asa ng bayan ang kabataan.

c.

Galak dahil patuloy ang kabataan sa pagpapaunlad ng bayan.

b. Lungkot dahil tila bibiguin ng mga kabataan ang paniniwala ni Rizal. d. Dalamhati sapagkat naaalala niya ang kabataan ni Rizal.

47

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE May ibong pambihira

Lumang payong ang kanyang tuka Katawa’y kabit-kabit na lata Ng karne norte’t sardinas

Mata’y galing sa manyikang Nasira at tinapon

Pugad niya’y mabahong tambakan Pagsikat ng buwan na parang duyan sa langit, Lilipad siya upang umawit:

Meme na, mga batang inaantok At walang makain.

Anghel ako ng inyong panaginip. Huni ako ng inyong daing.

Pangit man at kinakalawang

Ang aking binasurang katawan, Matamis ang awit ko,

Ako’y mabuting kaibigan. Meme na, meme na, mahal kong kabataan. Bantay ako ng mga hindi naghapunan. Ng mga sanggol na walang unan.

41. Saan matatagpuan ang ibong delata na siyang paksa ng tula? a.

Sa isang munting tahanan

c.

Sa tindahan ng laruan

b. Sa mabahong tambakan ng basura

d. Sa isang punong malapit sa basurahan

READING COMPREHENSION

48

upsidlangan 42. Ano ang saloobin ng may-akda ukol sa ibong delata? a.

Binibigyan ito ng may-akda ng mataas na pagpapahalaga.

b. Para sa may-akda walang sayang na bagay hangga’t mahahanapan

c.

ito ng gamit.

Masaya ang may-akda dahil nakagawa siya ng bagong kagamitan

mula sa isang bagay na patapon.

d. Lahat ng mga nabanggit

43. Anong uri ng tayutay (figure of speech) ang naipakita sa ikaapat hanggang ikaanim na saknong (Awit ng Ibon)? a.

Metapora

b. Pagmamalabis

c.

Personipikasyon

d. Simili

In most human relationships, one gives a little more

than the other, and one, perhaps, receives a little more.

Because of our human nature, our background, and our

individual needs, there is always that inequality in giving and receiving love. A perfectly mutual and reciprocal love is a

very rare gift. Imagine what love would be like if each side

both gave and received a hundred percent! But St. Augustine says that kind of perfect love exists only in God.

It’s much easier for most of us to give love than to

receive it. That may sound strange, but I think it’s true. When

we give love, we are in control. We can pick the person to love, we can decide how much love to give, and we know

when to love. But when we receive love, we are no longer in

control. All we can do is accept the love that is offered. To a certain extent, we are helpless. And that is much, much harder.

49

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE 44. What is the main thought expressed by the author? a.

It is easy to love.

c.

Love is a myth perpetuated by St. Augustine.

b. Love is not equal between two persons.

d. One must always strive to be loved by another.

45. With which of the following statements would the author agree? a.

We can only be loved if we are perfect.

c.

We should always look for love to be happy.

b. It is easier to give love than to receive love.

d. We are in control if we are being loved by others. 46. Which is the most appropriate title for the passage? a.

Love Thy Neighbors

c.

Love is a Many Splendored Thing

b. The Inequality of Love

d. St. Augustine’s Doctrine of Perfect Love 47. What reason is given by the author as to why it is easier to give love than to receive love? a.

We cannot choose whom to love.

c.

St. Augustine taught us to give perfect love.

b. We are in control when we give love.

d. We give 100 percent love but receive less than 100 percent in return.

READING COMPREHENSION

50

upsidlangan Live One Day At A Time Francis J. Kong My father isn’t the expressive, sentimental type. He isn’t

the hugging, “I love you” kind of guy. But I recall as a young

boy, he showed his love to me the only way he knew best: He spent on enormous pizza joint weekends, and simply

talked. (Actually, I’d do the talking and he’d do the listening). My father was my best friend.

A few months ago, Dad was trying to fix a light bulb in

our garage. Standing on a chair for a greater reach, he lost

his balance and went crashing down. His head hit the concrete floor and immediately, blood spurted out like water from an open faucet.

Because of the impact, there was like a dripping faucet

inside his brain as well. Blood clots started to appear in his

X-rays, and he began to experience paralysis in his body.

Even after brain surgery, he lost his language ability because

of a new blood clot, found even deeper than the others— too deep for another surgery to reach.

The gravest blow was severe pneumonia, an infection

that developed after a few months of staying in the hospital.

His lungs were now filled with fluid, and that was when the crisis hit. He was hooked up to a respirator, and the long wait began: the doctors told us frankly that he could go anytime. At that point, he was only absorbing 20% of the oxygen they were pumping into him. Someone doesn’t last too long in that state.

I looked at Dad’s hands and face, and they were bluish

in color. I whispered to his ear, “I love you, Dad.”

That was when he regained consciousness for a few

minutes. He looked at me with so much sadness in his eyes.

Then he did something that he has never done in my entire

51

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE life. He raised his hands towards my face, and clasped me on both cheeks. Then he brought me down towards him, and gave me a hug. My father gave me a hug. He was telling me that he loved me, too.

He was also probably bidding farewell.

My emotions were running wild inside me.

I was both grieving and joyful. Joyful because for the

first time, my tough, unsentimental father gave me a hug. Grieving because he was going away. Grieving because it might be the last hug I’ll ever get from him.

“Dad, we should have done this a long time ago,” I

muttered to myself.

Today, my father has recovered a little bit, narrowly

escaping that ordeal. I hug him more often now. Hug someone today, while there’s time.

48. What is the main purpose of the author? a.

To ask

b. To entertain

c.

To inform

d. To inspire

49. What does the word ordeal in the last paragraph mean? a.

Circumstance

b. Examination

c.

Situation

d. Tribulation

50. According to the author, his father experienced paralysis due to _____. a.

Infection

b. Pneumonia

c. Brain surgery

d. Blood clots in his brain

51. What type of figure of speech was used in the 2nd paragraph? a.

Hyperbole

b. Metaphor

c.

c. Personification

d. Simile

READING COMPREHENSION

52

upsidlangan The Cask of Amontillado Edgar Allan Poe “. . .1I had scarcely laid the first tier of my masonry when I

discovered that the intoxication of Fortunato had in a great measure worn off. 2 The earliest indication I had of this was

a low moaning cry from the depth of the recess. 3 It was NOT the cry of a drunken man.

4

There was then a long and

obstinate silence. I laid the second tier, and the third, and 5

the fourth; and then I heard the furious vibrations of the chain.

6

The noise lasted for several minutes, during which,

that I might hearken to it with the more satisfaction, I ceased

my labours and sat down upon the bones. 7 When at last the

clanking subsided, I resumed the trowel, and finished

without interruption the fifth, the sixth, and the seventh tier. 8

The wall was now nearly upon a level with my breast.9 I

again paused, and holding the flambeaux over the masonwork, threw a few feeble rays upon the figure within.

A succession of loud and shrill screams, bursting

suddenly from the throat of the chained form, seemed to

thrust me violently back. For a brief moment I hesitated -- I

trembled. Unsheathing my rapier, I began to grope with it about the recess; but the thought of an instant reassured

me. I placed my hand upon the solid fabric of the catacombs, and felt satisfied. I reapproached the wall. I

replied to the yells of him who clamoured. I reechoed -- I aided -- I surpassed them in volume and in strength. I did this, and the clamourer grew still.

It was now midnight, and my task was drawing to a

close. I had completed the eighth, the ninth, and the tenth tier. I had finished a portion of the last and the eleventh;

there remained but a single stone to be fitted and plastered in. I struggled with its weight; I placed it partially in its

53

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE destined position. But now there came from out the niche a low laugh that erected the hairs upon my head. It was succeeded by a sad voice, which I had difficulty in recognising as that of the noble Fortunato . . .� 52. What is the main theme of the passage? a.

agony

c.

b. Love

bitterness

d. revenge

53. In sentence 9, what does flambeaux mean? a.

Cement

c.

b. Torch

brick

d. stone

54. In what perspective is the passage written? a.

1st

b. 2nd

c.

3rd

d. 4th

55. All can be inferred from the passage, except. . . a.

The person hated Fortunato

c.

Fortunato was intoxicated

b. The person wanted to save fortunate from the catacombs d. There was no hesitation when the person carried out his plan.

READING COMPREHENSION

54

upsidlangan

56. What is the purpose of the comic strip? a.

inform

c.

b. persuade

entertain

d. argue

57. In what tone was the punchline delivered? a.

persuasive

c.

b. ironic

mundane

d. lethargic

I, the consumer: An open letter to capitalist enterprise Panos Mourdoukoutas, 2013 � Dear Capitalist,

1

I am the consumer, your immediate or ultimate customer, the beginning and end of everything you do. 3

Every activity, every function, and every operation your

enterprise performs. I’ m the beginning and end of your R&D; 5

the beginning and end of your production;

the beginning and the end of your branding and marketing; the beginning and the end of your warehousing; the beginning and end of your distribution;

55

READING COMPREHENSION

COLLEGE ENTRANCE EXAM MODULE the beginning and end of your retailing; 10

the beginning and the end of your sales and customer

service; the beginning and end of your financing; and the beginning and the end of your accounting and control. Your labs, your offices, your factories, your warehouses, your distribution centers, 15

your retail outlets, customer service, repairing outlets, and

your finance and accounting departments exist because of me, to serve and accommodate my needs and desires. I’m the beginning and end of everything your partners and suppliers and their own partners and suppliers do; every activity, every function and every operation they perform; their own factory and office facilities; their own warehouses and retail outlets; and their own finance and accounting departments exist because of me.

20

Dear Capitalist, I am your immediate or ultimate boss, and the boss of your managers, and employees; the boss of your lab manager and researcher; the boss of the factory manager and floor employee; the boss of the warehouse manager and employee; and the boss of your supermarket and its employees. 25

You all work for me.

I’m the one who puts you in business and out of business. I’m the one who pays each and every one of you. I’m the one who writes your dividend check. I’m the one who pays the salary, bonuses and the healthcare and retirement benefits of your managers and employees. 30

I’m the one who pays their healthcare and retirement

benefits.

READING COMPREHENSION

56

upsidlangan I am the boss of your partners and suppliers, and the boss of their own partners and suppliers. I keep all of them in business, and pay for their profits and for the salaries, the bonus, the health insurance, and the pension contributions of their managers and employees. Sincerely, I, the Consumer

35

P.S Never take me for granted like a hostage in a prison cell. I do have a commodity that each and every capitalist wants: money. You have a commodity that not every consumer wants. I can take my money and buy the products of your competitors. I can turn to the products of competing sectors. And I can take 40the money off the table, refusing to buy your products altogether. 58. Which line summarizes the whole point of the poem/open letter? a.

3

b. 11

c.

25

d. 30

59. What does the poem/open letter imply? a.

Capitalists have the control over consumers since they’re the ones

who could produce commodities used by the people

b. Capitalism is harmful to consumers

c.

Consumers determine the fate of capitalists

d. Consumers are taken for granted by the capitalists. 60. What commodity makes the author powerful to capitalists? a.

Business establishments

b. Money

57

READING COMPREHENSION

c.

Factories

d. Healthcare and Retirement benefits

COLLEGE ENTRANCE EXAM MODULE

LANGUAGE PROFICIENCY GENERAL DIRECTIONS ONE Read each problem carefully and decide which the

best answer among the given choices is.

TWO Appropriately

blacken the circle your answer

corresponds to after the appropriate item number on your answer sheet. CORRECT METHOD OF SHADING THE BUBBLE A

B

D

WRONG METHODS OF SHADING THE BUBBLE A

B

C

D

A

B

C

D

A

B

C

D

LANGUAGE PROFICIENCY

58

upsidlangan ENGLISH Identifying sentence errors 1.

She is not sure if she should go to the mall now or wait for her friends A

B

to arrive. No Error 2.

C

D

Jammy, together with her friends, visit the museum at least once every A

B

year to check for new exhibits. No Error 3.

C

D

My brother and me ate lunch together at the cafeteria near the tall A

B

building. No Error 4.

D

Everyone in our family except my sister and I has eaten breakfast. A

B C

No Error 5.

D

Neither his friends nor his classmate were able to attend his birthday. A

No Error 6.

B

C

D

Megan is unsure which among the two remaining desserts is more delicious. No Error

7.

A

59

B

C

D

She, according to her friend, has a very unique taste when it comes to home decorations. No Error

8.

C

A

B

C

D

He can’t hardly wait for the awarding ceremonies to be conducted next A

LANGUAGE PROFICIENCY

B

COLLEGE ENTRANCE EXAM MODULE week in his hometown. No Error 9.

C

D

However, the interest in improving the teaching automotive courses A

B

have not subsided. No Error C

D

10. Science refer to that dynamic cumulative systems of verifiable concepts A

B

and processes which seek to understand natural phenomena. No Error C

D

Word Usage 11. Corruption is considered the most detrimental practice for a country. a.

Damaging

b. Destructive

c.

Annihilating

d. Deceiving

12. Leo made a disappointed, misunderstood face, from the many creases at his disposal. a.

Regulation

b. Garbage unit

c.

Distribution

d. Authority

13. The speaker of the event wore a resplendent gown that awed everyone. a.

Magnificent

b. Splendid

c.

Beautiful

d. Significant

14. The use of grandiloquent words in speeches does not guarantee comprehension from the listeners’ part. a.

Vague

b. Gaudy

c.

Irrelevant

d. Simple

LANGUAGE PROFICIENCY

60

upsidlangan 15. The professor took an immaculate piece of cloth and used it to wipe his glasses.

a.

Spotless

b. Error-free

c.

Pure

d. Flawless

16. Her answer to the question was sure and crisp. It did not take long before she was able to get rid of the person. a.

Lively

b. Fragile

c.

Brittle

d. Concise

17. Terrie kept on fumbling the art materials, picking some and shuffling them as if they were cards.

a.

Juggling

b. Playing with

c.

Moving clumsily

d. Groping for

18. The lady slipped off her headband so she could fix her hair. a.

Wore in

b. Threw away

c.

Removed quickly

d. Slid out of place

19. Imelda Marcos is known to have built edifices all around the metro. a.

Chaos

b. Huge Hospitals

c.

Tall buildings

d. Corrupt government

Figures of Speech. Determine the figure of speech used in each sentence. 20. “I die, I sleep, I faint” –Percy Shelley, The Indian Serenade a.

Anti-climax

b. Assonance

61

LANGUAGE PROFICIENCY

c.

Irony

d. Climax

COLLEGE ENTRANCE EXAM MODULE 21. “Tell me not in mournful numbers”- Henry Longfellow, A Psalm of Life a.

Personification

b. Litotes

c.

Hyperbole

d. Paradox

22. “He whom the gods favour dies in youth”-Plautius, Bacchides a.

Oxymoron

b. Irony

c.

Metonymy

d. Paradox

23. “Death, be not proud.”-John Donne, Divine Poems Holy Sonnet a.

Irony

b. Apostrophe

c.

Metonymy

d. Allusion

24. “Common sense is not so common”-Voltaire, Philosophical Dictionary a.

Irony

b. Oxymoron

c.

Paradox

d. Antithesis

Fill in the blanks. Choose the best word/phrase that will fit the sentence. 25. Jeff has many friends because he is a _______ person; he wants to socialize with every person he meets. a.

gregarious

b. tame

c.

kind

d. famous

26. The strong ______ between parents and teachers is that they have the students’ best interests at heart. a.

laiason

b. liason

c.

laiason

d. liaison

LANGUAGE PROFICIENCY

62

upsidlangan 27. Lita is going to Europe ______ May next year. Specifically, she would be leaving ______ eight o’clock AM ______ New Year’s Day.

a.

in-at-on

b. at-on-at

c.

in-on-on

d. in-at-in

28. I used too ______ of the bleach so the stain remained on the shirt. a.

few

b. little

c.

small

d. some

29. How she topped the board exam is certainly an ______ among her friends. a.

eccentricity

b. archetype

c.

enmity

d. enigma

30. The prime minister bowed, scraped, and behaved ______ before the new queen.

a.

ostensibly

b. obsequiously

c.

ubiquitously

d. sinuously

31. He lives ______ #385 Zamora Street ______ Tacloban City. a.

in-at

b. on-in

c.

in-on

d. at-in

32. John and Susie own that yacht. ______ yacht is beautiful. a.

John’s and Susie

b. John’s and Susie’s

63

LANGUAGE PROFICIENCY

c.

both a and b

d. John and Susie’s

COLLEGE ENTRANCE EXAM MODULE 33. According to Machiavelli, it is not imperative that a ruler ______ good, he just has to appear so. a.

was

b. were

c.

is

d. be

34. I must explain my position ______ so the panel would understand my argument.

a.

farther

b. farthest

c.

further

d. furthest

35. Anna already ______ to town when her parents ______ for breakfast. a.

had gone-wake up

b. went-has woke up

c.

had gone-woke up

d. went-had woken up

Sentence Structure. Choose the sentence that best delivers logic and meaning while considering grammar and sentence structures. 36.

a.

She jogs every afternoon to the park to exercise before going home.

c.

To exercise, she jogs every afternoon before going home to the park.

a.

He had run only twenty miles when he fainted.

c.

He only ran twenty miles when he fainted.

a.

My father is going to have business trip to New York in America in

b. She jogs every afternoon to the park before going home to exercise. d. She jogs every afternoon before going home to the park to exercise.

37.

b. He had only run for about twenty miles when he fainted

38.

d. He has only ran twenty miles when he fainted.

August next year.

LANGUAGE PROFICIENCY

64

upsidlangan b. My father is going to have a business trip in New York in America c.

next year in August.

My father is going to have a business trip to New York in America on August next year.

d. Next year, in August, my father is going to have a business trip to New York in America.

39.

a.

Filipino historians were captives of Spanish and American

historiography, both of which viewed Philippine history through the prism of their own prejudices.

b. As captives of Spanish and American historiography, Philippine

history and Filipino historians viewed Philippine history through the

c.

prism of their own prejudices.

Filipino, Spanish, and American historiography held Philippine

history captive and viewed it through the prism of their own prejudices.

d. Filipino historians held Spanish and American historiography and

viewed Philippine historiography through the prism of Spanish and American prejudices.

Analogy 40. paragraph: sentence :: a.

b.

picture : pencil wax : crayon

c.

word : letter

c.

Amorphous: distinct

d. note : bar

41. Virulent: deadly :: a.

Abstemious: ascetic

b. Surrogate: original

65

LANGUAGE PROFICIENCY

d. Negligent: Conscience

COLLEGE ENTRANCE EXAM MODULE 42. Homeostasis : Balance :: Entropy : a.

b.

Chaos

Peace

c.

Work

c.

Earthquake Intensity

c.

Wimple

c.

mercurial: unpredictable

d. Energy

43. Barometer: Pressure :: Odometer a.

Rainfall

b. Mileage

d. Wind Speed

44. Queen: Crown :: Nun : a.

Burqa

b. Habit

d. Aura

45. assuage: provoke a.

abstruce: straightforward

b. belligerent: quarrelsome

d. lugubrious: morose

46. Virgil: Inferno :: a.

Miguel de Cervantes: Don Quixote

c.

Medea: Euripides

b. John Milton: Paradise Lost

d. Canterburry Tales: Geoffrey Chaucer

47. Song of Roland: France :: a.

Beowulf: England

b. The Iliad: Spain

c.

Ramayana: India

d. Romeo: Paris

LANGUAGE PROFICIENCY

66

upsidlangan 48. Which of the following sentences does not contain a gerund phrase? a.

The family will go out during the weekend to watch the crowning of the new pageant winner.

b. She is very good at swimming that her teacher has nothing more to c.

teach her.

Marius just keeps on listening to the professor despite the latter’s pointless arguments.

d. Reading is a great activity for a pastime. FILIPINO 49. Siya ay natutulog ng mahimbing ng dumating ang kanyang mga magulang. Wasto

A

B

C

D

50. Noong panahon ng pananakop ng mga dayuhan, iba ang pagtrato sa A

B

mga bababe at sa mga lalaki. Wasto C

D

51. Sila Pedro ang kinikilalang mga tapat na kawal kay Heneral Isidro. A

B

Wasto

C

D

52. Ang panahon na ito ay puno ng pag-asa para sa mga A

B

nasalanta ng delubyo. Wasto C

D

53. Panglima na siya sa pila sa kanyang pagdating kaya hindi na niya A

nakuha ang premyo. Wasto

B

C

D

54. Hindi dapat manghihinayang ang isang magaaral sa oras na ginugugol A

67

LANGUAGE PROFICIENCY

B

C

COLLEGE ENTRANCE EXAM MODULE niya sa pagbabasa. Wasto D

55. Ang sabi niya inilagay niya ang lapis ______ sa ibabaw ng mesa. a.

roon

b. doon

c.

doon

d. rine

56. Sa nobelang Noli Me Tangere ni Rizal, sino ang pinaghihinalaang baliw dahil sa kakaiba niyang mga gawain? a.

Pilosopong Tasyo

b. Sisa

c.

Kabesang Tales

d. Pia Alba

57. Sino sa mga suusunod ang hindi kapatid ni Jose Rizal? a.

Olympia

b. Trinidad

c.

Virginia

d. Paciano

58. Sa Panitikang Pilipino, ano ang pamagat ng akda ni Marcelo del Pilar

kung saan binigyang katatawanan ang mga dasal na itinuro ng mga Kastila? a.

Dasalan at Tocsohan

b. Dasal ng Pari

c.

Aba Ginoong Barya

d. Fray Botod

59. Dahil sa kanyang ______ pag-uugali, hindi niya mapigilang magalit sa kanyang kausap. a.

malabong

b. mapanlibak na

c.

mapusok na

d. masinop na

60. Ang kanyang ginawang pag-uulat ay isang ______ ng mga natutunan niya sa klase. Ipinaliwanag niya ito sa pamamgitan ng pagbibigay ng ilustrasyon at buod. a.

pagbubungad

b. pagguhit

c.

paglalagum

d. pagpapaliwanag LANGUAGE PROFICIENCY

68

POINTERS MATHEMATICS PEMDAS (order of operations)

QUADRATIC FORMULA

Parenthesis Exponent Multiplication / Division Addition / Subtraction

ax2 + bx + c = 0

FORM:

MEAN = average =

2đ?‘Žđ?‘Ž

= b2 – 4ac

DISCRIMINANT

STATISTICS

−đ?‘?đ?‘?Âąâˆšđ?‘?đ?‘? 2 −4đ?‘Žđ?‘Žđ?‘Žđ?‘Ž

đ?‘Ľđ?‘Ľ =

���� ��

MEDIAN = middle value when arranged in increasing order MODE = the number that s repeated most often RANGE = highest number – lowest number

Probability of an event = EXPONENTS

đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘œđ?‘œđ?‘œđ?‘œ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚

đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒ đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚đ?‘‚

Zero Exponent Property Negative Exponent Property Products of Power Property Quotient of Powers Property Power of a Product Property Power of a Quotient Property Power of a Power Property Rational Exponent Property

69

đ?‘Žđ?‘Ž0 = 1, đ?‘Žđ?‘Žâˆ’đ?‘?đ?‘? =

1

đ?‘Žđ?‘Žđ?‘Žđ?‘Ž

( �� ≠0 )

, ( �� ≠0 )

đ?‘Žđ?‘Žđ?‘?đ?‘? ∙ đ?‘Žđ?‘Žđ?‘?đ?‘? = đ?‘Žđ?‘Žđ?‘?đ?‘?+đ?‘?đ?‘? ,

( �� ≠0 )

đ?‘Žđ?‘Žđ?‘?đ?‘? ∙ đ?‘?đ?‘? đ?‘?đ?‘? = (đ?‘Žđ?‘Žđ?‘Žđ?‘Ž)đ?‘?đ?‘? ,

( đ?‘Žđ?‘Ž, đ?‘?đ?‘? ≠0 )

đ?‘Žđ?‘Žđ?‘?đ?‘? đ?‘Žđ?‘Žđ?‘?đ?‘?

đ?‘Žđ?‘Žđ?‘?đ?‘? đ?‘?đ?‘?đ?‘?đ?‘?

= đ?‘Žđ?‘Žđ?‘?đ?‘?−đ?‘?đ?‘? , đ?‘Žđ?‘Ž

= ( )đ?‘?đ?‘? , đ?‘?đ?‘?

(đ?‘Žđ?‘Žđ?‘?đ?‘? )c = đ?‘Žđ?‘Žđ?‘?đ?‘?đ?‘?đ?‘? đ?‘Žđ?‘Ž

đ?‘?đ?‘? đ?‘?đ?‘?

đ?‘?đ?‘?

( đ?‘Žđ?‘Ž, đ?‘?đ?‘? ≠0 )

( đ?‘Žđ?‘Ž, đ?‘?đ?‘? ≠0 )

= √đ?‘Žđ?‘Žđ?‘?đ?‘? = √đ?‘Žđ?‘Ž đ?‘?đ?‘?

đ?‘?đ?‘?

POINTERS LOGARITHMS a.

log đ?‘?đ?‘? đ?‘Ľđ?‘Ľđ?‘Ľđ?‘Ľ = log đ?‘?đ?‘? đ?‘Ľđ?‘Ľ + log đ?‘?đ?‘? đ?‘Śđ?‘Ś đ?‘Ľđ?‘Ľ

b. log đ?‘?đ?‘? = log đ?‘?đ?‘? đ?‘Ľđ?‘Ľ - log đ?‘?đ?‘? đ?‘Śđ?‘Ś c.

đ?‘Śđ?‘Ś

log đ?‘?đ?‘? đ?‘Ľđ?‘Ľ đ?‘›đ?‘› = n log đ?‘?đ?‘? đ?‘Ľđ?‘Ľ

d. log đ?‘?đ?‘? đ?‘Ľđ?‘Ľ =

e. f.

TRIGONOMETRY csc Ó¨ =

sec Ó¨ = cot Ó¨ =

tan Ó¨ = cot Ó¨ =

1

sin Ó¨ 1

cos Ó¨ 1

tan Ó¨ sin Ó¨

log đ?‘?đ?‘? 1 = 0 log đ?‘?đ?‘? đ?‘?đ?‘? = 1

đ?œ‹đ?œ‹

sin(−Ө) = −sin Ө

cos Ө = sin( − Ө) 2

đ?œ‹đ?œ‹

cos(−Ө) = cos Ө

cot Ө = tan( − Ө) 2

đ?œ‹đ?œ‹

tan(−Ө) = −tan Ө

csc Ө = sec( − Ө) 2

đ?œ‹đ?œ‹

sin Ө = cos( − Ө) 2

cos Ó¨

đ?œ‹đ?œ‹

tan Ө = cot( − Ө)

cos Ó¨

2

sin Ó¨

đ?œ‹đ?œ‹

sec Ө = csc( − Ө) 2

y

cos 2 Ó¨ + sin2 Ó¨ = 1

1

1 + tan Ó¨ = sec Ó¨ 2

logđ?‘Žđ?‘Ž đ?‘Ľđ?‘Ľ

logđ?‘Žđ?‘Ž đ?‘?đ?‘?

2

1 + cot 2 Ó¨ = csc 2 Ó¨

-1

+ sin + csc – cos – sec – tan – cot

+ sin + csc + cos + sec + tan + cot

– sin – csc – cos – sec + tan + cot

– sin – csc + cos + sec – tan – cot

1

x

-1

70

POINTERS POINTS OF SPECIAL INTEREST ON THE UNIT CIRCLE (source: www.regentsprep.org)

GEOMETRY PLANE FIGURES

PERIMETER

AREA

Rectangle

2l + 2w

lw

Square

4s

s2 1

Triangle

2

Parallelogram

bh

1

Trapezoid Circle

CIRCUMFERENCE: C = 2πr = πd

71

bh

2

h (b1 + b2) πr2

POINTERS SOLID FIGURES

SURFACE AREA

VOLUME

Rectangular Solid

2lw + 2lh + 2wh

Lwh

Cube

6 ∙ s2

s2

Right Circular Cylinder

2Ď€r2 + 2Ď€rh

Ď€r2h

Right Circular Cone

πr2 + πrs

1

(đ?‘ đ?‘ = √đ?‘&#x;đ?‘&#x; 2 + â„Ž2 )

Sphere

4

4Ď€r2

PYTHAGOREAN THEOREM

applies to right triangles with

hypotenuse c and whose other legs

3

TRIANGLE WITH SIDE S

A(s) = 2

đ?‘Žđ?‘Ž + đ?‘?đ?‘? = đ?‘?đ?‘?

2

The NUMBER OF DIAGONALS OF A POLYGON having

LINES AND PAIRS OF ANGLES

a

e

d c

angle a = angle b

angle b = Angle d

angle a + angle b = 180°

g

đ?‘ đ?‘ 2 √2 4

P(n) = ��

n sides is given by the polynomial function:

b

Ď€r2

AREA OF AN EQUILATERAL

measure a and b: 2

Ď€r2h

3

(đ?‘›đ?‘›âˆ’3) 2

f h

angle e = angle f

angle g = angle h

angle e + angle f = 180°

72

POINTERS CHEMISTRY 9

T (oF) = T (oC) + 32

T (oC) = (T(oF) – 32)

3

T ( K ) = T (oC) + 273.15 K

5 9

Avogadro’s Number = 6.022 x 1023 moles =

đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š

molarity (M) =

������������������ ��������ℎ��

M1V1 = M2V2

c=

��Q = heat transferred

����

đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š

đ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Łđ?‘Ł (đ??żđ??ż)

đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š

TABLE OF ELEMENTS on page 77

PHYSICS

v=Îťf đ?‘Łđ?‘Ł

n1 sin Ó¨1 = n2 sin Ó¨2

h

= height

L

= frequency or focal length = distance

M = Magnification

sin Ó¨đ?‘?đ?‘? =

��2 ��1

n

= index of refraction

đ?‘ đ?‘ đ?‘–đ?‘–

đ?‘“đ?‘“

s

= distance

x

= position

1

+

f=

1

đ?‘ đ?‘ 0

=

đ?‘…đ?‘… 2

1

d sin Ó¨ = mÎť xm ~

73

= separation

f

đ?‘?đ?‘?

n=

d

đ?‘šđ?‘šđ?‘šđ?‘šđ?‘šđ?‘š đ?‘‘đ?‘‘

m = an integer R v Îť

Ó¨

= radius of curvature

= speed

= wavelength = angle

POINTERS 1

Fs = -kx đ??şđ??ş đ?‘šđ?‘š1 đ?‘šđ?‘š2

FG = T=

2đ?œ‹đ?œ‹

ac =

đ?œ”đ?œ”

Ux = kx2 đ?‘&#x;đ?‘&#x; 2

đ?‘&#x;đ?‘&#x;

r̂

UG = -

1

=

đ?‘Łđ?‘Ł 2

2

đ?‘šđ?‘š

T = 2Ď€ ďż˝

đ?‘“đ?‘“

= ω2r

a

a

Ď„=r x F I = âˆŤ đ?‘&#x;đ?‘&#x; 2 đ?‘‘đ?‘‘đ?‘‘đ?‘‘ = ÎŁ mđ?‘&#x;đ?‘&#x; 2 v = rω

I=rxp=Iω 1

K= Iω 2

1

Ө = Ө0 + ω0I + ���� 2 2

v = v0 + at

1

x = x0 + v0t + at 2

2

v2 = v02 + 2a (x – x0) Σ F = Fnet F=

J = âˆŤ đ??šđ??š đ?‘‘đ?‘‘đ?‘‘đ?‘‘ = Δp p = mv

Ffric ≤ ΟN

W = âˆŤ đ??šđ??š đ?‘‘đ?‘‘đ?‘‘đ?‘‘ 1

K = đ?‘šđ?‘šđ?‘Łđ?‘Ł P=

2 đ?‘‘đ?‘‘đ?‘‘đ?‘‘

2

đ?‘‘đ?‘‘đ?‘‘đ?‘‘

P = Fv

ΔUg = mgh

T = 2Ď€ ďż˝

= acceleration

đ?‘“đ?‘“

��

= angular acceleration

F

= force

Îź

= friction (coefficient)

ω = angular speed F

J

L

l

= frequency = height

= rotational inertia = impulse

= distance = length

m = mass N

= normal force

p

= momentum

P

K

đ?‘‘đ?‘‘đ?‘‘đ?‘‘

đ?‘˜đ?‘˜

= angular momentum

l

ω = ω0 + at

đ?‘&#x;đ?‘&#x; 2

L

h

2

đ?‘‘đ?‘‘đ?‘‘đ?‘‘

đ??şđ??ş đ?‘šđ?‘š1 đ?‘šđ?‘š2

k

= power

= kinetic energy

= spring constant

r

= radius or distance

T

= period

��T = temperature difference τ

= torque

U

= potential energy

t

= time

v

= velocity or speed

x

= position

W = work done on a system

74

POINTERS

IUPAC

NOTES - IUPAC 2011 Standard atomic weights abridged to four significant digits (Table 4 published in Pure Appl. Chem. 85, 1047-1078 (2013); http://dx.doi.org/10.1351/PAC-REP-13-03-02. The uncertainty in the last digit of the standard atomic weight value is listed in parentheses following the value. In the absence of parentheses, the uncertainty is one in that last digit. An interval in square brackets provides the lower and upper bounds of the standard atomic weight for that element. No values are listed for elements which lack isotopes with a characteristic isotopic abundance in natural terrestrial samples. See PAC for more details.

75

POINTERS

TABLE OF

ELEMENTS

- “Aluminum” and “cesium” are commonly used alternative spellings for “aluminium” and “caesium.”

- Claims for the discovery of all the remaining elements in the last row of the Table, namely elements with atomic numbers 113, 115,

117 and 118, and for which no assignments have yet been made, are being considered by a IUPAC and IUPAP Joint Working Party. For updates to this table, see iupac.org/reports/periodic_table/. This version is dated 1 May 2013. Copyright © 2013 IUPAC, the International Union of Pure and Applied Chemistry.

INTERNATIONAL UNION OF

PURE AND APPLIED

76

CHEMISTRY

ANSWER KEY

MATHEMATICS 1. 2.

3.

4.

5.

B (24 ∗ 76) + 462 = 2286 D 2 1 2 Ă— = 5 3 15 Let x be the students in the 2 class, đ?‘Ľđ?‘Ľ = 6, đ?‘Ľđ?‘Ľ = 45 15

B 5+2 = 7 420 á 7 = 60 Since the ratio is 5: 2, 60 Ă— 5 = 300. There are 300 students in the field trip. 3+2 = 5 300 á 5 = 60 60 Ă— 3= 180 C 1 3 Since was taken, remains. 4 4 3 2 1 Ă— = 4 3 2 Let đ?‘Ľđ?‘Ľ be the whole cake 1 đ?‘Ľđ?‘Ľ = 8 2 đ?‘Ľđ?‘Ľ = 16 C The rate at which Matt works is 1 1 while Stan’s is . 24

12

If we add these 1 1 1 + = in which đ?‘Ľđ?‘Ľ = the 24

6.

77

12

7.

8. 9.

10.

đ?‘Ľđ?‘Ľ

number of days it will take to finish the job together Solving the equation, đ?‘Ľđ?‘Ľ = 8. C Find the slope m. 1 (7 − 6)/(2 − 4) = − 2 Equation of the line is

ANSWER KEY | MATHEMATICS

11.

1 đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ + đ?‘?đ?‘? 2 To find the y-intercept, input the values of đ?‘Ľđ?‘Ľ and đ?‘Śđ?‘Ś. For example, (4,6) 1 6 = −( )4 + đ?‘?đ?‘? 2 6 = −2 + đ?‘?đ?‘? 8 = đ?‘?đ?‘? The complete equation of the 1 line is đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ + 8 2

D Since 2 + 3 + 5 = 10, 10 parts will be used. Dividing 6 by 10 we get 0.6 for 1 part. So red paint used was 0.6 Ă— 2 = 1.2 Blue paint used was 0.6 Ă— 5 = 3 3 − 1.2 = 1.8 C (82 + 77 + 86 + 89 + đ?‘Ľđ?‘Ľ)/5 = 85 Solving for đ?‘Ľđ?‘Ľ, we get đ?‘Ľđ?‘Ľ = 91. B 400/8 = 50 km/h ďƒ speed of bus 400/10 = 40 km/h ďƒ speed of car 50-40 = 10 km/h D đ?‘Ľđ?‘Ľ 3đ?‘Ľđ?‘Ľ đ?‘Ľđ?‘Ľ − = 4 4 3đ?‘Ľđ?‘Ľ 1 3đ?‘Ľđ?‘Ľ 2đ?‘Ľđ?‘Ľ đ?‘Ľđ?‘Ľ − ďż˝ �� ďż˝ = = 4 3 4 4 2 B Let đ?‘Ľđ?‘Ľ be Jake’s interest in decimal. 935 = 850 + (850)đ?‘Ľđ?‘Ľ đ?‘Ľđ?‘Ľ = 0.1 Converting 0.1 to percent, 0.1 Ă— 100 = 10%

ANSWER KEY 12. C The rate of work of pipe 1 is while pipe 2’s is

1

.

1.5

1

15. B

Let �� be Sofia’s age now.

1

Since pipe 2 empties the tank, we subtract the rates of work. 1 1 1 − = ďƒ where đ?‘Ľđ?‘Ľ is the 1

1.5

đ?‘Ľđ?‘Ľ

time to fill the tank if both pipes are opened 2 1 1− = 3 đ?‘Ľđ?‘Ľ 1 1 = 3 đ?‘Ľđ?‘Ľ đ?‘Ľđ?‘Ľ = 3 13. C If 60% of students are 16 years old and above, that means the remaining 40% are the students that are below 16 years old. 96 = (0.4)đ?‘Ľđ?‘Ľ ďƒ where x is the total number of students in the school. đ?‘Ľđ?‘Ľ = 240 14. D

Since he had an average of 42 in his first three exams, we can assume that his scores were 42 for all three exams. Since he had an average of 37 in the next two exams, we can assume that the scores he got in these two exams are both 37. Since we have the scores for his first 5 exams, (42+42+42+37+37+x)/6 = 41 ďƒ where đ?‘Ľđ?‘Ľ is the score for his last exam Solving for đ?‘Ľđ?‘Ľ, we find đ?‘Ľđ?‘Ľ = 46

16.

17.

18.

19.

đ?‘Ľđ?‘Ľ + 4 ďƒ Mike’s age 10 years ago: đ?‘Ľđ?‘Ľ − 10 ďƒ Sofia’s age (đ?‘Ľđ?‘Ľ + 4) − 10 ďƒ Mike’s age Since Sofia was half as old as Mike, 2(đ?‘Ľđ?‘Ľ − 10) = (đ?‘Ľđ?‘Ľ + 4) − 10 2đ?‘Ľđ?‘Ľ − 20 = đ?‘Ľđ?‘Ľ – 6 đ?‘Ľđ?‘Ľ = 14 Since đ?‘Ľđ?‘Ľ = 14, we can find Mike’s age đ?‘Ľđ?‘Ľ + 4 = 14 + 4 = 18 A The circumference of the wheel is 2đ?œ‹đ?œ‹đ?œ‹đ?œ‹ = 2đ?œ‹đ?œ‹(6) = 12đ?œ‹đ?œ‹ (144đ?œ‹đ?œ‹)/(12đ?œ‹đ?œ‹) = 12 B The ladder, the ground and the wall make a right triangle with the ladder being the hypotenuse. 4² = 3² + đ?‘Ľđ?‘ĽÂ˛ ďƒ where x is the distance of the bottom end of the ladder to the wall 16 – 9 = đ?‘Ľđ?‘ĽÂ˛ 7 = đ?‘Ľđ?‘ĽÂ˛ đ?‘Ľđ?‘Ľ = √7 D (đ?‘?đ?‘? + 2)/2 = đ?‘?đ?‘? – 4 đ?‘?đ?‘? + 2 = 2(đ?‘?đ?‘? – 4) đ?‘?đ?‘? + 2 = 2đ?‘?đ?‘? – 8 10 = đ?‘?đ?‘? Since đ?‘?đ?‘? = 10, đ?‘Žđ?‘Ž = đ?‘?đ?‘? − 4 = 10 – 4 = 6 D Line A perpendicular to line B has slope equal to the negative reciprocal of line B. MATHEMATICS | ANSWER KEY

80

ANSWER KEY Knowing that, we get 3 đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ + đ?‘?đ?‘? 2 Substituting the đ?‘Ľđ?‘Ľ and đ?‘Śđ?‘Ś for point (2,4), 3 4 = −( )(2) + đ?‘?đ?‘? 2 đ?‘?đ?‘? = 7 The complete equation is 3 đ?‘Śđ?‘Ś = − đ?‘Ľđ?‘Ľ + 7 2 20. D

20/5 = 4 ďƒ time it took for James to finish 20/3 = 6 + (2/3) ďƒ time it took for Jimmy to finish 2 6 + (2/3) – 4 = 2 + hours 3

21. B Let x be the smallest number. đ?‘Ľđ?‘Ľ ďƒ smallest number đ?‘Ľđ?‘Ľ + 12 – 7 ďƒ middle number đ?‘Ľđ?‘Ľ + 12 ďƒ largest number x + (x + 12 – 7) + (x + 12) = 242

81

3đ?‘Ľđ?‘Ľ + 17 = 242 đ?‘Ľđ?‘Ľ = 75 đ?‘Ľđ?‘Ľ + 5 = 75 + 5 = 80 22. B 3đ?‘Ľđ?‘Ľ + 4đ?‘Śđ?‘Ś = 10 2đ?‘Ľđ?‘Ľ – đ?‘Śđ?‘Ś = 3 đ?‘Śđ?‘Ś = 2đ?‘Ľđ?‘Ľ − 3 Substituting this value, 3đ?‘Ľđ?‘Ľ + 4(2đ?‘Ľđ?‘Ľ − 3) = 10 3đ?‘Ľđ?‘Ľ + 8đ?‘Ľđ?‘Ľ – 12 = 10 11đ?‘Ľđ?‘Ľ = 22 đ?‘Ľđ?‘Ľ = 2 2đ?‘Ľđ?‘Ľ – đ?‘Śđ?‘Ś = 3 2(2) – đ?‘Śđ?‘Ś = 3 4 – đ?‘Śđ?‘Ś = 3 đ?‘Śđ?‘Ś = 1 23. A đ?‘Śđ?‘Ś −đ?‘Śđ?‘Ś To find the slope, đ?‘šđ?‘š = 2 1

đ?‘Ľđ?‘Ľ2 −đ?‘Ľđ?‘Ľ1

ANSWER KEY | MATHEMATICS

đ?‘šđ?‘š =

3 1 3−6 = − = − 6 2 2 − (−4)

24. C Let đ?‘Ľđ?‘Ľ be the original price of the television. đ?‘Ľđ?‘Ľ – (0.2)đ?‘Ľđ?‘Ľ = 5000 0.8đ?‘Ľđ?‘Ľ = 5000 đ?‘Ľđ?‘Ľ = 6250 25. C 1 ďƒ Eddy’s rate of work 1.25 1

đ?‘Ľđ?‘Ľ

1

1.25

ďƒ Joe’s rate of work

+

1

đ?‘Ľđ?‘Ľ

=

1

0.5

Solving for đ?‘Ľđ?‘Ľ, we get đ?‘Ľđ?‘Ľ =

5 6

26. D sin θ = opposite/hypotenuse cos θ = adjacent/hypotenuse tan θ = (sin θ)/(cos θ) = 7 opposite/adjacent = 4

27. A Area of circle = 7²Ď€ = 49(3.14) = 153.86 Find the height. Since it is equilateral, we can divide the triangle into two congruent triangles with base 15. 25² = 15² + đ?‘Ľđ?‘ĽÂ˛ ďƒ where đ?‘Ľđ?‘Ľ is the height, đ?‘Ľđ?‘Ľ = 20 Area of triangle : (1/2)đ?‘?đ?‘?â„Ž = (1/2)(30)(20) = 300 300 – 153.86 = 146.14 28. B 25 m 60°

tan θ= opposite/adjacent 25 đ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ą 600 = đ?‘Ľđ?‘Ľ

ANSWER KEY 𝑠𝑠𝑠𝑠𝑠𝑠 600 25 = 0 𝑐𝑐𝑐𝑐𝑐𝑐 60 𝑥𝑥 �√3�

� 2 � 1 2

=

�√3� =

25

𝑥𝑥 25

34.

𝑥𝑥

25/�√3� = 𝑥𝑥 29. B 1 1 48 = � � 𝑏𝑏ℎ = � � (12) 2 2 = 6ℎ ℎ = 8 Dividing the triangle into two congruent triangles, with base 6 and height 8, 𝑥𝑥² = 6² + 8² = 100 𝑥𝑥 = 10  side of triangle 12 + 10 + 10 = 32 cm 30. A 𝑥𝑥 +𝑥𝑥 𝑦𝑦 +𝑦𝑦 Midpoint = ( 1 2 , 1 2 ) (4, 6) = (

4= 6=

𝑥𝑥2

2 2 0+𝑥𝑥2 7+𝑦𝑦2

, 𝑥𝑥2 = 8

2 7+𝑦𝑦2 2

2

,

2

, 12 = 7 + 𝑦𝑦2 ,

)

𝑦𝑦2 = 5 31. D Area of larger circle = 𝜋𝜋𝜋𝜋² = 6²𝜋𝜋 = 36𝜋𝜋 Area of smaller circle = 𝜋𝜋𝜋𝜋² = 3²𝜋𝜋 = 9𝜋𝜋 36𝜋𝜋 − 9𝜋𝜋 = 27𝜋𝜋 32. C 𝑛𝑛 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙 (𝑥𝑥 𝑛𝑛 ) 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 + 𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦 = 𝑙𝑙𝑙𝑙𝑙𝑙 (𝑥𝑥𝑥𝑥) 𝑙𝑙𝑙𝑙𝑙𝑙 48 = 𝑙𝑙𝑙𝑙𝑙𝑙 (12 𝑥𝑥²) 48 = 12𝑥𝑥² 4 = 𝑥𝑥² 𝑥𝑥 = 2 33. B Substitute. 𝑦𝑦 = 2𝑥𝑥² − 2𝑥𝑥 + 𝑐𝑐

35.

36.

37. 38.

39.

40.

4 = 2(3)² − 2(3) + 𝑐𝑐 4 = 18 – 6 + 𝑐𝑐 4 = 12 + 𝑐𝑐 −8 = 𝑐𝑐 D (𝑥𝑥 𝑚𝑚 )𝑛𝑛 = 𝑥𝑥 𝑚𝑚𝑚𝑚 2(3𝑥𝑥²)³ = 2 (27𝑥𝑥 6 ) = 54𝑥𝑥 6 D 22 + 22 = 𝑥𝑥 2 = 8 𝑥𝑥 = 2√2  base of triangle Height of triangle = Diagonal of square - 2√2 𝐻𝐻 = 6√2 – 2√2 = 4√2 Area of triangle = (1/2)𝑏𝑏ℎ = (1/2)( 2√2)(4√2) = 8 cm² Area of square = 𝑠𝑠² = 6² = 36 𝑐𝑐𝑐𝑐² Area of shaded region = 36 – 8 = 28 𝑐𝑐𝑐𝑐² C A= s² 𝑠𝑠 2 𝑠𝑠 2 𝐴𝐴 � � = = 4 2 4 D (𝑥𝑥 4 𝑦𝑦 2 )3 = 𝑥𝑥 4∗3 𝑦𝑦 2∗3 = 𝑥𝑥 12 𝑦𝑦 6 B 𝑥𝑥 + 66 = 3𝑥𝑥 66 = 2𝑥𝑥 33 = 𝑥𝑥 A [(420 ÷ 6) − 6 × 8] + [3 − 4(7 × 2 − 21) − (4 × 3 − 6)²] [70 – 48] + [ 3 – 4(14 − 21) – (12 – 6)²] 22 + [3 – 4(−7) − 6²] 22 + [3 + 28 – 36] = 17 B 2 + 3 + 5 + 7 + 11 = 28 MATHEMATICS | ANSWER KEY

82

ANSWER KEY 41. D (3.25 Ă— 0.4) + (1.96 á 0.28) = 8.3 42. B Inverse proportion 4 = đ?‘˜đ?‘˜/21 đ?‘˜đ?‘˜ = 84 7 = đ?‘˜đ?‘˜/đ?‘Ľđ?‘Ľ 7 = 84/đ?‘Ľđ?‘Ľ đ?‘Ľđ?‘Ľ = 84/7 = 12 43. C đ?‘Ąđ?‘Ą ďƒ time train A travelled đ?‘Ąđ?‘Ą − 2 ďƒ time train B travelled 40đ?‘Ąđ?‘Ą = 60(đ?‘Ąđ?‘Ą − 2) 40đ?‘Ąđ?‘Ą = 60đ?‘Ąđ?‘Ą – 120 20đ?‘Ąđ?‘Ą = 120 đ?‘Ąđ?‘Ą = 6 hours 44. D

The sum of the lengths of two sides of a triangle must always be greater than the length of the third side. 2 + 3 < 7 45. B Find angle C. 180 – (80 + 55) = 180 – 135 = 45⠰ Since Angle B > Angle A and Angle B > Angle C, the side opposite angle B must be longest. 46. D 6! = 6 × 5 × 4 × 3 × 2 × 1 3! = 3 × 2 × 1 We can cancel 3 × 2 × 1, such that what’s left is 6 × 5 × 4 which equals 120. 47. D 12 + 8 + 16 = 36

83

ANSWER KEY | MATHEMATICS

Since there are 20 marbles that are not blue, the chance of getting a marble that is not blue 20 5 is = . 36

9

48. A For the calculation to be simpler, we do the square root first. √196 = 14 Then we calculate 14Âł = 2744 49. B 9 km 6 km 6 km 4 km

Since the slope of the two hypotenuses is equal, we can just combine the length of the two hypotenuses to create one big triangle with base 10 km and height 15 km. 10² + 15² = đ?‘Ľđ?‘ĽÂ˛ 100 + 225 = đ?‘Ľđ?‘ĽÂ˛ = 325 đ?‘Ľđ?‘Ľ = 5√13 50. C đ?‘Ľđ?‘Ľ ďƒ number of P20 bills đ?‘Śđ?‘Ś ďƒ number of P50 bills đ?‘§đ?‘§ ďƒ number of P100 bills đ?‘Ľđ?‘Ľ + đ?‘Śđ?‘Ś + đ?‘§đ?‘§ = 15 đ?‘Ľđ?‘Ľ = đ?‘Śđ?‘Ś + 3 20đ?‘Ľđ?‘Ľ + 50đ?‘Śđ?‘Ś + 100đ?‘§đ?‘§ = 610 (đ?‘Śđ?‘Ś + 3) + đ?‘Śđ?‘Ś + đ?‘§đ?‘§ = 15 2đ?‘Śđ?‘Ś + đ?‘§đ?‘§ = 12 đ?‘§đ?‘§ = 12 – 2đ?‘Śđ?‘Ś 20(đ?‘Śđ?‘Ś + 3) + 50đ?‘Śđ?‘Ś + 100đ?‘§đ?‘§

ANSWER KEY = 610 20đ?‘Śđ?‘Ś + 60 + 50đ?‘Śđ?‘Ś + 100đ?‘§đ?‘§ = 610 70đ?‘Śđ?‘Ś + 100đ?‘§đ?‘§ = 550 70đ?‘Śđ?‘Ś + 100(12 – 2đ?‘Śđ?‘Ś) = 550 70đ?‘Śđ?‘Ś + 1200 – 200đ?‘Śđ?‘Ś = 550 −130đ?‘Śđ?‘Ś = −650 đ?‘Śđ?‘Ś = 5 51. C Volume of a cube = đ?‘ đ?‘ Âł = 512 mÂł Solving for s, we find đ?‘ đ?‘ = 8 m. Solving for area of one face of a cube, Area = đ?‘ đ?‘ ² = 8² = 64 m² Since a cube has 6 faces, we multiply this value by 6. 64 Ă— 6 = 384 m² 52. C Using distance formula, A = ďż˝(3 − 0)2 + (−2 − 4)2 =√117 2

B = ďż˝(5 − 3)2 + ďż˝7 − (−2)ďż˝

= √85 C = ďż˝(5 − 0)2 + (7 − 4)2 = √34 Since the lengths of the sides are not equal, this triangle is scalene. 53. B

Since the base is the sum of the diameters of the three circles, 4(2)(3) = 24 m Height is the radius A, which is equal 4 m. To find the area of the shaded region, 1 1 Area = ďż˝ ďż˝ đ?‘?đ?‘?â„Ž = ďż˝ ďż˝ (24)(4) = 48 m²

2

2

54. B Interest = (Principal Amount) (Interest Rate) (Duration) Interest = (20000)(0.03)(3) = 1800 Php 20000 + Php 1800 = Php 21800 55. C Volume of Cone = (1/3)đ?œ‹đ?œ‹đ?œ‹đ?œ‹²â„Ž Volume of Square Pyramid = (1/3)đ?‘?đ?‘?²â„Ž (1/3) đ?œ‹đ?œ‹đ?œ‹đ?œ‹²â„Ž = (1/3)đ?‘?đ?‘?²â„Ž đ?œ‹đ?œ‹đ?œ‹đ?œ‹² = đ?‘?đ?‘?² = 49 đ?‘&#x;đ?‘&#x; = 7/√đ?œ‹đ?œ‹ 56. C đ?‘Ľđ?‘Ľ+2 đ?‘Ľđ?‘Ľ+2 1 = = 2 đ?‘Ľđ?‘Ľ −4

(đ?‘Ľđ?‘Ľ+2)(đ?‘Ľđ?‘Ľâˆ’2)

đ?‘Ľđ?‘Ľâˆ’2

57. D The nth term of an arithmetic progression is given by đ?‘Žđ?‘Žđ?‘›đ?‘› = đ?‘Žđ?‘Ž1 + (đ?‘›đ?‘› − 1)đ?‘‘đ?‘‘, where đ?‘Žđ?‘Žđ?‘›đ?‘› is the nth term, đ?‘Žđ?‘Ž1 is the first term, and d is the common difference. đ?‘Žđ?‘Ž50 = đ?‘Žđ?‘Ž1 + (50 − 1)đ?‘‘đ?‘‘ = 3 + 49(3) = 150 The sum of an arithmetic progression is given by đ?‘›đ?‘›(đ?‘Žđ?‘Ž1 +đ?‘Žđ?‘Žđ?‘›đ?‘› ) 50(3+150) 7650 = = = 2 2 2 3825 58. B The sum of a geometric progression is given by đ?‘Žđ?‘Ž(1−đ?‘&#x;đ?‘&#x; đ?‘›đ?‘› ) 1−đ?‘&#x;đ?‘&#x;

where a is the first term,

r is the common ratio, and n is the number of terms. We find that the common ratio is 4. đ?‘Žđ?‘Ž(1−đ?‘&#x;đ?‘&#x; đ?‘›đ?‘› )

4095 = = 1−đ?‘&#x;đ?‘&#x; −(1 − 4đ?‘›đ?‘› ) -4095 = 1 - 4đ?‘›đ?‘›

3(1−4đ?‘›đ?‘› ) 1−4

=

MATHEMATICS | ANSWER KEY

84

ANSWER KEY 4096 = 4đ?‘›đ?‘› , n = 6 59. B Area of circular base = đ?œ‹đ?œ‹đ?œ‹đ?œ‹² = 36đ?œ‹đ?œ‹ Circumference of circle = 2đ?œ‹đ?œ‹đ?œ‹đ?œ‹ = 12đ?œ‹đ?œ‹ = đ?‘™đ?‘™ Area of rectangle = đ?‘™đ?‘™ Ă— đ?‘¤đ?‘¤ = 4 Ă— 12đ?œ‹đ?œ‹ = 48đ?œ‹đ?œ‹

Since there are two circular bases, we multiply the area of the circle by 2. 2(36đ?œ‹đ?œ‹) = 72đ?œ‹đ?œ‹ 72đ?œ‹đ?œ‹ + 48đ?œ‹đ?œ‹ = 120đ?œ‹đ?œ‹ 60. B 25đ?œ‹đ?œ‹ 1800 Ă— = 1125â ° 4 đ?œ‹đ?œ‹

SCIENCE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

B Corundum D Caldera C Alfred Wegener C hemoglobin in red blood cells D polarity D control normal cell growth and division A phylogeny C mRNA A cerebrum C Organic substance in solid form A Nucleus D They have stable electronic configuration D He noted periodic trends of known elements surrounding the undiscovered ones C Ionic E Scientific law B Weight C an unreactive colourless gas C Single-replacement A A liquid water freezes into an ice cube

20. A

85

21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

C 75 mL B 3.5 moles C Condensation A Higher D 1.6 g cm-3 A 0.127 mol S D 1.755 g C 6.9 x 1017 atoms K-40 D 0.6 C 1.06 N D Force of repulsion/attraction is directly proportional to the distance between two poles. B 7.5 cm A yellow B particles remain suspended even after long standing C 0.35 seconds D 3.5 meters per second B 0.073 kg-mps A 10.583 km/s A Both Superman and the ice cream will have zero momentum. D 6780 kJ A 6.7 min

42. C

ANSWER KEY | MATHEMATICS / SCIENCE

Hydrogen bonds

ANSWER KEY 43. 44. 45. 46. 47. 48. 49. 50. 51.

B False 52. C 16 N B False 53. C have the same acceleration A True when they reach the ground B straight line sloping upward 54. A 31.3 meters per second to the right 55. B 4.5 seconds D 5.69 N 56. A 24.9 meters C I and II only 57. B 22.1 meters per second A 3.87 m/s 58. B 3.3 seconds D vx = 0 and ax > 0 59. A 17.9 meters 2 60. D none of the above B 0.11 m/s

LANGUAGE PROFICIENCY 1. 2.

A A

3.

A

4.

D

5.

6. 7.

8. 9.

“if” should be “whether”

11. A

Science is singular; should

is the subject

12. C

magnanimous is showing

should be visits; Jammy

Nominative pronouns used

as subjects; “me” should be “I”

C

Subject-verb

agreement;

the noun closer to the verb is singular so it should be “was”

D A

there are only two dessert

choices so “between” must be used instead of “among”

B

unique can’t have a degree;

A

should be “can hardly”

no adverb can modify unique

10. C

subject-verb

agreement

“have” should be “has” because the subject is “the interest in improving…”

be “refers” nobility

of

feeling

generosity of mind

13. D

Disposal

could

and

mean

a

garbage unit or administration. Considering the context clues, disposal means authority in the sentence.

14. B

resplendent means shining

brilliantly, characterized by a glowing splendour

15. B

grandiloquent means an

extravagantly language

16. A

colourful

A handkerchief cannot be

flawless/error-free/pure.

Therefore

immaculate

handkerchief means spotless

SCIENCE / LANGUAGEMATHEMATICS PROFICIENCY | ANSWER KEY

86

ANSWER KEY 17. D

Brittle and fragile are used

to describe items. A reply that is crisp means concise.

18. C

Fumbling

is

to

handle

something in an awkward or clumsy way

19. C

instigated- To have caused

20. C

Edifice- A large and usually

time, and “on” for saying a specific day.

29. B

bleach is a mass noun,

30. D

Enigma is something that is

therefore, “little” must be used

difficult explain

understand

or

something to happen or begin

31. D

Ubiquitously- seeming to

impressive building (such as a

32. C

people don’t raise the social

church or government building)

21. A

Anti-climax: begins with the

22. B

Litotes: an understatement

highest down to the lowest

in

which

an

affirmative

is

expressed by the negative of the contrary

23. D

Paradox: statement that is

contradictory to common sense but is true

24. B

Apostrophe:

addressing

someone or something that is

be seen everywhere ladder;

it

is

the

people

themselves that rise up the social ladder

33. D

“at” is used when there is an

address number and “in” is used when pertaining to a city/town

34. D

John

and

Susie

is

considered as one subject “’s” must follow after Susie

35. C

“Further” pertains to ideas

while

“farther”

distance

pertains

to

absent

36. B

Fuchsia

contradictory to common sense

37. C

In a Past Perfect tense, the

25. C

Paradox: statement that is

but is true

26. A

Gregarious means enjoying

the company of other people; someone who is sociable

spelling past

“In” is used when stating a

38. A

“at” is used when pertaining to

40. A

the

correct

month without a specific date,

ANSWER KEY | MATHEMATICS LANGUAGE PROFICIENCY

that

correct

happened

that happened after takes the

28. A

is

the

participle form while the action

Liaison

spelling

action

is

earlier takes the had+ past

27. D

87

to

simple past tense form of the verb

39. A

ANSWER KEY 41. D

a paragraph is composed

of sentences while a note is composed of bars

50. D

with balance; Entropy is concerned with chaos

Barometer measures

mileage

44. B

A queen wears a crown; a

45. A

Assuage (v. appease) is

nun wears a habit

opposite to provoke; abstruse (adj. obscure) is opposite to straightforward

Virgil wrote Inferno; Miguel

de Cervantes wrote Don Quixote

47. C

Song of Roland is the most

famous literary piece from

France; Ramayana is the most famous literary piece from India

48. B

51. A

dapat “Sina” dahil isang

52. A

dapat “Ang panahong

53. A

dapat “Panlima”; ginagamit

pangalan lang ang binanggit

pressure; odometer measures

46. A

dapat “nang” kapag ang

susunod na salita ay pandiwa

42. A Homeostasis is concerned

43. B

as a noun

49. B

ito…”; pang-ayon

ang “n” kapag ang susunod na letra ay d,l,r,s,t. “m” naman kapag p,m

54. A 55. B

dapat “manghinayang”

Ang panghalip na doon

ang nararapat

56. A 57. C

walang kapatid si Rizal na

nagngangalang Virginia

58. A 59. C

Mapusok- pag-uugaling

mainit; madaling magalit

60. C pag-lalagum- pagbibigay ng kahulugan sa mga payak na

A gerund is a verb acting

itinuro

READING COMPREHENSION 1.

D

6.

B

11. D

16. D

21. B

3.

A

8.

B

13. D

18. D

23. C

2. 4. 5.

B C

D

7. 9.

D C

10. C

12. E

14. B 15. B

17. E 19. E

20. B

22. A 24. A 25. C

MATHEMATICS | ANSWER KEY LANGUAGE PROFICIENCY / READING COMPREHENSION

88

ANSWER KEY 26. D

33. A

40. B

47. B

54. A

28. A

35. D

42. A

49. D

56. C

30. C

37. A

27. E

29. A 31. A

32. D

89

34. C

36. D 38. D 39. A

41. B 43. C

44. B 45. B 46. B

ANSWER KEY | MATHEMATICS READING COMPREHENSION

48. D 50. D 51. D 52. D 53. B

55. B 57. B 58. C 59. C

60. B

NOTES

NOTES

NOTES

NOTES

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