Preview dr john chung sat math

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CONTENTS 50 TIPS

Page

50 Tips

1

Tips Answer

75

Test 1

20 PRACTICE TESTS 93

Test 2

121

Test 3

149

Test 4

177

Test 5

203

Test 6

229

Test 7

257

Test 8

283

Test 9

309

Test 10

335

Test 11

361

Test 12

387

Test 13

413

Test14

441

Test 15

467

Test 16

495

Test 17

523

18

551

Test 19

577

Test 20

605

Test

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Dr.

John Chung's SAT Math

50 TIPS

Dr. John Chung's SAT Math

-1 -

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50 TIPS

-

2

-

Tip1

Absolute Value

Tip26

Coordinates of a Circle

Tip2

Ratio of Similar Figures

Tip27

Paths in Grid

Tip3

Combined Range

Tip28

Transformation

Tip4

Classifying a Group

Tip29

The Least & Greatest Number

Tip5

Direct Variation

Tip30

Maximum & Minimum

Tip6

Inverse Variation

Tip31

Percentage

Tip?

Special Triangles

Tip32

Proportion & Ratios

Tip8

Exponents

Tip33

Probability

Tip9

Geometric Probability

Tip34

Number of Guarantee

Tip10

Domain & Range

Tip35

Midpoint & Distance

Tip11

Linear Function

Tip36

Odd & Even Numbers

Tip12

Triangle Inequality

Tip37

Inequality

Tip13

Permutation & Counting

Tip38

Solids

Tip 14

Handshake

Tip39

Sequences & Series

Tip15

Percent of Solution

Tip40

Defined Operation

Tip 16

Slope of a Line

Tip41

Functions as Models

Tip17

Number of Factors

Tip42

Data Interpretation

Tip18

Composition of Functions

Tip43

Expected Value

Tip19

Consecutive Numbers

Tip44

Counting Digits

Tip20

Must be or Could be True

Tip45

Counting Multiples

Tip21

Sum of Consecutive Numbers

Tip46

Average Speed

Tip22

No Solution

Tip47

Factorings

Tip23

Identical Equations

Tip48

Divisibility & Prime

Tip24

Pythagorean Theorem

Tip49

Rate of Work

Tip25

Similar in Right Triangle

Tip50

Parallel Lines

B

SAT Practice

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Note: Figure not 1.

In the

figure above,circle P and Q are inscribed in a circle. Ifthe radius ofcircle P is 4, and the radius ofcircle Q is 2, what is the ratio ofthe shadedregion to the area ofthe largest circle?

2.

t.ABC above, AB II PQ II RS and the ratio of the lengths, AQ: QS: SC = 2: 2: 3. Ifthe area of quadrilateral PRSQ is 4 8,what is the area of t.ABC ?

In

(A) 84

(B)

2 (A)

92

105 (D) 1 44 (E) 147 (C)

9

4

(B)

drawn to scale.

9

5

(C)

9

(D) 2._

12

(E) }_

12

Note: Figure not drawn to scale.

3.

In the

figure above, PQ is parallel to RS. Ifthe ratio ofthe area of t::,PQM to the area of t::,SRM is 4:9 and the perimeter of t.PQM is 15, what is the perimeter of t.SRM ?

(A) 22.!.

(B) (C)

(D) (E)

-

6

-

2 3 3�4

35.!.

2 37.!.

2 39.!.

3

2.

A group of workers can harvest all the grapes from

SAT Practice

10 square meters of a vineyard in .!..

3

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minutes. At this rate, how many minutes will the group need to harvest all the grapes from 300 square meters of this vineyard?

3.

1.

(Sol) The area of the vineyard is directly proportional to time. area - 10 - 300 x = 10 minutes. time ---:;--

Ans:

In the figure above, 6.ABC is similar

to t:,,DEF . What is the length of DF ?

(A) 6 (B) 82

}j' -

13 90 (C) 13

10 minutes

(D) 8 (E) 100

13 To make an orange dye, 5 parts of red dye are mixed with 3 parts of yellow dye. To make a green dye, 4 parts of blue dye are mixed with 2 parts of yellow dye. If equal amount of green and orange are mixed,what fraction of the new mixture is yellow dye?

(Sol) Orange Green

5 red + 3 yellow

8 parts 4 blue + 2 yellow 6 parts =

=

To make equal amount, LCM= 24 parts Orange Green

15 red + 9 yellow 16 red + 8 yellow Total

Therefore, there are new mixture.

Ans:

-1 0.

17 48

24 parts 24 parts 48 parts

=

=

17 parts of yellow in the

2.

In the table above,

y

is directly proportional to

x, where a* 0. Which of the following is the value of a?

(A)

3

(B) 4

(C) 5

(D) 6 (E) 7

SAT Practice

B

A

c 3.

D

Inthe

figure above,the radius ofcircle 0 is 8 and LAOB 60째 What is the area of 6.AOB?

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=

1.

Inthe

figure above, ABDE is a square and 6.BCD is an equilateral triangle. If the area of 6.BCD is 16./3, what is the area ofthe square?

.

(A) 8./3 (B) 10.J3

(C) 12,J2

(A) 32

(D) 15,fj,

(B) 32./3

(E) 16./3

(C) 64

(D) 64-J2 (E) 72

B

C

A

D

B

A

figure above, AB = BC = CD = 10 and AE = ED . What is the perimeterofthe figure?

Inthe

(A) 40

Inthe

(B) 100.J2.

(C) 30+10./3

(D) 200,fj, (E) 200./3

16

-

2o.J3 3

NC

figure above, M is the midpoint of AB, AM = MC,and the length of MC is 20. What is the area of 6.ABC?

(B) 50

(E) 30+

-

4.

(A) 200

(D) 30+20./3

.JV

Note: Figure not drawnto scale.

Note: Figure not drawnto scale.

2.

.c

(C) 100.J3

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TIP 8

52 =25

{

2.

Exponents

43 + 43 + 4 3 + 43 = 2",what is the value of n?

If

( A) 2

(B) 4 (C) 6

5 =b ase

(D) 8

2=exponent

(E) 10

25=power The Operations of exponents

am an= am+n (2) (am r = amn (3) (ab r = a"b" ( 1)

( 4)

(�J = ::

(6)

(ab)" =a"b"

(7) ( 8)

a-n = J_ a" m a-;;= Y

SAT Practice

1.

3.

I

1 I

If m and n are positive and 5m5n-3 20m3n, what is the value of m in tenns of n? =

1 ( A) _ 4n

(B) _i_1 n

4 If { ( -2 )3 ·82 } = (24 r 'what is the positive

(C) _i_3

value of n?

(D) 2n2

( A) 6

(E) 4n2

(B) 7

n

(C) 8

(D) 9

(E) 10

Dr. John Chung's SAT Math

-

17

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Dr. John Chung's SAT Math

TEST 5

Dr. John Chung's SAT Math Test 5

. 203 .

I

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3.

3 D D 3DD 3 D D 3

Two acatbasebal eam areareto15beplselayersected astheatpieplam,tcaheryershowandmany cher.diffIerlftethere nt outcomes are possible?

(A) 515 30210 225 in

in

5.

Igreatf -3estspossis -1ble andvalue0 ofs s 2? , what is the ((BA)) --26 02 6 m

n

mn

(C)

(B)

(D)

(C)

(E)

(D)

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(E)

4.

A/j / 12 4 AB Note: Figure not drawn to scale. point andid. Whatare onis thethe vertlengththeicesfiofgurofthee above, rect an gul ar sol (not shown)?

(A) 1413 1516 17 I I I I I I

/)..

Note: Figure not drawn to scale. the Iffigure above,65째 andis perpendicul78째ar t,owhat is the value of ?

(A) 2512 3547 53

In

DO .

(B)

(C)

(D)

(E)

AO

LAOC = LBOC

LBOD =

6.

In

_ _ _ _

A

B

AB

(B) (C)

(D) (E)

>

I GO ON TO THE NEXT PAGE . 208 .

IO.f Oxlmgal2lons10of water is added, then =-.

Therefore 100 m+x 2 2 xlOO � 10m+l0x=m • O l m lO(m+x)=O. x= m2 -lOm 10 y

b=

--

4.

---

19. (B)

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Ifd = 160.20, then a = 160 , c = 20 , and Therefore, a+c+d=340. =100% Day 1 and2 � 20-10 10 Day 3 and4 � 4025-25 - 60o/c Day4 and 5 � 6040-40 - 50o/c 30-60 50% decreased Day 5 and6 � --= 60 20-30 Day 6 and � --= 30 33.3% decreased Sianices lefourss thofansix numbers must be less than Since (5 t) = 6 and (3 .1.) = 2 , (5t)(3.1.) =12.

Therefore, 13-1-= 12. { 1, 2, 3 } � I 2 -2(1 ) + 1 = -2 (False) { 0, 1 , 2 } � 02 -2(0)+1=1, 1 2 -2(1) +1=0, 2 2 -2(2)+1=1 ( T rue) { -1, 0,1 } �(-1) 2 -2(-1 ) +1=3 (False) 0, 2 �02 -2(0)+l=l(False) (A)

--

--

0

0

7

natievselofy.point PISinnandthceePRHifigures=(22above, ,and0) andQHt(3,he=0coordi )1,respect the area of t:.PQR 2xl is 2 =l.

-lOt x-Theintmi(et-10) rceptdpoisn=0.tarefS t5.= 0 and t = 10. �x A TheTherefore, maximtumht�5 heightmumoccursheigatht tis 5. e maxi h(5) =-10(5)2 +100(5) = 250.

20.

5.

7.

6.

(B)

7.

I

s

(B) (B)

2.

3.

(C)

-

43 6

-

(B)

(D)

}

y

SECTION 5

(Proport D) ion: Since 2 minutes is equal to 120 120w seconds, -=w -.

120x Therefore, x = -k=-1, 11-2(-1)1 =-1+4 �3=3.

1.

8.

7,

(E)

{

=

TEST 1 3

(A)

s

O P(8-J3, 0) In the figure above, t:.OPQ is a special tradirianglus,et.hIfe areaOP=ofs,J3,the ciPQrcle=is8.JrSir2n=ce64Jr8 is. the -���......

�--___. x

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9.

3 a= 3b c = 5b, 5ac = 5(3b)5b = 3.

45 =a =3a. a+3a2 a=l5.

--=2a=30 3a = 2.5 ,% and

Since

10.

2.

In the figure above, each triangle has an area of Therefore, the unshaded region has an area of 8.

and larger number

Let smaller number

TimeA�B .!2 and TimeB�A .!2 .

Therefore,

�

or

y

10

17.

8

+

4

and y 8 .

x

48 mph.

82 .

From can be any real number. Or If can be any real number.

If = Therefore, the smallest value of

(x + y)(x - y)

x

hours. Therefore,

and Sum.students 8 + Therefore, Summ+n students Thus,

13. 80

x+ x-y=

48mph.

Summstuctents

Therefore,

Thus,

5D � . There1ore, -

16. 4

K(constant)

Inverse proportion:

2D DI

Average speed=

and OB = 4, height

Therefore, the slope of OA

12.

the average speed =

Time A.-.B - + -

B(4, 0)

= 25 AH= 5.

125 (m)(n2 ) = 2 )=m(o.22 ). )(5 2 (0. m= 0.0.2 x2522 125. = 36. y=361 12 9 66 2 = X 20 x )( = 10 =

Since the area is

D

=

Or, use a convenient number. Let distance from is a multiple of because A to B and 40. Now

A

H

D

.

The entire time

45.

11.

= 40 .

-+ 40 120 60 -= 5 /120 = 60 = 120, 120 . = 12060 12040 = 5 2405 = = 80m 0m 90n= 90n . = m+n = m=4n. mn = 4nn =4.

100 (p -lO)(q -10)=0, pq = 1010,, qp p2 q2 = 102 0 0 102 42 = 60

15. 48

18.

+

or

+

•

B

14. 8

b

Dr.

a

a b

John Chung's SAT Math Test 1 3

, a+b=l8,m+n=24, a+ m n =

In the figure above,

DE II AC

and LDFA = LFA C (alternate angles are congruent). AADF and AVEF are isosceles triangles. Therefore, the 42. b+ + perimeter of ABDE is -

43 7

-

7

7

7

SECTION 7 Time- 20 minutes 16 Questions

7

Tum to Section 7 (Page 2) of your answer sheet to answer the questions in this section .

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r

Directions: For this section, solve eachproblem and decide which is 1he best of1he choices given. Fill in 1he corresponding circle on 1he answer sheet You may use any available space for scratchworlc.

1 . The use of a calculator is pennitted 2. All nwnbers used are real numbers.

3. Figures that accompany problems in this test are intended to provide infonnation useful in solving 1he problems.

They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. All figure lie in a plane unless other indicated 4. Unless otherwise specified, the domain ofany function f is assumed to be set of all real numbers x for which f ( x) is a real number.

"'

�

�

'-

s

G1

0

'i <8 i::

A = trr2 C = 2;rr

...... <U

g

� �

A = Cw

l w � LJwh b 1 A = -bh 2

c V = Cwh

t=j h � V = ;rr2h

c2 = a2 + b2

The numbers of degrees of arc in a circle is 360°.

The sum of the measures in degrees of the angles is 1 80°.

�

1.

c

If a six-pack of soda costs k cents, how many individual cans can be purchased for d dollars?

(A) :!_ k

(B) 6dk (C) (D) (E)

lOOd k

2.

45

Special Right Triangles

If the average (arithmetic mean) of 1 0, is 20, what is the average of a and b ?

a, and b

(A) 25

(B) 28 30

(C)

(D) 40 (E) 50

600d

k kd 600

I -

�x s r:t xf3 s

622

-

>

GO ON TO THE NEXT PAGE

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3.

7

7

7

Abby, Bernard, and Cabin made a total of95 candy bars. Bernard made 5 times as many as Cabin, and Cabin made three times as many as Abby. How many candy bars did Abby make?

(A) (B) (C) (D) (E)

5 10 15 45 75

7

y

Note: Figure not drawn to scale.

5.

In the figure above, what is the equation of

line ÂŁ ?

4.

2 (A) y = - - x - 2 3 3 (B) y = --x - 2 2 3 (C) y = -- x - 3 2 2(D) y = x - 2 3 3(E) y = x - 3 2

If O. lk percent of n is 5, what is 3k percent of n ?

(A) (B) (C) (D) (E)

15 50 75 120 1 50

6.

If x < 0, which of the following could have solution?

I. II. III .

j xj = -x j xj = x

j xj = N

(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III

>

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John Chung's SAT Math Test 20

-

62 3

-

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II. lxl == x , for x < 0 , no solution.

III. lxl == N , for any x < 0 will be the solution.

---7.

(C)

The pairs of ( x, y ) are as follows.

(1, 1 9) (2, 1 8) (3, 1 7) .... (1 0, 10) . The difference between two numbers must be even integers.

Or, Let x - y == k ---- (1) , x + y 20 --- (2) From (1)+(2) 2 x = k + 20 , that is, k + 20 x == -- .

2 Because x is an integer, k should be even integers. ==

8.

(B) The probability that the arrow lands on 5 is -3 8

Year

1

2

3

4

5

Profit

10

12

16

24

28 30 3 1 3 1 .2

Increased by

(B)

8

4

4

2

8

7

1

0.2

In the table, increase faster, but later on slow.

(E) is the best representing the table.

14.

(D) From cross-multiplication, 2(a - 2b) == 3(b - 2a) 7b Sa = 7b , a = - . Therefore, 4

(7:)

2 2a -- -7 = == b b 4 15.

(B) 3 k + 3 k + 3k 3 3 k 3 i+k , and (27) 5 == ( 33 )5 = 31 5 Therefore, 1 + k = 1 5 , that is, k = 14 . ==

The expected times= 24 x � = 9 times.

8 9.

2

6

16.

·

==

(B)

5

In the figure above, n(X U Y) == n(X) + n(Y) - n(X n Y) 45 == 25 + 30 - k ' k = 10 10.

(D) Only number of movie Y == 30 - 1 0 == 20

11.

(C)

12.

(B) 2 (n + (n + 1)) = 5n - k , n == k + 2 . Therefore, The larger one is, n + 1 == k + 3

13.

(E)

AB 2 = AD x AC , AB 2 == 3 x 1 5 == 45 .

AB == J45

Dr. John Chung's SAT Math Test 20

In the graph, the value of p and t can be obtained from the equation. 3 = -p 2 + 12 . p 2 = 9 , then p == ± 3 . you can find the value of t. The greatest slope will be between (-3, 3) and (-4, -4) .

3 - (-4) = 7 .

Therefore, the greatest slope -3 - (-4) =

-

633

-