Thinking Cap 6

1

Algebra

otes

Algebra uses letters to represent unknown numbers in expressions or equations.

5n

coefficient

unknown / variable

xample 1 A pharmacist had 24 bottles of vitamin pills in stock. j bottles of vitamin pills were sold. He then restocked another 4â&#x20AC;&#x2030;j bottles. (a)

In terms of j, how many bottles of vitamin pills did he have in the end?

(b)

If he had 60 bottles of vitamin pills in the end, how many bottles were sold?

(c)

How many bottles of vitamin pills did he restock?

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Mathematics Primary 6 Unit 1 Algebra

olution (a)

24 – j + 4 j = 24 + 3 j

He had 24 + 3j bottles of vitamin pills in the end.

(b)

Number of bottles of vitamin pills sold = j

24 + 3 j = 60 3 j = 60 – 24 = 36 36 12 j = 31 = 12

12 bottles of vitamin pills were sold.

(c)

j = 12

Number of bottles of vitamin pills restocked = 4 j = 4 × 12 = 48 He restocked 48 bottles of vitamin pills.

xample 1 The average amount of liquid in Test Tubes P, Q and R is 3h ml. Test Tubes P and Q contain 9 ml and 5 ml of liquid respectively. (a)

Express the amount of liquid in Test Tube R in terms of h.

(b)

If h = 4, find the total amount of liquid in Test Tubes P, Q and R.

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Mathematics Primary 6 Unit 1 Algebra

olution (a)

Total number of test tubes = 3

Total amount of liquid = 3 × 3h ml = 9h ml Amount of liquid in Test tube R = 9h ml – 9 ml – 5 ml = 9h ml – 14 ml = (9h – 14) ml

The amount of liquid in Test Tube R is (9h – 14) ml.

(b)

If h = 4,

Amount of liquid in Test Tube R = (9h – 14) ml = 9 × 4 ml – 14 ml = 36 ml – 14 ml = 22 ml Total amount of liquid in Test Tubes P, Q and R = 9 ml + 5 ml + 22 ml = 36 ml The total amount of liquid in Test Tubes P, Q and R is 36 ml.

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Mathematics Primary 6 Unit 1 Algebra

ractice Solve the following word problems. 1. When a = 8, find the value of

a + a2 . 4

2. Simplify 24x + 8 – 8x – 3 + 2x.

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Mathematics Primary 6 Unit 1 Algebra

3. The table shows the breakfast menu of a cafe. The eggs costs twice as much as the toast. If the price of the eggs is $r,

Item

Price per unit

Sausages

$4

Eggs and toast

$6

(a) find the price of the toast in terms of r. (b) find the value of r. (c) find the total price of sausages and eggs.

4. At the funfair, Tod won k chips that were worth 50¢ each. Vincent and Willy each won 8 chips that were worth 60¢ each. In terms of k, (a) find the total number of chips they won. (b) find the total value of the chips they won.

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Mathematics Primary 6 Unit 1 Algebra

5. A teacher ordered reference books for his Primary 4, 5 and 6 classes. The Primary 4 class received u books while the Primary 5 class received thrice that of the Primary 4 class. The Primary 6 class received 18 reference books less than the Primary 5 class. (a) Find the total number of reference books ordered in terms of u. (b) If u = 140, find the number of reference books received by the Primary 6 class.

6. In the figure below, VWXY is a rectangle. In terms of p, (a) find the area of the shaded part. (b) find the area of the unshaded part.

V

4p cm Z 2p cm Y

8 cm

W

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Mathematics Primary 6 Unit 1 Algebra

7. There are q pupils in a class. 45% of the pupils join the Science Club while 35% of the pupils join the Math Club. If 15% of the pupils join both clubs, how many pupils do not join any of the clubs?

8. Mrs Thomas gave $m to her two daughters, Joan and Betty, in the ratio 2 : 3. How much money did Joan receive?

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Mathematics Primary 6 Unit 1 Algebra

9. Andrew was 6n years old 16 years ago. (a) How old was Andrew 4n years ago? (b) If n = 3, how old will Andrew be in 5 years?

10. The average height of Calvin and Marcus is 24x cm. If Marcus is 10x cm taller than Calvin, find Calvin’s height in terms of x.

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Mathematics Primary 6 Unit 1 Algebra

11. Jane went to an amusement park with her 5 cousins. They had a $120 admission ticket voucher to share. It was not enough so each of them had to pay $x extra. (a) Find the total admission fee paid in terms of x. (b) If the admission fee was $68 per person, find the value of x.

12. Amber and her sister were playing Spillikins with their father. Father had 45n points. Amber picked up 3 blue sticks and scored 15n points. Her sister picked up 8 red sticks. 1 (a) If the value of each red stick was of the value of each blue stick, how 2 many points did her sister score? (b) At least, how many more points must Amber and her sister score together to beat their father in the game? Give your answers in terms of n.

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Mathematics Primary 6 Unit 1 Algebra

3 of the 7 remainder. In terms of t, how much money does he have left in a month?

13. Mr Paul earns $42t a month. He gives $14t to his parents and saves

14. The breadth of a rectangle is 6r cm. Its length is 5 times its breadth. (a) Express the perimeter of the rectangle in terms of r. (b) If r = 13, find the area of the rectangle. Give your answer in m2.

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Angles in Geometric Figures

2

1. The following figure is not drawn to scale. ABC and ACD are isosceles triangles. Find ∠n. A

C n 26° 54°

D

B

2. The figure below is not drawn to scale. PQRS is a parallelogram. (a) Find ∠SPT. (b) Find ∠PTR. P

S 124°

20°

Q

T

R

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Mathematics Primary 6 Unit 2 Angles in Geometric Figures

3. The following figure is not drawn to scale. EFGI and IJGH are 2 parallelograms overlapping each other. (a) Find ∠IHG. (b) Find ∠FJG. E

I 36° J H 36°

F

G

4. The figure below is not drawn to scale. PQRS is a square and PRT is an isosceles triangle. SRT is a straight line. Find ∠x. P

Q x

S

O

R

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T

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Mathematics Primary 6 Unit 2 Angles in Geometric Figures

5. The following figure is not drawn to scale. ABCD is a trapezium and DEF is an isosceles triangle. Find ∠r. A

E

r O

B

D

C 46° F

6. The figure below is not drawn to scale. In the figure, EFG is an isosceles triangle and IH  FG. Find ∠y. E 58° I F

y

H G

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Mathematics Primary 6 Unit 2 Angles in Geometric Figures

7. The following figure is not drawn to scale. PQRS is a parallelogram and PUT is a triangle. Find ∠m. P

U

Q 102°

S

64°

R

m O T

8. The figure below is not drawn to scale. In the figure, AF and BE are straight lines and AB  CD. Find ∠p. A

B

p O

134° C 128°

F

E

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D

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Mathematics Primary 6 Unit 2 Angles in Geometric Figures

9. The following figure is not drawn to scale. JKLM is a square and JKO is an equilateral triangle. Find ∠x. J

K

O M

x

N

L

10. The figure below is not drawn to scale. ABCD is a rhombus and ADE is an isosceles triangle. Find ∠m. B

A

124°

C

D m

E

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