© John Wiley & Sons Australia, Ltd 1

WorkSHEET 8.1 Algebra Name: ___________________________ 1 If tickets to a tennis match cost $23 for adults

and $11 for children, write an expression for the cost of the following. (a) p adult tickets (b) q children tickets (c) x adult and y children tickets

Answers: (a) $ 23p (b) $11q (c) $( 23 11x y+ )

2 Bob is now d years old. (a) Write an expression for his age in 6 years

time. (b) How old was Bob 3 years ago? (c) Write an expression for Mary’s age, if

she is q years older than Bob.

Answers: (a) 6d + (b) 3d - (c) d q+

3 Are the following statements true or false? If 3 and 2d e= = , then: (a) 3 9d e+ =

(b) 2 45d

- =

(c) 64 107de- = -

Answers: (a) 3 + 3 ´ 2 = 3 + 6

3 + 3 ´ 2 = 9 True

(b) 2 3 65 5

- ´=-

False

(c) 4 ´ 2 - 6 3 1887 7´

= -

= 38 357 7æ öç ÷è ø

False

WorkSHEET 8.1 Algebra

© John Wiley & Sons Australia, Ltd 2

4 The circumference (perimeter) of a circle is pD, where 3.14p = and D is the diameter of a circle. Find the perimeter of a circle when: (a) D = 4 cm (b) D = 0.2 cm (c) D = 11 mm

Answers: (a) pD = 3.14 ´ 4

= 12.56 cm

(b) pD = 3.14 ´ 0.2 = 0.628 » 0.63 cm

(c) pD = 3.14 ´ 11

= 34.54 mm

5 (a) If 6p = , what is q when 3 12q p- = ? (b) If 2x = - , what is y when -2x + y = 0?

Answers: (a) q - 3p = 12

q - 3 ´ 6 = 12 q - 18 = 12 30q =

(b) -2x + y = 0

-2 ´ -2 + y = 0 4 + y = 0 4y = -

6 Substitute 1 and 2f g= = into the following expressions. (a) (2 )( )f g g f+ -

(b) (7 3 2 )10g g f- +

(c) 1(3 4 )3 3

ff g æ ö+ +ç ÷è ø

Answers: (a) (2 1 2)(2 1)´ + -

= 4 ´ 1 = 4

(b) 2 (7 3 2 2 1)10

- ´ + ´

= 15

(7 - 6 + 2)

= 0.2 ´ 3 = 0.6

(c) 1 1(3 1 4 2)3 3æ ö´ + ´ +ç ÷è ø

= 2(3 8)3æ ö+ ç ÷è ø

= 11 ´ 23

= 223

= 7 13

WorkSHEET 8.1 Algebra

© John Wiley & Sons Australia, Ltd 3

7 Choose the correct answer. When p = 8 and

q = 2 is substituted into the expression 85pq

- ,

the value is: A 36 B 40 C 42 D 45 E 49

Answer:

5p - 89

= 5 ´ 8 - 82

= 40 - 4 = 36 A

8 Substitute 4 and 5a b= - = - into the following expressions. (a) 2 ( 2 )a b a-

(b) 4 3 ( )ab baæ ö+ +ç ÷è ø

(c) 215 4b a

b-

Answers: (a) 2a(b - 2a)

= 2 ´ -4(-5 - 2 ´ -4) = -8(-5 + 8) = -8 ´ 3 = -24

(b) 4 3 ( )ab baæ ö+ +ç ÷è ø = 4 3 ( 4 5 5)

4æ ö+ - ´- + -ç ÷-è ø

= (-1 + 3)(20 - 5) = 2 ´ 15 = 30

(c) 215 4b a

b-

= 2 5 415 4 5´- -

-´-

= -10 415 20

-

= - 40 1260 60

-

= -1315

9 Substitute 9 and 4z y= - = into the following expressions. (a) 2y z- (b) 2.5z

(c) 12 (6 3 )zy

-

Answers: (a) y - 2z = 4 - 2 ´ -9

= 4 + 18 = 22

(b) 2.5z = 2.5 ´ - 9

= -22.5

(c) 12 12(6 3 )4

zy

- = (6 - 3 ´ -9)

= 3(6 + 27) = 3 ´ 33 = 99