Page 193 - Cambridge+Checkpoint+Mathematics+Coursebook+9

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21 Simplify each expression. a x × x b 25t ÷ 5t 3
22 Write an expression for: 2x + 3
a the perimeter b the area of this rectangle. 4
Write each expression in its simplest form.
23 Use the formula T = ma + w to work out the value of:
a T when m = 8, a = 5 and w = 12 b a when T = 46, w = 18 and m = 4.
24 a Factorise each expression. i 5x − 15 ii 12xy − 8y

b Simplify each expression. i x + x ii 2x + y
2 5 3 4
c Expand and simplify each expression. i (x + 6)(x − 2) ii (x + 4) 2

25 An athletics coach must pick either Taj or Aadi to represent the athletics club in a long-jump
competition.
These are the distances, in cm, that the boys have jumped in their last 10 training sessions.

Taj 295 265 273 297 305 265 290 265 315 286
Aadi 295 294 275 282 275 296 280 276 284 308

a Calculate the mean, median, mode and range of both sets of data.
b Who do you think the coach should choose to represent the
athletics club? Explain your decision. y
26 The diagram shows shapes A, B, C, D, E, F and G on a grid. 4 C
Describe the single translation, reflection, rotation or D 3
enlargement that transforms: 2
a shape A to shape B b shape B to shape C 1 E
0
c shape C to shape D d shape B to shape E –4 –3 3 3 3 3 3 –2 –2 2 –1 –1 0 0 1 2 3 4 x
1
e shape F to shape G. –1 –1 1
G –2 2 B
2
2
2
27 Brad buys a house for $130 000. F –3 –
Five years later he sells it for $140 400. –4 A
a What is his percentage profit?
b Show how to check your answer.
28 A goat is tied by a rope to a post in a field. The rope is 12 m long.
Draw the locus of points that the goat can reach when the
rope is tight.
Use a scale of 1 cm to 3 m.

29 a Solve this equation. 5x – 3 = 3x + 11
b Solve these simulataneous equations. 2x + y = 11
5x + 3y = 29
c Solve this inequality. 6x − 4 ≤ 29
2
d The equation x − 3x = 13 has a solution between x = 5 and x = 6.
Use trial and improvement to find the solution to the equation, correct to one decimal place.
30 When Sven makes bread rolls he uses rye flour and wheat flour in the ratio 2 : 3.
Sven makes bread rolls using 250 g of rye flour.
What mass of wheat flour does he use?

192 End-of-year review