4 y x – 1 1 0 2 3 4 5 6 7 8 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10 – 1 1 2 3 4 5 6 – 2 – 3 – 4 – 5 – 6 – 7 – 8 A B C

(a) Describe fully the single transformation that maps

(i) shape A onto shape B [2]

(ii) shape A onto shape C [3]

(b) On the grid, draw the image of shape A after a reflection in the line x 2 = - . [2] , ,

3 In the USA, one gallon of fuel costs $4.83 .

In the UK, one litre of fuel costs £1.62 .

The exchange rate is £1 = $1.215 .

1 gallon = 3.785 litres

In which country does 1 litre of fuel cost more and by how much?

Give your answer in dollars by $ [3]

5 (a) These are the first 5 terms of a sequence.

1 8 27 64 125

Find the 10th term of this sequence [1]

(b) These are the first 5 terms of a different sequence.

5 8 13 20 29

Find the nth term of this sequence [2]

(c) The sum of the first n terms of another sequence is ( ) n n 2 5 1

.

(i) Use n 2

to find the sum of the first two terms in this sequence [1]

(ii) Find the 3rd term of this sequence [2] , ,

1 Solve.

c 4 9 13

=

c = [2] , ,

9 In a sale, the original price of a sewing machine is reduced by $38.

This is an 8% reduction in the original price.

Work out the original price of the sewing machine.

$ [2]

12 42° 115° 12.5 cm Q R P NOT TO SCALE

The diagram shows triangle PQR.

Calculate the shortest distance from Q to PR cm [3] 13 Make x the subject of this formula.

A w x 5 2 2

x = [3] , ,

6 Expand.

( ) x x 5 3 2 2

[2]

7 y – 2 – 1 0 1 2 3 4 5

Write down the inequality in y shown by the number line [2] , ,

8 Hadi buys a dishwasher.

He can either pay a single payment of $980 or he can pay using a monthly plan.

The monthly plan is 20% of $980 plus 12 payments of$75.25 .

(a) Hadi uses the monthly plan.

Calculate the total amount Hadi pays.

$ [2]

(b) Find the percentage increase in the cost using the monthly plan compared to a single payment % [2]

10 (a) Write down all the factors of 18 [2]

(b) Factorise. y xy x 3 15 5

[2]

(c)

y xy x 3 15 5 18

=

where x and y are positive integers.

Using your answers to part (a) and part (b), find one possible value of x and the corresponding value of y.

x = , y = [2] 11 A warehouse has a floor area of 800 m2.

The plan of the warehouse is drawn to a scale of 1 : 50.

Calculate the floor area on the plan.

Give your answer in square centimetres cm2 [3] , ,

18 x x 2 12 2 2 +

• can be written in the form ( ) a x b c 2

• .

Find the values of a, b and c.

a = , b = , c = [3]

2 Work out 8 6 3 5 16 71 46 13 2 2

Give your answer correct to 2 significant figures [2]

14 The table shows some values for y x x 5 4 2 3

• . x -2 -1 0 1 2 3 4 5 y 24 -4 8 14 -4

(a) Complete the table. [3]

(b) On the grid, draw the graph of y x x 5 4 2 3

• for x 2 5 G G

. y x 30 20 10 0 – 10 – 1 1 2 3 4 5 – 2

[4]

(c) By drawing a suitable straight line on the grid, solve the equation x x x 5 14 0 3 2

= .

x = or x = or x = [4]

15 The height of each of 140 basketball players is recorded.

The table shows the results. Height (h cm) h 0 0 16 18 1 G h 0 18 185 1 G h 0 185 19 1 G h 0 2 0 19 0 1 G h 200 210 1 G Frequency 7 12 31 70 20

(a) Calculate an estimate of the mean height cm [4]

(b) Two of the players are chosen at random.

Find the probability that both players have a height greater than 190 cm and no more than 200 cm [2] , ,

(c) Complete the histogram to show the information in the frequency table. y h 6 7 8 5 4 3 2 1 0 170 160 180 190 Height (cm) Frequency density 200 210

[3] 16 Mateo invests $1250 at a rate of r % per year compound interest.

At the end of 6 years the total value of his investment is $1484.

Calculate the value of r.

r = [3] , ,

17 56° 47° 12.1 cm 15.8 cm 9.6 cm B A D C NOT TO SCALE

The diagram shows a quadrilateral ABCD.

(a) Calculate AD.

AD = cm [3]

(b) Calculate the obtuse angle BDC.

Angle BDC = [4]

(c) Calculate the area of the quadrilateral cm2 [3] , ,

19 NOT TO SCALE 126° 7.5 cm

The diagram shows a major sector of a circle with radius 7.5 cm.

Calculate the perimeter of the major sector cm [4]

20 NOT TO SCALE A D O M B C 24 cm 10.5 cm 10.5 cm

The diagram shows a pyramid OABCD.

The pyramid has a square base, ABCD, with sides 10.5 cm.

The vertex O is vertically above the centre of the base, M.

The height of the pyramid is 24 cm.

(a) Calculate the angle that OA makes with the base [4] , ,

(b) NOT TO SCALE A D M B C 16 cm 10.5 cm 10.5 cm

The diagram shows a frustum of the pyramid OABCD.

The height of the frustum is 16 cm.

Calculate the volume of the frustum cm3 [5] Question 21 is on page 16. , ,