5 B A

(a) In triangle ABC, AB = 8 cm, AC = 7 cm and BC = 5 cm.

Using a ruler and compasses only, construct triangle ABC.

The side AB has been drawn for you. [2]

(b) Measure angle ACB [1]

(c) Triangle ABC is a scale drawing of a field.

(i) The scale is 1 : 10 000.

Find the actual distance from A to B.

Give your answer in kilometres km [1]

(ii) B is due east of A.

Find the bearing of A from B [1] , ,

7 (a) x – 5 – 4 – 3 – 2 – 1 1 0 2 3

Write down the inequality represented in the diagram [2]

(b) Write down the integer values of x that satisfy the inequality x 4 2 8 1 G

[2] , ,

12 Some students are asked if they like football (F) or rugby (R).

The Venn diagram shows the results. R F 33 7 6 4 %

(a) Find the number of students who do not like rugby [1]

(b) Use set notation to describe the region containing students who like rugby but not football [1] , ,

14 A cube contains a solid metal sphere.

The sphere touches all the faces of the cube.

The side length of the cube is 8 cm.

(a) Show that the volume of the sphere is rcm 3 256 3.

[1]

(b) Calculate the percentage of the cube that is not occupied by the sphere % [3]

(c) The density of the metal of the sphere is 7.86 g/cm3.

Calculate the mass of the sphere.

Give your answer in kilograms.

[Density = mass ' volume]

kg [2] , ,

(d) The sphere is melted down and made into a solid cylinder with radius 3.1 cm.

Calculate the total surface area of the cylinder cm2 [4] , ,

18 10 2 0 8 Speed (m/s) Time (seconds) NOT TO SCALE 0

The diagram shows part of the speed–time graph for an athlete in a race.

(a) Calculate the distance the athlete runs in the first 10 seconds m [2]

(b) The length of the race is 100 m.

After 10 seconds, the athlete continues to run at a speed of 8 m/s until the end of the race.

Calculate the total time the athlete takes to complete the 100 m race s [2] , ,

24 Martha walks a distance of 10 km at a speed of x km/h.

She then runs a distance of 5 km at a speed of ( ) x 4 + km/h.

The total time taken for the whole journey is 3.5 hours.

(a) Write down an expression in terms of x for the time Martha is walking h [1]

(b) Show that x x 7 2 80 0 2 -

= .

[4]

(c) Solve x x 7 2 80 0 2 -

= , giving your answers correct to 2 decimal places.

You must show all your working.

x = or x = [3]

(d) Calculate the difference between the time Martha is walking and the time she is running.

Give your answer in hours and minutes correct to the nearest minute. h min [3] , ,

25 Kai sorts parcels into two types, light and heavy. Type of parcel Mass (m kg) Light m 0 2 1 G Heavy m 2 5 1 G

The histogram shows some information about the number of parcels Kai sorts in one day. m 5 0 Frequency density Mass (kg) 0 20 40 10 30 1 2 3 4

(a) Find the number of light parcels [1]

(b) There are 102 heavy parcels.

Complete the histogram. [2] , ,

28

( )x 7 f x 4

Find the value of x when

(a) ( )x 1 f

x = [1]

(b) ( )x 1 f 1

.

x = [2]

29 NOT TO SCALE D C B A y° 38° 97° 14 cm 13 cm 10 cm

(a) Calculate the value of y.

y = [3]

(b) Calculate BD. BD = cm [5] , ,