6 The scatter diagram shows the value, in thousands of dollars, of ten paintings in 2005 and the value of the same paintings in 2025. 0 0 10 20 30 40 50 60 70 80 90 100 20 40 60 80 100 120 Value in 2025 ($thousands) Value in 2005 ($ thousands) 140 160 180 200

(a) The value of one of the paintings in 2025 is less than expected.

Draw a circle around the point that represents this painting. [1]

(b) Another painting had a value of $75 000 in 2005 and$140 000 in 2025.

On the scatter diagram, plot this point. [1]

(c) Write down the number of paintings with a value of less than $53 000 in 2005 [1]

(d) What type of correlation is shown on the scatter diagram?

[1] , ,

1 x° 25° NOT TO SCALE

The diagram shows an isosceles triangle.

Find the value of x.

x = [2]

5 12º xº yº E A B F C D G NOT TO SCALE

The diagram shows a rectangle ABCD.

EFG is an equilateral triangle that touches the rectangle at F and G.

Find the value of x and the value of y.

x = y = [2]

7 (a) The sum of all the prime numbers less than 10 is equal to 17.

Find the sum of all the prime numbers less than 16 [2]

(b) x is an integer.

The sum of the prime numbers greater than 6 and less than x is equal to 18.

Find a possible value for x.

x = [1] 3 e o , ,

8 DE 3 4 = - e o

(a) Find 5DE.

f p [1]

(b) Find DE [2]

(c) D is the point (‒2, ‒3).

Find the coordinates of the point E. ( , ) [2]

20 Work out . . 0 114 0 2 + o o .

Give your answer as a fraction [3]

2 Find the largest odd number that is a common factor of 90 and 120 [1]

9

n n n x 15 5 '

Find the value of x.

x = [1]

10 C A B 11 cm 8 cm NOT TO SCALE x°

The diagram shows a right-angled triangle ABC.

(a) Work out the exact length of AC cm [3]

(b) cos x k

Write down the value of k.

k = [1]

11 Sarah rolls a fair 6-sided dice twice.

Find the probability she rolls a number greater than 4 both times [2] 12 (a) Write down the value of 730 [1]

(b) Find the value of 3 7 2

• [2]

(c) Write 27 812

in the form 3n [2] , ,

4 A rectangle measures 5 cm by 19 cm. 19 cm 5 cm NOT TO SCALE

Two of these rectangles are joined to make a shape. NOT TO SCALE

Work out the perimeter of the shape cm [2] , ,

3 The diagram shows a net for a dice.

The dice has six faces numbered 1 to 6.

The sum of each pair of opposite faces on the dice is 7.

Write the missing numbers on the net 1 4 5 [1]

13 D O C A E B x° 44° NOT TO SCALE

A, B, C and D are points on the circumference of a circle with centre O.

ED and EB are tangents to the circle.

AC is parallel to EB.

Angle AOD = 44°.

Find the value of x.

x = [4] 14 The minimum point on a quadratic curve is (–3, –5).

(a) Find the equation of the line of symmetry of the curve [1]

(b) Write the equation of the curve in the form ( ) y x a b 2

• .

y = [1] , ,

23 30° NOT TO SCALE A C B 10 cm 6 cm

Work out the area of triangle ABC cm2 [3]

15 Factorise.

(a) x x 7 12 2 - +

[2]

(b) x y ny nx 5 10 6 3 + + +

[2] 16 The table shows three sequences. 1st term 2nd term 3rd term 4th term 5th term nth term Sequence A 8 13 18 23 28 Sequence B 2 3 3 4 4 5 5 6 6 7 Sequence C 4 1 2 1 1 2 4

Complete the table to show the nth term of each sequence.

[5] , ,

17 (a) Sketch the graph of ° ° cos y x x 0 360 for G G

. 1 360° 180° x y –1 0

[2]

(b) ° cos x 2 1

and x is a reflex angle.

Find the value of x.

x = [2] , ,

19 60° A B O NOT TO SCALE

The diagram shows a circle, centre O, radius 12 cm.

(a) Work out the area of the minor sector AOB.

Give your answer in terms of r in its simplest form cm2 [2]

(b) Calculate the length of the major arc AB.

Give your answer in terms of r in its simplest form cm [3] , ,

21 m 10 c + ` j° p° y° m° NOT TO SCALE

The diagram shows a cyclic quadrilateral.

The ratio p m 2 3 | |

.

Find the value of y.

y = [4]

22 The equation of line L is y x 2 1 7 =-

• .

Find an equation of the line perpendicular to line L that passes through the point (3, 5).

Give your answer in the form y mx c

• .

y = [3]

24 (a) Simplify.

125 20

[2]

(b) NOT TO SCALE cm 2 2 cm 3 8

The area of this rectangle is cm k 2.

Work out the value of k.

k = [2]

(c) Rationalise the denominator.

7 1 2 +

[2] , ,

25 Mahir picks one number at random from the numbers 5, 10 and 15.

He then picks one number at random from the numbers 4, 5 and 6.

He adds the two numbers.

The sample space diagram shows some of the possible outcomes. 4 + 5 5 6 14 10 First number Second number 15 16 19 15 20 21

(a) Complete the sample space diagram. [1]

(b) Given that the total of the two numbers is odd, find the probability that one of the numbers added is 15 [2] 26 Write as a single fraction in its simplest form.

(a) y mp m 25 15

[2]

(b) x x 2 5 3 3 4

[3] , ,