1 (a)

Shade one more small square so that the diagram has one line of symmetry. [1]

(b)

Shade one more small square so that the diagram has rotational symmetry of order 2. [1]

2 The scale drawing shows the positions of two villages, P and Q.

The scale is 1 cm represents 0.5 km. North P North Q

(a) Find the actual distance between village P and village Q km [2]

(b) Measure the bearing of village Q from village P [1]

10 NOT TO SCALE 45° O 18 cm

The diagram shows a sector of a circle, centre O.

The length of the arc is r n cm .

Find the value of n.

n = [2] 11 (a) Write 0.007 08 in standard form [1]

(b) Work out . . ( ) ( ) 3 8 10 3 8 10 22 23

.

Give your answer in standard form [2] , ,

3 NOT TO SCALE 45° 65° y° x°

The diagram shows two straight lines intersecting two parallel lines.

Find the value of x and the value of y.

x = y = [3] , ,

4 1

2

3

4

5

6

7

Samira picks one of these cards at random and replaces it.

(a) Find the probability that she picks an odd number [1]

(b) Samira repeats this 35 times.

Calculate the number of times Samira is expected to pick an odd number [1]

5 y x 4 2 3 1 0 – 2 – 3 – 1 – 4 – 2 – 3 – 1 2 1 3 4 – 4 T U

(a) Translate triangle T by the vector 0 2

e o. [1]

(b) Describe fully the single transformation that maps triangle T onto triangle U [3] , ,

6 Solve.

(a) x 8 7 39 +

x = [2]

(b) ( ) y 2 5 1 24

=

y = [3]

7 These are the first 4 terms of a sequence.

  11   8   5   2

(a) Find the next term of this sequence [1]

(b) Find the nth term of this sequence [2] , ,

8 Find the highest common factor (HCF) of 36 and 54 [2]

9 A is the point ( , ) 3 1

.

AB 2 4 = - e o

(a) AC AB 2

Find the coordinates of the point C.

( , ) [2]

(b) The length of AB is k 5.

Find the value of k.

k = [2]

(c) P is a point on AB.

AP PB 1 3 | |

Find the position vector of P.

f p [2] , ,

12 NOT TO SCALE 74° P Q R

P, Q and R lie on a circle.

QR is a diameter.

Find angle PRQ.

Give geometrical reasons for your answer. Angle PRQ = because [2] , ,

16 6 cm 5 cm NOT TO SCALE

The diagram shows a solid made by joining a hemisphere to a cylinder.

The radius of both the hemisphere and the cylinder is 6 cm.

The height of the cylinder is 5 cm.

Find the total surface area of the solid.

Give your answer in terms of r cm2 [4] 17 Find the value of

(a) 125 3 2

[2]

(b) 4 2 5

• [2] , ,

13 (a) 100 students solve a puzzle.

The table shows information about the time taken by each student to solve the puzzle. Time (t seconds) t 20 40 1 G t 40 60 1 G t 60 100 1 G Frequency 30 40 30

(i) Work out an estimate of the mean s [4]

(ii) Complete the histogram to show the information in the table. t 3 4 2 1 0 40 30 50 70 90 20 60 Time (seconds) 80 100 Frequency density

[2] , ,

(b) 80 adults solve the same puzzle as the students.

The cumulative frequency table shows information about the time taken by each adult to solve the puzzle. Time (t seconds) t 20 G t 40 G t 60 G t 80 G t 100 G t 120 G Cumulative frequency 0 12 36 60 74 80

(i) On the grid, draw a cumulative frequency diagram. t 30 40 50 60 70 80 20 10 0 40 30 50 70 90 20 60 Time (seconds) 80 100 110 120 Cumulative frequency

[3]

(ii) Use your cumulative frequency diagram to find an estimate for

(a) the median

s [1]

(b) the lower quartile s [1] , ,

14 Write .0 25o as a fraction [2] , ,

15 y x 4 5 3 2 1 0 – 2 – 3 – 5 – 1 – 4 – 2 – 1 – 3 – 5 – 7 2 4 1 3 5 7 6 8 – 4 – 6 – 8

The diagram shows the graph of y x 2 1

• .

(a) Write down the coordinates of the point where the graph crosses the x-axis.

( , ) [1]

(b) Write down the equation of each asymptote [2]

(c) By drawing a suitable straight line on the grid, solve x x 2 1 0

= .

x = or x = [3] , ,

18 (a)

3 9

Rationalise the denominator.

Give your answer in its simplest form [2]

(b) ( )( ) c k 5 2 1 3 2 2

= +

Find the value of c and the value of k.

c = k = [2] 19 Write as a single fraction in its simplest form.

(a) a a b 6 5 3

[2]

(b) p t 2 4 3 +

[2]

(c) x x 2 2 1 3

[3]

20 y x 1 \

(a) When , x y 9 2

= .

Find the value of y when x 36

.

y = [3]

(b) When x is increased by a factor of 4, the value of y changes by a factor of p.

Find the value of p.

p = [1]

21 NOT TO SCALE y x A B O P Q

The diagram shows the graph of y x x 3 3

.

The graph crosses the x-axis at A, at O and at B.

The turning points of the graph are at P and at Q.

(a) Find the x-coordinate of A and the x-coordinate of B.

Give your answers as exact values.

x-coordinate of A x-coordinate of B [3]

(b) (i) Differentiate x x 3 3

[2]

(ii) Find the coordinates of P and Q.

P ( , )

Q ( , )

[4] , ,

22 (a) Write down the exact value of tan 60° [1]

(b) Solve sinx 2 1 0

= for x 0 3 0 6 ° ° G G .

x = or x = [3] , ,