1 Write 24.
07839
(a) correct to 2 decimal places
................................................. [1]
(b) correct to the nearest 10.
................................................. [1]
2 Write down the number that is 9 greater than -23.
................................................. [1]
3 v = u+at
Find the value of v when u = 30, a =-2 and t = 7.
v = ................................................. [2]
4 Change 62 000 millimetres into kilometres.
............................................ km [1]
50°
The diagram shows two intersecting straight x° NOT TO
lines crossing two parallel lines. SCALE
114°
Find the value of x.
x = ................................................. [2]
2
6 (a) Explain why 111 is not a prime number.
.....................................................................................................................................................
[1]
(b) Find a prime number between 110 and 120.
................................................. [1]
7
North
NOT TO
North SCALE
P
39°
Q East
Find the bearing of Q from P.
................................................. [2]
1 3
8 Without using a calculator, work out 38 – 14
You must show all your working.
Give your answer as a mixed number in its simplest form.
................................................. [3]
3
9 Write 90 as a product of its prime factors.
................................................. [2]
10 Expand and simplify.
2(t + w) + 3(w – t)
................................................. [2]
11
6.3 cm NOT TO
h cm SCALE
5 cm
9 cm
The two shapes are mathematically similar.
(a) Find the value of h.
h = ................................................. [2]
(b) The area of the smaller shape is 16cm2. Calculate the area of the larger shape.
.......................................... cm2 [2]
4
12
10
Speed NOT TO
(m/s) SCALE
0
0 12 16
Time (seconds)
The diagram shows a speed–time graph for 16 seconds of a car journey.
(a) Find the deceleration of the car in the final 4 seconds.
......................................... m/s2 [1]
(b) Find the total distance travelled during the 16 seconds.
.............................................. m [2]
13
(a) 33p × 32p = 729
Find the value of p.
p = ................................................. [2]
(b) Simplify.
1
(32𝑥10 )5
................................................. [2]
5
14 y = 2w2 – x
Rearrange the formula to make w the subject.
w = ................................................. [3]
15 (a) On the Venn diagram, shade the region P U Q’.
P Q
[1]
(b) n ( ) = 20 n(A U B)’ = 1 n(A) = 12 n(B) = 10
Complete the Venn diagram.
A B
............. .......... .............
..........
[2]
16 Find the lowest common multiple (LCM) of 12x8 and 8x12.
................................................. [2]
6
17 (a)
C NOT TO
O
B SCALE
28°
A B
A, B and C are points on a circle, centre O.
Angle OBA = 28°.
Find angle ACB.
Angle ACB = ................................................. [2]
(b)
NOT TO
SCALE
R 52°
47°
T U
P
P, Q and R are points on a circle.
TU is a tangent to the circle at P.
Angle TPR = 47° and angle PRQ = 52°.
Find angle RPQ.
Angle RPQ = ................................................. [2]
7
18 (a) Sketch the graph of y = sin x for 0 ≤ x ≤ 360
[2]
(b) If sin-1 x = 0.43 and 0 ≤ x ≤ 360 . Find the values of x.
x =.................or x = ....................[2]
19 Find the nth term of each sequence.
(a) 11, 8, 5, 2, -1, …
................................................. [2]
(b) 1, 5, 25, 125, 625, …
................................................. [2]
8
20 The area of a rectangle is 55.2 cm2, correct to 1 decimal place.
The length of the rectangle is 9cm, correct to the nearest cm.
Calculate the upper bound of the width of the rectangle.
............................................ cm [3]
21 The line y = x + 1 intersects the curve y = x2 + x – 3 at two points.
Solve the equations simultaneously to find the coordinates of the two points.
( ...................... , ...................... ) ( ...................... , ...................... ) [4]
9
22 x is inversely proportional to the square root of w.
When w = 16, x = 3.
Find x in terms of w.
x = ................................................. [2]
23 Write x2 + 6x – 4 in the form (x + p)2 – q, where p and q are integers.
............................................ [2]
24 The derivative of 2ax7 +3xk is 42x6 +15xk-1.
Find the value of a and the value of k.
a = ................................................. k = ................................................. [2]
10
25 Simplify.
................................................. [4]
26 Make y the subject of the formula:
h2y = x2 + 2y
................................................. [3]
END OF EXAM
[TOTAL 70 MARKS]
