Whitley Abbey Community School
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Contents
Section A (Questions 1-10)
Multiple Choice Spectacular
Section B (11-14)
Quadratics Excitement-ville
Section C (15–17)
Surds and Numbers Excellence
Section D (18-23)
Algebraic Wonderland
Section E (24-26)
Trig-o-rama
Section F (27-28)
Equations that love to happen at the same time
Section G (29-32)
Proof and wordy fun
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1.
(x + 3)2 =
x2 + 9
x2 + 6x + 9
2x + 6
x2 + 3x + 9
x2 + 6x + 6
A
B
C
D
E
(Total 1 mark)
2.
A plane is flying at a speed of 1440 kilometres per hour.
How long, in seconds, will the plane take to fly a distance of 1 kilometre?
0.4 seconds
2.4 seconds
2.5 seconds
4 seconds
24 seconds
A
B
C
D
E
(Total 1 mark)
3.
What is 0.0007 when written in standard form?
0.7 × 103
0.7 × 10–3
7 × 10–3
7 × 104
7 × 10–4
A
B
C
D
E
(Total 1 mark)
4.
Factorise
x2 + 14x + 24
(x + 8)(x + 3)
(x + 6)(x + 4)
(x + 14)(x + 24)
(x + 12)(x + 2)
(x + 12)(x + 12)
A
B
C
D
E
(Total 1 mark)
5.
The length of a piece of string is 16 cm, correct to the nearest cm.
What is the greatest possible length the piece of string could be?
15.95
15.5
16.05
16.4
16.5
A
B
C
D
E
(Total 1 mark)
6.
6x4 + 6x2
Factorise completely
x2(6x2 + 6)
6x2(x2 + 6)
6x2(6x2 + 1)
6x2(x2 + 1)
6x4(6x2 + 1)
A
B
C
D
E
(Total 1 mark)
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7.
One of the factors of 3x2 – 13x – 10 is (x – 5)
What is the other factor?
(3x + 2)
(3x – 2)
3(x + 1)
(x – 2)
(3x – 5)
A
B
C
D
E
(Total 1 mark)
8.
(2x – 7)(x – 3) =
2x2 – 13x + 21
2x2 + 21
2x2 – 21
2x2 + 13x + 21
2x2 + 4x + 21
A
B
C
D
E
(Total 1 mark)
9.
What are the coordinates of the midpoint of the line joining P (–3, 2, 4) to Q (5, 1, 8)?
(1, 1.5, 6)
(2, –1, 4)
(8, –1, 4)
(1, –0.5, 2)
(2, 3, 12)
A
B
C
D
E
(Total 1 mark)
10.
1 2
2 1
4 3
3
3
4
A
2
11
12
B
3
2
12
C
2
2
12
D
3
11
12
E
(Total 1 mark)
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11.
(a)
Factorise
x2 + 6x + 8
………………………
(2)
(b)
Solve
x2 + 6x + 8 = 0
x =………………………
or x =………………………
(1)
(Total 3 marks)
12.
Solve 3x2 + 7x – 13 = 0
Give your solutions correct to 2 decimal places.
x = ................................ or x = ................................
(Total 3 marks)
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13.
x+2
Diagram NOT
accurately drawn
x–5
x+6
The diagram shows a trapezium.
The lengths of three of the sides of the trapezium are x – 5, x + 2 and x + 6.
All measurements are given in centimetres.
The area of the trapezium is 36 cm2.
(a)
Show that x2 – x – 56 = 0
(4)
(b)
(i)
Solve the equation x2 – x – 56 = 0
…………………………
(ii)
Hence find the length of the shortest side of the trapezium.
…………………… cm
(4)
(Total 8 marks)
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14.
Given that
x2 – 14x + a = (x + b)2 for all values of x,
find the value of a and the value of b.
a = .........................................
b = .........................................
(Total 3 marks)
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15.
Work out the value of
(i)
(22)3
.................................
(ii)
 3
2
.................................
(iii)
24  9
.................................
(Total 4 marks)
16.
(a)
Simplify
(i)
x6
x2
..................................
(ii)
(y4)3
...................................
(2)
(b)
Expand and simplify
(t + 4)(t – 2)
...................................
(2)
(c)
Write down the integer values of x that satisfy the inequality
–2  x < 4
...................................
(2)
(d)
Find the value of
–
(i)
36
1
2
...................................
(ii)
27
2
3
...................................
(2)
(Total 8 marks)
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17.
(a)
Rationalise the denominator of
1
3
....................................
(1)
(b)
Expand (2  3 )(1  3 )
Give your answer in the form a  b 3 where a and b are integers.
....................................
(2)
(Total 3 marks)
18.
(i)
Solve the inequality
5x – 7 < 2x – 1
………………………
(ii)
On the number line, represent the solution set to part (i).
–5
–4
–3
–2
–1
0
1
2
3
4
5
(Total 3 marks)
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19.
Solve the equation
x
4

1
2x – 3 x  1
x = .................................
(Total 5 marks)
20.
Write
x
3

as a single fraction in its simplest form.
x  2 x( x  2)
.............................................
(Total 2 marks)
Whitley Abbey Community School
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21.
(a)
Solve
40 – x
=4+x
3
x = ....................
(3)
(b)
Simplify fully
4x 2 – 6x
4x 2 – 9
........................................
(3)
(Total 6 marks)
Whitley Abbey Community School
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22.
A straight line has equation y = 2x – 3
The point P lies on the straight line.
The y coordinate of P is –4
(a)
Find the x coordinate of P.
.................................
(2)
A straight line L is parallel to y = 2x – 3 and passes through the point (3,4).
(b)
Find the equation of line L.
.................................
(3)
(Total 5 marks)
Whitley Abbey Community School
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23.
On the grid, show by shading, the region which satisfies all three of the inequalities.
y > –2
x<3
y<x
(Total 4 marks)
24.
R
Diagram NOT
accurately drawn
5 cm
x°
Q
PQR is a triangle.
12.5 cm
Angle PQR = 90.
Calculate the value of x.
PQ = 12.5 cm.
P
QR = 5 cm.
Give your answer correct to 1 decimal place.
.........................................
(Total 3 marks)
Whitley Abbey Community School
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25.
A
Diagram NOT
accurately drawn
11.7 m
67°
B
28.3 m
C
AB = 11.7 m.
BC = 28.3 m.
Angle ABC = 67.
(a)
Calculate the area of the triangle ABC.
Give your answer correct to 3 significant figures.
…………………………. m2
(2)
(b)
Calculate the length of AC.
Give your answer correct to 3 significant figures.
…………………………. m
(3)
(Total 5 marks)
Whitley Abbey Community School
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26.
Diagram 1 is a sketch of part of the graph of y = sin x°.
(a)
Write down the coordinates of
(i)
P,
( …… , ……)
(ii)
Q.
( …… , ……)
(2)
Diagram 2 is a sketch of part of the graph of y = 3 cos 2x°.
(b)
Write down the coordinates of
(i)
R,
( …… , ……)
(ii)
S
( …… , ……)
(2)
(Total 4 marks)
Whitley Abbey Community School
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27.
Solve
2x – 3y = 11
5x + 2y = 18
x = ......................
y = ......................
(Total 4 marks)
28.
Solve the simultaneous equations
2x + 3y = –3
3x – 2y = 28
x = …………………
y = …………………
(Total 4 marks)
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29.
Prove that (3n + 1)2 – (3n –1)2 is a multiple of 4, for all positive integer values of n.
(Total 3 marks)
30. Prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2
when divided by 4.
(Total 3 marks)
31.
The length of a rectangle is twice the width of the rectangle.
The length of a diagonal of the rectangle is 25 cm.
x
2x
Work out the area of the rectangle.
Give your answer as an integer.
................................... cm2
(Total 3 marks)
Whitley Abbey Community School
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32.
O
Diagram NOT
accurately drawn
40°
9 cm
The diagram shows a sector of a circle, centre O.
The radius of the circle is 9 cm.
The angle at the centre of the circle is 40°.
Find the perimeter of the sector.
Leave your answer in terms of π.
...........................cm
(Total 4 marks)
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