MATHS GCSE REVISION QUESTIONS
Test 2
Aiming for Grades 9/8/7 (Old A/A*)
40 Inputs
CALCULATOR ALLOWED

For multiple choice questions place a, b, c or d in the box.

3 sf means answer to 3 significant places.                
1 dp means to 1 decimal place.




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Question 1:
 Use your calculator to work out

a)
 Write the first 6 figures on your calculator
(1)

b)
Give your answer to 3 significant figures
(2)


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Question 2:

 Henry is using Trial and Improvement to find a solution
to the equation


Continue the table to find a solution to the equation
Give your answer to 1 decimal place
(3)

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Question 3:

 An ordinary 6-sided dice is biased
The probabilities of the dice landing on each of the numbers
are:

Work out the value of p
(4)

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Question 4:
a) Solve the inequality



(5)

b) Write down the inequality shown by following diagram


(6)

c)
Write down all the integers that satisfy both inequalities in
part (a) and (b)
-starting with lowest and in ascending order separated by a comma,   eg  -2,-1,0,1,2,3      no spaces.

(7)

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Question 5:
 a)
 Multiply out       m(m2 + 5).

a)      m3 + 5m b)      m3 + 5
c)      m2 + 5m d)      m2 + 5
(8)
b)
 Multiply out and simplify       4(x - 2) + 3(x + 2)

a)      7x + 14 b)      7x - 14
c)      7x + 2 d)      7x - 2
(9)

c)
 Multiply out and simplify       (n + 3)2


a)      n2 + 6n + 9 b)      n2 + 9
c)      2n + 6 d)      6n
(10)

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Question 6:
 Factorise completely the following expressions

a)2a2 + a

a)      a(2a + 1) b)      (a + 1)(2 + a)
c)      (2a + a)(a + 1) d)      2(2a2 + 1)
(11)

b)8x3y2 - 4xy3

a)      x(8x2y2 - 4y3) b)      y(8x3y - 4xy2)
c)      2xy(4x2y - 2y2) d)      4xy2(2x2 - y)

(12)

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Question 7:
 The star Alpha Centauri is approxomately
40 653 230 000 000 kilometres from earth.
Write this number in standard form to 3 significant figues.

x 10

Light travels at approximately 298 000 kilometres per second.
THere are 86 400 seconds in a day.
How many days will light take to reach the earth from
Alpha Centauri.
Write your answer to the nearest 10

days(15)

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Question 8

 A tin of diameter 7 cm and height 12 cm has a label around it.
The lapel is clued together using a 1 cm overlap.
There is a 1 cm gap between the lapel and the top and
the bottom of the tin


Find the length and height of the lapel

length = cm (16)

height = cm(17)

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Question 9:
 Make   x   the subject of the equation

3x + 2y = 8y - 3

Simplify your answer as much as possible

a)      x = 2y - 1 b)      3x = 6y - 3
c)      x = 6y - 3 d)      x = (10y - 3)/3

(18)

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Question 10:
Mr and Mrs Smith are buying a washing machine in a sale.

What was the original price of the washing machine?

(19)

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Question 11
 £4500 is invested at 3.2% compound interest per annum
How many years will it take for the investment to exceed
£5000?
(20)years

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Question 12
 Solve the equation
9(x - 1) = 5(x - 2)
x = (21)

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Question 13
 Solve the equation


x = (22)

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Question 14:
y is inversley proportional to the square of x
When y = 3, x = 2
Find the value of y and x = 4
y = (23)

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Question 15




P is a point on the shaded shape at coordinates (3,2)
The shaded shape is enlarged by a scale factor
(minus half) with a centre of enlargement (-1,0)

After enlargement the point P becomes P'
What are the coordinates for P'
(Coordinates in answer box must be written with brackets and a comma and no spaces
eg (1,2)    (4,-2)    (-2,3)    (-4,-2)    )
(24)

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Question 16

The histograms show the pulse rates of some members
of a golf club


60 of the members have a pulse rate lower than
50 beats per minute.
How many members have a pulse rate greater than
90 beats per minute.
(25)

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Question 17

Complete the table of values for y = (0.8)x
x y
0 1
1 0.8
2 (2dp)
3 (2dp)
4 (2dp)


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Question 18
Rationalise the denominator of



(29)

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Question 19
A child's rugby ball is 10 cm long and has a volume of 200 cm3.
It is similar in shape to a full size rugby ball.
A full size rugby ball is 22 cm long.


Find the volume of the full size ball.
cm3(30)

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Question 20
The diagram shows a float made from 2 cones with
dimensions as shown


Calculate the total surface area of the float.
(to 3 significant figures)
cm2(31)

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Question 21

AB is a chord of a circle, centre 0, radius 6 cm
AB = 7 cm


a)Find the angle AOB
(32) 0 (1dp)
b)Find the area of the triangle AOB
(33) cm 2 (1dp)
c)Find the area of the sector formed by 2 radii OA, OB
(34) cm2 (1dp)
d)Find the area of the shaded segment
(minor segment formed by the line AB)
(35) cm2(1dp)


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Question 22

ABCD is a quadrilateral.
AB = 7 cm, AD = 5cm and BC = 9 cm .
Angle ABC = 70o and angle ADC = 90o.


a) Calculate the length of the diagonal AC.
(36) cm (1dp)
b) Calculate the perimeter of ABCD.
(37) cm(1dp)


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Question 23

A water tank is 50 cm long, 34 cm wide and 24 cm hide.
It contains water to a depth 18 cm.


4 identical spheres are placed in the tanks and fully submerged.
The water level rises by 4.5 cm.

a) Calculate the volume of water displaced.
(38) cm3
b) Calculate the volume of one sphere.
(39) cm3(1dp)
c) Calculate the radius of the spheres.
(40) cm (1dp)

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