MATHS GCSE REVISION QUESTIONS
Test 1
Aiming for 9/8/7 (old Grades A*/A)
40 Inputs
NON CALCULATOR
For multiple choice questions place a, b, c or d in the box.
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Question 1:

 Using the fact that      67    x    38    =    2546

a) What is the value of    0.67    ×    38    =
         (1)
b) What is the value of    6700    ×    3.8    =
         (2)

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Question 2:

 Here are the first four terms of an arithmetic sequence.

8,      12,      16,      18

Find an expression for the nth term of the sequence.

    a)     7n + 1
    b)     6n + 2
    c)     5n + 3
    d)     4n + 4

     (3)

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Question 3:

 A grey card is in the shape of a right angled triangle 4 cm by 5 cm


A square of side 2 cm is cut away from the triangle as shown
What is the area of the card that is left?
(shown in grey)
cm2    (4)

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Question 4:

 The cash price of a washing machine is £500
Mrs Smith buys the washing machine.
She pays

a deposit of 25% of the cash price
and £35 each month for 12 months.
Mrs Smith pays, in total, more than £500
How much more?
£     (5)

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Question 5:
 a)
 Expand       5(x - 3).

    a)      5x - 15
    b)      5x + 15
    c)      5x + 15x
    d)      5x - 15x

    (6)
b)

 Factorise       6m2 + 7m

    a)     6(m2 + 7m)
    b)     7(6m2 + m)
    c)     m2(6 + 7m)
    d)     m(6m + 7)

     (7)
c)

 Simplify       y6    x    y3                
y                      

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Question 6:

 This is a solid metal cuboid


a)

 Calculate the volume of the cuboid

cm3    (9)

b)
 The metal cuboid is melted down to make cubes of side 0.5 cm
If all the metal is used how many cubes are made

    (10)

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Question 7:
 x=   -5        and        y =   4

What is the value of        2x2 + y2

    (11)

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Question 8

 Fred is baking several apples pies
For the crust part he uses
sugar, butter and flour in the ratio of 1:3:6
Fred uses 100g of apples to every 200 g of crust topping
Fred will use 2 kg of apples, altogether

What is the amount of sugar, butter and flour he will use

sugar =   g    (12)
butter = g     (13)
flour =   g     (14)

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Question 9:

 'Chelmsfords Cars' and 'Abbey Autos' are two car hire companies.
Chelmsfords Cars charges £40 plus £40 per day to hire a car.
Abbey Autos charges £100 plus £35 per day to hire a car.
Fred wants to hire a car for 10 days.

a)
 How much will Chelmsfords Cars charge for 10 days

£     (15)
b)
 How much will Abbey Autos charge for 10 days
£     (16)

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Question 10:
 a) Write the number 580 000 in standard form.
                x 10                      

b) Write 4.23 × 10-2 as an ordinary number.
            (19)

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Question 11
 Factorise       x2 + 4x - 12

    a)     (x + 4)(x - 3)
    b)     (x + 6)(x - 2)
    c)     (x - 4)(x + 3)
    d)     (x - 4)(x + 2)

     (20)

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Question 12

ABCDE is a regular pentagon.
PBA and PCD are straight lines.
Work out the size of the angle marked x.
 O   (21)

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Question 13
 In the diagram below

Point A has coordinates (0, 0, 0)
Point B is 8 units from A
Point D is 4 units from A
Point E is 2 units from A



(a)
What are the coordinates for H
(,  ,  )      ((22),(23),(24))

m     is the midpoint of the EF
(b)
What are the coordinates for m
(, , )      ((25),(26),(27))

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Question 14:
What is the value
a) 50      (28)
b) 23      (29)
c) 22 x 23      (30)

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Question 15

    a)     
    b)     
    c)     
    d)     
     (31)

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Question 16

A straight line has equation y = 6 – 4x

(a)
What is an equation of a line parallel to y = 6 – 4x
a)      y = 2 - x b)      y = 5 - 3x
c)      y = 5 - 4x d)      y = 6 - 6x

     (32)
(b)
What is an equation of the straight line that is perpendicular
to the line y = 6 – 4x and passes through the point (-8, 1).

a)      y = 0.25x + 3 b)      y = 4x - 6
c)      y = -8x + 1 d)      y = 0.25x + 1

     (33)

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Question 17


 O     (34)

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Question 18
The diagram shows a right-angled triangle.


AB is x + 2 cm long.
BC is x + 1 cm long.

What is the AREA of this triangle?


a)      (x + 1)(x + 2) b)      0.5(2x + 3)
c)      0.5(x2 + 3x + 2) d)      0.5(x2 + 3x + 3)

     (35)

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Question 19
Rearrange    3(y-x) = 2x + 8    to make y the subject

a)      (-x + 8)/3 b)      (5x + 8)/3
c)      5x + 24 d)      6x + 24

     (36)

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Question 20

Triangles ABC and PQR are similar
AB = 5cm, BC = 6 cm and QR = 21cm.

Calculate the length of PQ

 cm     (37)

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Question 21

For a cone of fixed volume, the height, h,
is inversely proportional to the square of the radius, r.

When the height is 4.5 cm, the radius is 4 cm
Find the radius when the height is 8 cm

r =  cm     (38)

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Question 22

a) What is the value of 9 3/2
     (39)

b) 9x = 274 solve for x

x =      (40)

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