1

List of formulas

1
Area, A, of triangle, base b, height h. A = 2 bh

Area, A, of circle of radius r. A = rr 2

Circumference, C, of circle of radius r. C = 2rr

Curved surface area, A, of cylinder of radius r, height h. A = 2rrh

Curved surface area, A, of cone of radius r, sloping edge l. A = rrl

Surface area, A, of sphere of radius r. A = 4rr 2

Volume, V, of prism, cross-sectional area A, length l. V = Al

1
Volume, V, of pyramid, base area A, height h. V = 3 Ah

Volume, V, of cylinder of radius r, height h. V = rr 2 h

1
Volume, V, of cone of radius r, height h. V = 3 rr 2 h

4
Volume, V, of sphere of radius r. V = 3 rr 3

-b ! b 2 - 4ac
For the equation ax2 + bx + c = 0, where a ≠ 0, x= 2a

For the triangle shown,

A a b c
= =
sin A sin B sin C

a 2 = b 2 + c 2 - 2bc cos A
c b
1
Area = 2 ab sin C

B a C
 2

1 Basma owns a toy shop.

(a) The sign shows the opening hours for the shop.

Saturday to Wednesday 10 30 to 18 00
Thursday and Friday 10 00 to 19 30

Work out the length of time the shop is open in one week.

........................................ hours [1]

(b) Basma employs 5 sales assistants and 2 supervisors.

On one particular week, the 5 sales assistants each work for 30 hours and the 2 supervisors each
work for 38 hours.

For that week, the total amount Basma pays these 7 employees is $3324.70 .
Basma pays each sales assistant $13.45 per hour.

Calculate the amount Basma pays each supervisor per hour.

$ ................................... per hour [3]

(c) The exchange rate between dollars ($) and pounds (£) is $1 = £0.77 .

Basma buys 50 identical games for a total of £245.

She makes a profit of 89% when she sells each game.

Calculate the selling price of one game in dollars.

Give your answer correct to the nearest cent.

$ ................................................. [4]
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(d) Basma invests $12 000 in an account paying compound interest at a rate of 1.5% per year.

At the end of year 1, she invests another $12 000 in the same account.
At the end of year 4, she takes $20 000 out of the account.

Calculate the amount of money remaining in the account at the end of year 4.
Give your answer correct to the nearest cent.

$ ................................................. [3]
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2
North

A NOT TO
SCALE
365

D
320

132

B
C 250

ABCD is a field.
AB = 320 m, BC = 250 m, CD = 132 m and AD = 365 m.
Angle BCD = 90°.

(a) Ray walks from A to B at an average speed of 1.6 m/s.

He then runs from B to C at an average speed of 2.8 m/s.

Calculate Ray’s average speed from A to B to C.

........................................... m/s [3]

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(b) The bearing of D from A is 243°.

Calculate the bearing of B from A.

................................................. [5]
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3 Bag A contains red balls and green balls.

The total number of balls in the bag is x.
The number of green balls in the bag is 6 more than the number of red balls.
x-6
(a) Show that the fraction of the balls in bag A that are red is .
2x

[2]

(b) Bag B also contains red balls and green balls.

The number of red balls in bag B is x.
The number of green balls in bag B is 4 times the number of green balls in bag A.
x
Show that the fraction of the balls in bag B that are red is .
3x + 12

[2]
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x-6 x
(c) =
2x 3x + 12
Show that x 2 - 6x - 72 = 0 .

[3]

(d) Solve by factorisation x 2 - 6x - 72 = 0 .

x = .................. or x = .................. [2]

(e) x is the total number of balls in bag A.

Use your answer to part (d) to find the number of green balls in bag A.

................................................. [1]
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4 Mia has 25 shapes.

She uses their properties to sort them into groups.
The table shows the number of shapes in each group.

Triangle Quadrilateral
Line symmetry 4 9
No line symmetry 5 7

(a) Mia takes one of the triangles at random, notes its properties and replaces it.

Find the probability that it has line symmetry.

................................................. [2]

(b) Mia takes one of the 25 shapes at random, notes its properties and replaces it.
She then takes a second shape at random, notes its properties and replaces it.

Find the probability that both shapes are not quadrilaterals.

................................................. [2]

(c) Mia takes three of the 25 shapes at random without replacement.

Find the probability that only one of the shapes is a triangle with line symmetry.

................................................. [3]
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5 (a) The table shows the age and value of 10 cars of the same model.

Age (years) 3 3 4 4 5 5 5 6 8 8
Value ($) 5500 6200 4200 4000 4000 3700 4500 3000 1500 2000

(i) Complete the scatter diagram.

The first 6 points have been plotted for you.

7000

6000

5000

4000
Value ($)
3000

2000

1000

0
0 1 2 3 4 5 6 7 8 9 10 11 12
Age (years)
[2]

(ii) Draw a line of best fit. [1]

(iii) Use your line of best fit to find an estimate for the value of a car of this model that is 7 years
old.

$ ................................................. [1]

(iv) Jay has a car of this model that is 12 years old and he wants to find its value.

Explain why Jay should not use this scatter diagram to find an estimate for the value of this
car.

.............................................................................................................................................

............................................................................................................................................. [1]
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(b) Jay records the distances travelled by 50 cars.

The frequency table shows the results.

Distance (d thousand km) 10 1 d G 4 0 40 1 d G 50 50 1 d G 60 60 1 d G 100

Frequency 8 14 11 17

(i) Work out the fraction of the cars that have travelled more than 50 000 km.
Give your answer in its simplest form.

................................................. [1]

(ii) Find the interval that contains the median.

................................................. [1]

(iii) Calculate an estimate of the mean distance travelled.

............................ thousand km [3]

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6
A

NOT TO
D SCALE
5.6
2.7

B E

3.9
9.8

ADB and AEC are straight lines.

BC is parallel to DE.
BC = 9.8 cm, BD = 2.7 cm, DE = 5.6 cm and CE = 3.9 cm.

(a) Complete the missing angles and reasons to show that triangle ABC is similar to triangle ADE.

In triangle ABC and triangle ADE,

angle BAC = angle ............. because common angle

angle ABC = angle ............. because ................................................................................

angle ACB = angle ............. because ................................................................................

As the three pairs of angles are equal, triangle ABC is similar to triangle ADE.
[3]

(b) Show that AD = 3.6 cm and AE = 5.2 cm.

[4]
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(c) Calculate angle DAE.

Angle DAE = ................................................ [3]

(d) Calculate the area of triangle ABC.

.......................................... cm 2 [2]
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7 (a) Two of the factors of 50 are square numbers.

One of these square numbers is 1.

Find the other square number that is a factor of 50.

................................................. [1]

(b) A = 2 x - 1 # 3 2y # 7
B = 2x+3 # 3 y # 5

The numbers A and B are written as the product of their prime factors, where x and y are positive
integers.

(i) Find the highest common factor (HCF) of A and B in terms of x and y.

................................................. [2]

(ii) Find the lowest common multiple (LCM) of A and B in terms of x and y.

................................................. [2]
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8 (a) Two companies move boxes.

Company A charges $0.50 for each box plus a fixed fee of $125.
Company B charges only a fixed fee of $350.

Find the number of boxes moved when Company A charges the same as Company B.

................................................. [2]

(b) The maximum mass a van can carry is exactly 770 kg.
The van carries boxes each of mass 4 kg, correct to the nearest kilogram.

Find the upper bound for the number of boxes this van can carry.

................................................. [2]

(c) A lorry contains boxes of three sizes S, M and L.

The ratio of the number of boxes S : M = 2 : 7.
The ratio of the number of boxes S : L = 6 : 4.
The lorry contains 72 boxes of size L.

Find the total number of boxes in the lorry.

................................................. [3]
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9 (a) The diagrams show the first four patterns in a sequence.

Pattern 1 Pattern 2 Pattern 3 Pattern 4

(i) Draw Pattern 5 on the grid below.

[1]

(ii) Complete the table.

Pattern (n) 1 2 3 4 5 6
Total number of triangles 1 4 9 16
Number of grey triangles 0 1 3
Number of white triangles 1 3 6
[2]
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(iii) Write an expression, in terms of n, for the total number of triangles in Pattern n.

................................................. [1]

(iv) Write an expression, in terms of n, for the number of white triangles in Pattern n.

................................................. [2]

(b) The 3rd term of a linear sequence is 34.

The 8th term of the same linear sequence is 14.

(i) Find the value of the first term of this sequence.

................................................. [2]

(ii) Find the value of the first negative term of this sequence.

................................................. [1]
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10
y
8

6
A
5

2
B
1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x

-1

-2

-3

(a) Describe fully the single transformation that maps shape A onto shape B.

.....................................................................................................................................................

..................................................................................................................................................... [2]

(b) Shape A is mapped onto shape C by an enlargement of scale factor 3.

Two of the vertices of shape C are (2, 5) and (5, 2).

(i) Find the coordinates of the centre of the enlargement.

( ...................... , .......................) [2]

(ii) Find the area of shape C.

...................................... units 2 [2]

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11 (a) In the Venn diagram, shade the region represented by ,

P Q.


P Q

[1]

(b) Use set notation to describe the shaded region in the Venn diagram.


X Y

................................................. [1]

(c)  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {x : x is a factor of 40}
B = {x : x is an odd number}

%
A B

10 1 3

(i) Complete the Venn diagram. [2]

(ii) List the elements of Al + B .

................................................. [1]
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12
E
A D
NOT TO
SCALE
x F
G

B C

ABCD is a rectangle with area 30 cm 2 .

AB = x cm.

Rectangle DEFG is removed from the corner of rectangle ABCD.

AE = CG = 2 cm.

(a) Write down an expression for BC in terms of x.

................................................. [1]

(b) Show that the shaded area, y cm 2 , is given by

60
y = 2x + - 4.
x

[3]
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60
(c) Complete the table for y = 2x + -4 .
x
Write your answer correct to 1 decimal place.

x 2 3 4 6 8 10 12 14
y 30 22 19 18 19.5 22 25
[1]

60
(d) Draw the graph of y = 2x + - 4 for 2 G x G 14 .
x
y
30

28

26

24

22

20

18

16
2 4 6 8 10 12 14 x
[3]

(e) The shaded area is 24 cm 2 .

The length of AB is less than the length of BC.

Use your graph to find the dimensions of rectangle ABCD.

.................... cm by .................... cm [2]