ABC Education · 11+ Practice

Week 41 · Maths Practice Paper

16 questions · 94 marks · Suggested time: 45 minutes.

Question 1

[8 marks]

Work out the following, showing all your working.

(a)

Bobby was given some money for his birthday. He bought a calendar for £7.42 and a ball for £3.55. How much did he spend?

(b)

He has £4.18 left in his wallet. How much did he originally have?

(c)

Multiply together 384 and 67.

(d)

Divide 8652 by 42.

Question 2

[6 marks]

Solve each of these equations to find the value of x.

(a)

x − 6 = 23

(b)

7x = 63

(c)

x12 = 5

(d)

18 + x = 27

(e)

(13)x = 8

(f)

9x = 54

Question 3

[8 marks]

Solve the following two-step equations to find the value of x.

(a)

6x − 11 = 7

(b)

x4 + 7 = 13

(c)

19 = 3 + 4x

(d)

9x + 21 = 3

Question 4

[6 marks]

Form an equation for each of the following problems and then solve it:

(a)

I think of a number, multiply it by 8, and the result is 48. What is the number I first thought of?

(b)

I think of a number, multiply it by 7 and then subtract 6. The result is 43. What is the number I first thought of?

Question 5

[6 marks]

(a)

What is the volume of a rectangular box which is 10cm long, 20cm wide and 5cm high?

(b)

How many 5cm cubes can be packed into the rectangular box in part (a)?

Question 6

[10 marks]

Calculate the following, using the most appropriate unit for your answers.

(a)

58 of 12.8m

(b)

0.4 × 3kg

(c)

32% of £60

(d)

70% of £180

(e)

58 of £9.68

Question 7

[4 marks]

The total running time for a film is 120 minutes. 5% of the time is taken up with the opening titles and credits. A total of 20 minutes of the film is shot outdoors. One quarter of the film is shot inside a hospital. 0.15 of the film is shot in a greenhouse. All the remainder of the film is shot inside the Manor House. How much of the film is shot inside the Manor House?

As a fraction:

As a decimal:

As a percentage:

In minutes:

Question 8

[5 marks]

Find the next number in each of these sequences:

(a)

1, 4, 8, 13, 19, ___

(b)

1, 2, 4, 8, 16, ___

(c)

100, 99, 96, 91, 84, ___

(d)

89, 55, 34, 21, 13, ___

(e)

Find the missing number: 1, 8, 27, ___, 125, 216

Question 9

[3 marks]

For a parallelogram that is not a rectangle:

(a)

How many pairs of equal sides does it have?

(b)

How many pairs of equal angles does it have?

(c)

How many pairs of parallel sides does it have?

Question 10

[6 marks]

Three vertices of a shape are W(-1,2), X(3,2) and Y(3,-2), joined in order with a fourth point Z to close the shape.

(a)

What type of shape is WXYZ, given all four sides are equal?

(b)

What is its area?

(c)

What are the coordinates of the midpoint of WY?

Question 11

[2 marks]

A square, a rectangle, a rhombus and a parallelogram all have two pairs of parallel sides.

Name one other property shared by all four shapes.

Question 12

[3 marks]

Explain why it is not possible for a quadrilateral to have exactly three right angles.

Question 13

[5 marks]

Calculate the size of the missing angles (diagrams not drawn to scale):

a =

b =

c =

d =

e =

Question 14

[3 marks]

In a money bag there are an equal number of 2p's, 5p's and no other coins. How many coins are in the bag if altogether there is £1.40?

Question 15

[8 marks]

A recipe for a pudding for 6 people requires 3 eggs, 300g flour, 120g sultanas, 180ml milk and 60g butter. I want to adapt this recipe.

(a)

For 8 people I would need ___ eggs and ___ ml of milk.

(b)

For 9 people I would need ___ g of sultanas and ___ g of butter.

(c)

I later find the recipe printed with 5 eggs instead. How many people is this version intended to serve?

(d)

In the 10-person version, how much flour would you need?

Question 16

[11 marks]

Emma invents a game. For any number she chooses, she works out all the whole numbers that divide exactly into it and adds them up to find its 'factor sum'. For example, the factor sum of 6 is 1 + 2 + 3 + 6 = 12.

(a)

Find the factor sum of 18.

(b)

If the factor sum of a number is 13, what is the number?

(c)

If the factor sum of a number is 18, there are two possible numbers. What are they?

(d)

The factor sum of three different numbers is 24. Two of them are consecutive numbers. Find the three numbers.