ABC Education · 11+ Practice

Week 53 · Maths Practice Paper

30 questions · 73 marks · Suggested time: 1 hour.

Question 1

[1 marks]

Add: 42 + 38

Question 2

[1 marks]

Subtract: 61 − 17

Question 3

[1 marks]

Multiply: 63 × 7

Question 4

[1 marks]

Divide: 126 ÷ 6

Question 5

[1 marks]

Find the cost of downloading 6 apps if each one costs £3.45

Question 6

[2 marks]

Work out the sum of: 8, 88, 888 and 8888

Question 7

[1 marks]

Divide 4 by 0.25

Question 8

[1 marks]

Shade 20% of this shape:

Question 9

[2 marks]

There is an even chance that I will pick a toffee from a large bag of sweets containing toffees, jellies and chocolates. If the bag contains 14 jellies and 9 chocolates, how many toffees are there?

Question 10

[1 marks]

The total attendance at Premier League football matches last season was 14,832,419. Round this number to the nearest ten thousand.

Question 11

[2 marks]

Stickers cost 7p each and badges cost 5p each. I buy some stickers and badges which cost 55p exactly. How many of each did I buy?

Question 12

[2 marks]

Use the fact that 84,527 × 156 = 13,186,212 to work out 84,528 × 156

Question 13

[4 marks]

Fill in the spaces with one of +, −, ×, ÷ to make each statement correct.

(a)
9 ___ 3 = 6 ___ 3
(b)
5 ___ 6 = 60 ___ 2

Question 14

[2 marks]

The three-digit number 58_ can be divided by 3 without a remainder. What is the largest possible value that the last digit could be?

Question 15

[2 marks]

At a busy railway station trains leave from platform 3 every 8 minutes and from platform 6 every 12 minutes. Trains leave from both platforms at 14:23. When do trains next leave both platforms at the same time?

Question 16

[3 marks]

The price of a one-day ticket to a theme park is £42.00. Joe buys a ticket and experiences 10 rides during the day.

(a)
Work out the average cost per ride.
(b)
Rishi pays an additional £28 for a special pass which gives front-of-line access to all rides throughout the day. He experiences 16 rides. Does the special pass provide value for money? Give reasons for your answer.

Question 17

[4 marks]

Match each object below to its most likely height or length: a lighthouse, a giraffe, a swimming pool, and a paperclip. The measurements (in no particular order) are: 0.456 km, 5.2 m, 2500 cm, 32 mm.

Question 18

[4 marks]

A teacher gives the following instructions: Think of a number. Subtract 17 from this number to get the first result. Go back to the original number and subtract 9 to get the second result. Multiply the first and second results together to get the final answer.

(a)
Savan follows the instructions starting with the number 30. Work out Savan's final answer.
(b)
Richard obtains a final answer of 0. What number might he have thought of? Give all possibilities.

Question 19

[3 marks]

Consider these six quadrilaterals: kite, rectangle, parallelogram, square, trapezium, rhombus. List all possible quadrilaterals from this list which have the following properties:

Diagonals are of equal length:
There is exactly one pair of parallel sides:
Opposite angles are equal but are not right angles:

Question 20

[3 marks]

48 children choose their favourite subject from English, Mathematics and Science. A pie chart shows that English takes up a quarter of the circle, and Mathematics takes up 33⅓%.

(a)
What fraction of the group chose English?
(b)
Work out the angle of the Mathematics sector.
(c)
How many children chose Science?

Question 21

[3 marks]

If it is snowing then I wear boots. If it is windy then I carry an umbrella. If I wear boots then I also wear either a scarf or gloves but not both. If I carry an umbrella I always wear gloves and sometimes wear a scarf as well. I never carry an umbrella and wear boots on the same day. For each of the following, state whether it is definitely true, false or uncertain.

(a)
It is windy (not snowing). I carry an umbrella and wear a scarf but no gloves.
(b)
It is snowy and windy. I wear boots, gloves and no scarf.
(c)
It is snowy but not windy. I wear boots, a scarf and no gloves.

Question 22

[4 marks]

A sunflower seed takes a week to germinate after it has been sown in the ground. After germination it grows the same number of centimetres each day. Maya sows a sunflower seed. She measures the height of the plant at midday on the 20th July and again at midday on the 25th July. These two measurements are recorded as 42cm and 72cm respectively.

(a)
Work out the height of the plant at midday on August 6th.
(b)
On what date did Maya sow the seed in the ground?

Question 23

[3 marks]

A rectangular playground has a top edge divided into 3 equal segments and each side edge divided into 2 equal segments, each segment being 30 metres.

(a)
Work out the length of the top edge (AB).
(b)
Work out the perimeter of the playground.
(c)
Ginny runs round and round the perimeter clockwise, starting at the bottom-left corner. Given that she runs a total distance of 2200m, how far along the top edge (from its left end) does she finish?

Question 24

[3 marks]

A clock shows the time 7:35.

(a)
Alice looks at this clock in a mirror. What time does the mirror image show?
(b)
On another day Alice looks at a clock in a mirror and, without thinking, says the time is 11:30. What time is it really?

Question 25

[4 marks]

Once upon a time, in the Ancient Land of Haberdasher's: One pound = 20 shillings, one shilling = 12 pence. A large Margarine-beer costs 1 pound 7 shillings and 6 pence. A small Margarine-beer costs 16 shillings and 8 pence.

(a)
Work out the difference in price between a large and small beer. Give your answer in shillings and pence.
(b)
Work out the total cost of one large and two small beers. Give your answer in pounds, shillings and pence.

Question 26

[3 marks]

An empty jug is filled with water at a constant rate. For each of the following jug shapes, describe the type of height-vs-time graph you would get:

(a)
A cylindrical jug (same width top to bottom).
(b)
A jug that gets wider towards the top (like an upside-down cone).
(c)
A jug that is narrow in the middle and wider at both ends (an hourglass shape).

Question 27

[2 marks]

Four rectangular shapes have the following width and area values: Shape A (width 3, area 12), Shape B (width 4, area 8), Shape C (width 2, area 12), Shape D (width 8, area 8).

(a)
Find the height of each rectangular shape.
(b)
A fifth shape, E, is a right-angled triangle with base 4 and area 12. Find its height.

Question 28

[3 marks]

The diagram shows one-way cycle paths in a park connecting five points A, B, C, D, E in a line. There are 3 different direct paths from A to B, 1 from B to C, 2 from C to D, and 2 from D to E. There is also 1 direct path from A to D (bypassing B and C), and 1 direct path straight from A to E.

ABCDE3 paths1 path2 paths2 paths1 direct path A→E1 direct path A→D
from A to C
from A to D
from A to E

Question 29

[3 marks]

A sequence of numbers which get multiplied (or divided) by a fixed amount each time is called a geometric progression (GP).

(a)
The 1st term of a GP is 6 and the 2nd term is 18. Work out the 3rd term.
(b)
The 1st term of a GP is 30 million and the 2nd term is 3 million. Work out the 9th term.
(c)
The 1st term of a GP is 6 and the 3rd term is 150. Work out the 2nd term.

Question 30

[4 marks]

Seven elves work in a toy workshop. As Head Elf, Holly earns as much as all seven elves put together. Echo gets 20 galleons a day. Hazel earns 25% more than Ivy. Fern earns twice as much as Oak who earns two more galleons than Echo. Willow gets 20 galleons a day more than Birch and between them they get five times that of Echo. Hazel earns three-quarters of Echo's salary.

Complete the table (Echo, Oak, Fern, Willow, Birch, Hazel, Ivy) and work out how much Holly earns in a day.