ABC Education

ABC Education · 11+ Practice

Week 52 · Maths Practice Paper

14 questions · 100 marks · Suggested time: 1 hour.

Question 1

[8 marks]

Pat collects stamps. She has 156 British stamps and 72 foreign stamps.

(i)
How many stamps does she have in total?
(ii)
How many more British stamps than foreign stamps does she have?
(iii)
Pat arranges her 156 British stamps in an album. Each page holds 6 stamps. How many pages does she use?
(iv)
Her brother, Lee, has 3 times as many foreign stamps as she does. How many foreign stamps does he have?

Question 2

[6 marks]
(a)
Write down the number which is 10 more than 347
(b)
Write down the number which is 10 less than 1256
(c)
Write down the number which is 100 times bigger than 35
(d)
Write down the number which is 10 times smaller than 97
(e)
The temperature in a fridge is 3°C. The temperature in the freezer is 12°C colder. What is the temperature in the freezer?

Question 3

[6 marks]

Here is the start of a number pattern: 3, 4, 7, 11, 18, 29, 47, 76, 123. From the numbers above, write down:

(i)
a multiple of 4
(ii)
a prime number bigger than 6
(iii)
two numbers with a difference of 15
(iv)
two numbers whose product is 28
(v)
the median of the nine numbers

Question 4

[5 marks]

Notby School won the final of the football tournament. A football pitch is 105.2 metres long. There were 2847 spectators at their final match. The trophy weighed three-quarters of a kilogram. The coach also surveyed which goal-scorers were right-handed, shown in the Venn diagram below.

right-handedscored a goal6432
(i)
Write the pitch length in centimetres.
(ii)
Write 2847 correct to the nearest hundred.
(iii)
How many grams is three-quarters of a kilogram?
(iv)(a)
Use the Venn diagram to find the number of right-handed children in the team.
(iv)(b)
Use the Venn diagram to find the number of left-handed children who scored a goal.

Question 5

[11 marks]

Points A(1,1), B(7,1) and C(4,5) are joined to form triangle A on a centimetre grid.

(iii)
Which special type of triangle is A?
(vii)
What is the order of rotational symmetry of triangle A?
(viii)
Find the area of triangle A.

Question 6

[8 marks]

Five teams took part in a relay race at sports day. Their results: SprintStars 47.65s, Thunderbolts 50.9s, RapidRunners 49.2s, Comets 58.4s, Flash 49.85s.

(i)
Complete the table to show their positions (1st to 5th).
(ii)
How much faster was the team which came first than the team which came fifth?
(iii)
The team SprintStars broke the school record by 2.3 seconds. What was the previous school record?
(iv)
Thunderbolts had 5 runners in their team. Find the mean time for each runner by dividing their total time by 5.

Question 7

[5 marks]

Robert asked all the children in his school on which day of the week they were born. Each small rectangle on his bar chart represents 3 people. The results are: Monday 18, Tuesday 27, Wednesday 15, Thursday 9, Friday 24, Saturday 12, Sunday 21.

(i)
How many people does each small rectangle represent?
(iii)
Use the results to complete a frequency table (list each day's total).
(iv)
Which day is the mode (i.e. has the highest count)?

Question 8

[7 marks]

Katherine has 10 coins in a bag. She has one £1 coin, two 50-pence coins, one 10-pence coin and the rest are 5-pence coins.

(i)
What is the total value of all the coins in her bag?
(ii)
What percentage of the coins are 50-pence coins?
(iii)(a)
One coin is picked at random. What is the probability that it is a 50-pence coin?
(iii)(b)
What is the probability that it is not a 50-pence coin?
(iii)(c)
What is the probability that the coin is worth less than £1?

Question 9

[7 marks]

Here are the ingredients needed to make a batch of 24 cookies: 240g butter, 300g flour, 180g sugar, 120g chocolate chips, 2 tsp vanilla.

(i)
Write out the ingredients needed to make 12 cookies.
(ii)
Kelly needs to make 60 cookies for a party. How much flour does she need?
(iii)
To make healthier cookies, you can use 23 of the recommended amount of sugar. How much sugar would you use to make 24 of these healthier cookies?

Question 10

[6 marks]

Alan climbs a mountain one day. His height above sea level at different times is: 9am 100m, 9:30am 200m, 10am 250m, 11am 420m, 12noon 650m, 1pm 800m (the top), 2pm 650m, 2:30pm 650m (a stop), 3pm 420m, 4pm 250m.

(i)
How many metres above sea level is he at 11am?
(ii)
At what time does he first reach 200 metres above sea level?
(iii)
How many metres above sea level is the top of the mountain?
(iv)(a)
Between which times does he stop on the way down?
(iv)(b)
Give a sensible suggestion for why he might have stopped at this time.

Question 11

[6 marks]

Adam's father gives instructions: 'From the post, walk 30 metres west, then walk 40 metres south.' Using a scale of 1 centimetre to 10 metres,

(i)
How long would the first leg (30m west) be on the map, in centimetres?
(ii)(a)
If Adam walks in a straight line from the post to where he ends up, how long is this route in metres? (Use Pythagoras)
(ii)(b)
How long would this straight route be on the map, in centimetres?

Question 12

[8 marks]

Bert and Chrissy enjoy 'think of a number' problems. Bert asks Chrissy to think of a number, treble it and add 7. She says the result is 40.

(i)
What was the number she thought of?
(ii)
Chrissy wants Bert to guess her favourite number. She asks him to write down 5 numbers. He chooses 5, 9, 3, 21 and 7. Find the mean of Bert's numbers.
(iii)
Chrissy tells him that her favourite number is equal to the mean of the numbers, minus 6. What is Chrissy's favourite number?
(iv)
Circle any of the words below which describe Chrissy's favourite number: prime number, square number, cube number

Question 13

[8 marks]

Farmer Fred needs to build a rectangular sheep pen. To save money, he builds it against his barn, so he only needs fencing on three sides. His first plan is 10m by 3m.

(i)(a)
What length of fence does he need for this pen?
(i)(b)
What is the area of this pen?
(ii)
He decides to buy 18 metres of fence instead. His new plan keeps one side at 4m. Find the length of his new pen.
(iii)
Farmer Fred instead builds a square pen with his 18 metres of fence (again with the barn covering the fourth side). How long should each side be?
(iv)
Given that 1 metre of fence costs £15, find how much it will cost Farmer Fred to buy 18 metres of fence.

Question 14

[9 marks]

Look carefully at this number pattern: Row 1: 1² − 0² → 1 − 0 → 1, and 1 + 0 = 1. Row 2: 2² − 1² → 4 − 1 → 3, and 2 + 1 = 3. Row 3: 3² − 2² → 9 − 4 → 5, and 3 + 2 = 5.

(i)
Complete rows 6 and 7 of this pattern.
(ii)
Complete row 12 of this pattern.
(iii)
Complete: row 25: ___ − 576 → ...; and row ___: ___ − 121² → ...
(iv)
What is the value of 2000² − 1999²?