ABC Education

ABC Education · 11+ Practice

Week 4 · Maths Practice Paper

11 questions · 65 marks · Suggested time: 45 minutes.

Question 1

[8 marks]

Calculate

(a)
234 + 567
(b)
23 × 45
(c)
8765 - 4321
(d)
23456 - 7890
(e)
2002 ÷ 7

Question 2

[6 marks]
(a)
What is the remainder when 345678 is divided by 4?
(b)
Calculate: 6 × 372 + 3 × 372 + 372
(c)
The digits 1,2,3,4,5 and 6 are put into six boxes to make two 3-digit numbers, and the second 3-digit number is taken away from the first to give a total. Each digit from 1 to 6 is used exactly once. What is the LARGEST total that can be made?

Question 3

[3 marks]

Put these fractions in ascending order according to their size. (Ascending means smallest to largest)

56        25        710        34        13
Answer:

Question 4

[7 marks]
A factor of a number is a number that divides (goes into) it. A prime number is a number whose only factors are itself and 1.
(a)
130 has 3 prime factors. List them.
(b)
130 has 8 factors in total. List all the factors of 130.
(c)
Write down the prime factors of 78.
(d)
How many factors does 78 have in total?

Question 5

[8 marks]
(a)
A square has a perimeter of 24cm. What is the square's area?
(b)
A rectangle has a perimeter of 24cm. Its length is 2cm longer than its width. What is the rectangle's area?
(c)
Another rectangle has a perimeter of 24cm. Its length is 3 times longer than its width. What is the rectangle's area?
(d)
Another square has an area of 64 cm2. What is the square's perimeter?

Question 6

[6 marks]
(a)
A car journey starts at 11:38am and finishes at 2:15pm. How many minutes did the journey take?
(b)
A child is 9 years old and their parent is 41 years old. In how many years' time will the parent be exactly 3 times the child's age?
(c)
I am facing North East. I then turn 315 degrees clockwise. What direction am I facing now?

Question 7

[7 marks]

Calculate the fraction of the following shapes that are shaded. Give your answers as fully simplified fractions.

(a)
(b)
(c)
(a)
Fraction shaded:
(b)
Fraction shaded:
(c)
Fraction shaded:

Question 8

[3 marks]

By writing a 1-digit number in the big box and an operation (+, -, × or ÷) in the small box, make the following calculation true:

(▢) (▢) (4 - 154) = 24
Answer:

Question 9

[4 marks]
(a)
I roll 2 fair 6-sided dice and add up the numbers shown on each to get a total score. What is the most likely total score that I can get?
(b)
I now roll 3 fair 6-sided dice and multiply the numbers shown on each dice to get a total score of 90. What numbers did I roll?

Question 10

[6 marks]

128 players enter a tennis tournament.

Each player plays another player in the first round and the winner of each match progresses to the second round. Then each player in the second round plays another player who progressed to the second round and the winner of that match progresses to the third round. And so on, until the final, where one player wins the whole tournament.
(a)
How many matches does the winner of the entire tournament play?
(b)
How many matches in total are played in the entire tournament?
(c)
Using your answer to (b), or otherwise, guess the value of: 1 + 2 + 4 + 8 + ... + 4096

Question 11

[7 marks]

The digit sum of a number is the sum of the digits of that number. For example the digit sum of 2862 is 18.

(a)
List all the 6-digit numbers that have a digit sum of 53.
(b)
How many 3-digit numbers have a digit sum of 24?
(c)
How many 4-digit numbers have a digit sum of 3?
(d)
How many 101-digit numbers have a digit sum of 908?