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13 × 13 = 169.

Properties of Numbers (Difficult)

This 11 Plus Maths quiz explores how numbers can be squared, cubed, or raised to higher powers and how these patterns appear in real-life problem solving.

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Fascinating Fact:

The number 64 is both a square number (8²) and a cube number (4³), a rare double identity in the world of integers.

In 11 Plus Maths, pupils study square, cube, and prime numbers to understand how patterns connect across number sets. Recognising these patterns supports quick reasoning and algebraic thinking.

Key Terms

Square Number: The product of a number multiplied by itself, such as 7 × 7 = 49.
Cube Number: The result of multiplying a number by itself twice, like 2 × 2 × 2 = 8.
Exponent: A small raised number that shows how many times to multiply the base number by itself.

Learn more about 11 Plus subjects in our guide for parents.

Frequently Asked Questions (Click to see answers)

How are square and cube numbers used in everyday life?

Square and cube numbers appear in area and volume calculations. Architects, engineers, and designers use them to measure surfaces, build shapes, and model structures accurately.

What is the relationship between exponents and powers?

Exponents show how many times a base number is multiplied by itself. Powers are the results of these multiplications, helping express very large or small numbers neatly.

Why is it useful to memorise square numbers for exams?

Memorising square numbers helps pupils calculate quickly without a calculator. It improves speed in mental maths, estimation, and factorisation questions in the 11 Plus.

Try These Related Quizzes

1 .

What is the smallest prime number?

-1

A prime number is a positive whole number that is only divisible by 1 and itself but does not include the number 1, e.g. 2, 3, 17, 41

2 .

Which of the following statements is wrong?

Two is an even number and a prime number

Other than the number 2, there are no even prime numbers

If you add two odd numbers, you get another odd number

If you add two even numbers, you get another even number

7 + 5 = 12 which is not odd. If you want to show that a statement is not always true, find one example that shows it is wrong - like we did here

3 .

Which number is the odd man out: 49, 15, 41, 9?

They are all odd, but 41 is also a prime number: a prime number is a positive whole number that is only divisible by 1 and itself but does not include the number 1

4 .

Which number is the odd man out: 64, 32, 144, 100?

144

100

They are all even numbers, but 32 is not a square number. A square number (perfect square) is a number formed by the multiplication of another number with itself, e.g. 144 = 12 × 12; 64 = 8 × 8; 100 = 10 × 10. Note: 1 × 1 = 1

5 .

Which number is the odd man out: 71, 17, 11, 39?

They are all odd numbers, but only 39 is a non prime number: a prime number is a positive whole number that is only divisible by 1 and itself but does not include the number 1

6 .

Which two prime numbers have to be added together to give 38?

11 + 27

19 + 19

23 + 15

29 + 9

This is the only choice that has two prime numbers

7 .

Which of the following statements is wrong?

If a number is divisible by 9, then it is divisible by 3

If you add two prime numbers together, you get another prime number

If you subtract 1 from an even number, you get an odd number

There are four prime numbers between 1 and 10

11 + 7 = 18 which is not a prime number. If you want to show that a statement is not always true, find one example that shows it is wrong - like we did here

8 .

How many prime numbers are there between 1 and 30?

Here they are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

9 .

Which of the following statements is wrong?

13 is an odd number

13 × 13 = 159

13 is a prime number

13 is the sixth smallest prime number

13 × 13 = 169! D'oh! By the way, just because 13 is odd, this doesn't prevent it from being a prime number too

10 .

For those of you with stamina: How many prime numbers are there between 1 and 100 inclusive?

Well done those of you who bothered to do this question. The rest of you - do it later. There are 25 prime numbers between 1 and 100. Here they are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Phew! Does anyone want to find out how many prime numbers there are between 1 and 1,000 inclusive? Just joking! Here's the answer anyway: 168 prime numbers. I wonder if your teacher knows that? By the way, prime numbers are a big thing in higher maths

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)