FUNCTIONAL SKILLSMaths
Functional Skills Level 2
Types of Numbers
Identify and work with odd, even, prime, square and cube numbers — comprehensive practice worksheet
📋 Stuck on a question? Each question maps directly to the Types of Numbers lesson on your course.
Specification Coverage

Odd & Even

Even: ends in 0, 2, 4, 6 or 8
Odd: ends in 1, 3, 5, 7 or 9

Prime Numbers

Exactly 2 factors: 1 and itself.
First primes: 2, 3, 5, 7, 11, 13, 17, 19…

Square Numbers

n × n. E.g. 3² = 9.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

Cube Numbers

n × n × n. E.g. 3³ = 27.
1, 8, 27, 64, 125, 216…

Section A — Odd and Even Numbers

Q1.
Circle the even numbers in the list below.
[1 Mark]Non-Calc
1742831002514,8369,99950,020
Q2.
State whether each result is odd or even, without calculating the exact answer.
[1 Mark]Non-Calc
(a) Odd + Odd =  
(b) Even × Odd =  
(c) 7 + 13 + 6 =  
(d) 3 × 5 × 4 =  
Q3.
Write down the largest even number less than 1,000 and the smallest odd number greater than 9,990.
[1 Mark]Non-Calc
Largest even number less than 1,000:  
Smallest odd number greater than 9,990:  
Q4.
A number is described as "a three-digit odd number where all three digits are the same." Write down all possible such numbers.
[1 Mark]Non-Calc
Show your working here
Answer:
Q5.
The sum of two whole numbers is 47. One number is even. What type of number must the other be? Explain your reasoning.
[1 Mark]Non-Calc
Explanation:
The other number must be:

Section B — Prime Numbers

Q6.
List all the prime numbers between 10 and 30.
[1 Mark]Non-Calc
Show your working here — list the factors of each number to test
Answer:
Q7.
For each number, list all factors then state whether it is prime or not prime.
[2 Marks]Non-Calc
(a) 29 — Factors:     Prime / Not prime (circle one)
(b) 33 — Factors:     Prime / Not prime (circle one)
(c) 51 — Factors:     Prime / Not prime (circle one)
(d) 61 — Factors:     Prime / Not prime (circle one)
Q8.
Explain why 1 is not a prime number.
[1 Mark]Non-Calc
Explanation:
Q9.
Write 48 as a product of its prime factors. Show your factor tree or repeated division.
[2 Marks]Non-Calc
Show your factor tree here
48 =
Q10.
Two prime numbers add together to make 20. Find all possible pairs.
[2 Marks]Non-Calc
Show your working here
Pairs:

Section C — Square Numbers

Q11.
Calculate each square number.
[1 Mark]Non-Calc
(a) 6² =  
(b) 9² =  
(c) 12² =  
(d) 15² =  
Q12.
Identify which of these numbers are square numbers. Circle them.
[1 Mark]Non-Calc
1620253640495081100120
Q13.
Find the square root of each number.
[1 Mark]Non-Calc
(a) √64 =  
(b) √121 =  
(c) √144 =  
Q14.
A square floor has an area of 196 m². What is the length of one side?
[1 Mark]Non-Calc
Show your working here
Answer:
Q15.
True or false? "All square numbers are even." Justify your answer with an example.
[1 Mark]Non-Calc
Explanation and example:
True / False:

Section D — Cube Numbers

Q16.
Calculate each cube number.
[1 Mark]Non-Calc
(a) 2³ =  
(b) 4³ =  
(c) 5³ =  
(d) 10³ =  
Q17.
Identify which of these numbers are cube numbers. Circle them.
[1 Mark]Non-Calc
16812273664100125216
Q18.
Find the cube root of each number.
[1 Mark]Non-Calc
(a) ∛27 =  
(b) ∛125 =  
(c) ∛1,000 =  
Q19.
A storage cube has a volume of 512 cm³. What is the length of one edge?
[1 Mark]Non-Calc
Show your working here
Answer:
Q20.
Without calculating, explain whether 1,000 is a cube number. What is its cube root?
[1 Mark]Non-Calc
Explanation:
∛1,000 =

Section E — Challenge Mixed Types

Q21.
Challenge Name a number that is both square and even. Then name a number that is both square and odd.
[2 Marks]Non-Calc
Square and even:  
Square and odd:  
Q22.
Challenge What is the only even prime number? Explain why no other even number can be prime.
[2 Marks]Non-Calc
Explanation:
The only even prime is:
Q23.
Challenge Which numbers from 1 to 30 are both square and cube? List them and explain what makes them special.
[2 Marks]Non-Calc
Show your working here — list square numbers and cube numbers then find the overlap
Answer:
Q24.
Challenge Find a prime number that is one less than a square number, for squares between 1 and 50. List all such pairs (square, prime).
[2 Marks]Non-Calc
Show your working here
Pairs:
Q25.
Challenge Write down the first four cube numbers. For each one, state whether it is also: (i) a square number, (ii) a prime number, (iii) an even number.
[3 Marks]Non-Calc
Complete the table below
Cube number Also a square? Also prime? Even or odd?
1³ = 1   
2³ = 8   
3³ = 27   
4³ = 64   

Student Progress Log

Section Marks Available Your Score Confidence Level
Section A — Odd and Even (Q1–5) 5 marks ___ / 5 ◯ Low    ◯ Medium    ◯ High
Section B — Prime Numbers (Q6–10) 8 marks ___ / 8 ◯ Low    ◯ Medium    ◯ High
Section C — Square Numbers (Q11–15) 5 marks ___ / 5 ◯ Low    ◯ Medium    ◯ High
Section D — Cube Numbers (Q16–20) 5 marks ___ / 5 ◯ Low    ◯ Medium    ◯ High
Section E — Mixed Challenge (Q21–25) 11 marks ___ / 11 ◯ Low    ◯ Medium    ◯ High
TOTAL 34 marks ___ / 34

🔒 Full Mark Scheme & Model Answers

Detailed step-by-step mark schemes, model answers and examiner tips for every question are available through your course.

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