Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 How many factors does 7 have?
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Only 1 and 7: 2 factors. That is what makes 7 prime.
2 Give these square numbers.
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5 × 5 = 25; 9 × 9 = 81.
3 What is the 5th triangular number?
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1 + 2 + 3 + 4 + 5 = 15.
Level 2 · Core
4 Which of these is composite?
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6 + 3 = 9, so 3 divides 63: 63 = 7 × 9 = 3 × 21. 63 is composite; the other four are prime.
5 There are two prime numbers between 20 and 30. What are they, smaller first?
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21 = 3 × 7, 25 = 5 × 5, 27 = 3 × 9 go; the evens go. 23 and 29 remain.
6 What is the smallest prime number greater than 90?
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91 = 7 × 13, 93 = 3 × 31, 95 = 5 × 19, and 92, 94, 96 are even. 97 is prime.
Level 3 · Challenge
7 Three statements are made about the numbers from 1 to 20.1 There are 8 prime numbers.
2 There are 4 square numbers.
3 There are 5 triangular numbers.
Which statements are correct?
2 There are 4 square numbers.
3 There are 5 triangular numbers.
Which statements are correct?
Show worked solution
Primes: 2, 3, 5, 7, 11, 13, 17, 19 — eight (1 ✓). Squares: 1, 4, 9, 16 — four (2 ✓). Triangular: 1, 3, 6, 10, 15 — five (3 ✓). 1, 2 and 3.
8 Give the sum of the first five prime numbers, and the product of the first three.
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2 + 3 + 5 + 7 + 11 = 28. 2 × 3 × 5 = 30.
9 What is the 10th triangular number?
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45 + 10 = 55. (10 × 11 ÷ 2 = 55.)