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.
15 questions · official format, shuffled order
1 Square tables are joined in a row. One table seats 4 people, two tables seat 6, three tables seat 8. How many people can sit at a row of 30 tables?
Show worked solution
People = 2 × tables + 2 (one seat each side of every table, plus the two ends). 2 × 30 + 2 = 62.
2 In a sequence, each term is made from the one before it by the rule "multiply by 3, then subtract 5". The 4th term is 43. What is the 2nd term?
Show worked solution
3rd term: (43 + 5) ÷ 3 = 16. 2nd term: (16 + 5) ÷ 3 = 7.
3 What is the next term in this sequence?
Show worked solution
Each term is double the one before, plus 1: 2 × 47 + 1 = 95.
4 This sequence goes down by the same amount each time. Which term is the first one that is less than 2?
Show worked solution
It must drop more than 2.5, and 2.5 ÷ 0.3 is a bit over 8, so 9 steps are needed. 9 steps after the 1st term is the 10th term: 4.5 − 2.7 = 1.8. (The 9th is 2.1.)
5 The table shows the first four terms of a pattern. What is the 40th term?
Show worked solution
3 × 1 + 2 = 5, so the rule is 3 × position + 2. For the 40th: 3 × 40 + 2 = 122.
6 A number goes into this machine and 45 comes out. What was the number?
Show worked solution
45 ÷ 5 = 9. 9 × 4 = 36. 36 − 8 = 28.
7 Look at this sequence.1 The 7th term is 49.
2 The differences between terms are 3, 5, 7, 9 … — the odd numbers.
3 50 is a term in this sequence.
Which statements are correct?
2 The differences between terms are 3, 5, 7, 9 … — the odd numbers.
3 50 is a term in this sequence.
Which statements are correct?
Show worked solution
The terms are 1², 2², 3² …, so the 7th is 7² = 49 (1 ✓). 4 − 1 = 3, 9 − 4 = 5, 16 − 9 = 7 (2 ✓). 7² = 49 and 8² = 64, so 50 is skipped (3 ✗). 1 and 2.
8 A sequence goes 0.4, 0.8, 1.2, 1.6, … Which term is equal to 6?
Show worked solution
The nth term is 0.4 × n. 6 ÷ 0.4 = 15, so the 15th term is 6.
9 Hexagonal tables are joined in a row. One table seats 6, two seat 10, three seat 14. How many people can sit at a row of 12 tables?
Show worked solution
4 × 1 + 2 = 6, so people = 4 × tables + 2. For 12 tables: 4 × 12 + 2 = 50.
10 Each term of a sequence is made from the one before by "subtract 3, then double". The 5th term is 62. What is the 3rd term?
Show worked solution
4th term: 62 ÷ 2 + 3 = 34. 3rd term: 34 ÷ 2 + 3 = 20.
11 Dots are arranged in triangles: figure 1 has 1 dot, figure 2 has 3, figure 3 has 6, figure 4 has 10. How many dots are in figure 12?
Show worked solution
1 + 2 + … + 12 = (12 × 13) ÷ 2 = 78. (Figure 11 has 66; adding 12 gives 78.)
12 This machine uses the same rule every time. What input gives the output 40?
Show worked solution
The rule is 3 × input + 1 (3 × 2 + 1 = 7 ✓). 3 × ? + 1 = 40, so ? = 39 ÷ 3 = 13.
13 A plant is 12 cm tall and grows 3.5 cm every week. After how many weeks is it first taller than 50 cm?
Show worked solution
38 ÷ 3.5 is a little under 11, so 10 weeks is not enough (12 + 35 = 47) and 11 weeks is (12 + 38.5 = 50.5).
14 What is the sum of the first ten odd numbers, 1 + 3 + 5 + … + 19?
Show worked solution
Five pairs of 20: 100. (The sum of the first n odd numbers is always n².)
15 Look at this sequence.1 The 100th term is 502.
2 97 is a term in the sequence.
3 Every term is an odd number.
Which statements are correct?
2 97 is a term in the sequence.
3 Every term is an odd number.
Which statements are correct?
Show worked solution
5 × 100 + 2 = 502 (1 ✓). 97 − 2 = 95 = 5 × 19, so 97 is the 19th term (2 ✓). 12 and 22 are even (3 ✗). 1 and 2.