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 Nothing is deducted for a wrong answer on this test. What does a blank answer score?
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Zero — which is why a guess is always at least as good as leaving it empty.
2 A test gives 45 minutes for 35 questions. Write the total number of seconds available, and the number of seconds left after 20 questions at 75 seconds each.
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45 × 60 = 2700 seconds. Twenty questions at 75 s is 1500 s, leaving 2700 − 1500 = 1200 seconds for the last 15.
3 A number is tripled and then 4 is subtracted, giving 20. What is the number?
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3 × 8 = 24, and 24 − 4 = 20, so the number is 8.
Level 2 · Core
4 Which of these is 23 × 17? Use the last digit and an estimate rather than multiplying it out.
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The last digit must be 1, which rules out 380 and 400. Of 371 and 391, the estimate 20 × 20 = 400 points to the larger, and 23 × 17 = 391.
5 A test has 35 questions and you have answered 28 with two minutes left. Write how many are unanswered, and how many marks those would score if you left them all blank.
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35 − 28 = 7 unanswered, scoring 0 between them. Guessing all seven would average about 1.75 marks.
6 You rule out 2 of the 4 options on a question. Out of 4 such questions, how many would a guess get right on average?
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Half of 4 is 2.
Level 3 · Challenge
7 A job needs at least 6 litres of paint. Tins hold 1.5 litres. You have 75 seconds and no calculator.1 3 tins are enough.
2 4 tins are exactly enough.
3 The answer is the smallest number of tins that reaches 6 litres.
Which statements are correct?
2 4 tins are exactly enough.
3 The answer is the smallest number of tins that reaches 6 litres.
Which statements are correct?
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3 tins hold 4.5 L, which is not enough (1 ✗). 4 tins hold exactly 6 L (2 ✓). "Smallest that is still enough" is the right reading of the question (3 ✓). 2 and 3.
8 A test is 45 minutes for 35 questions, and you spend 4 minutes on one hard question. Write how many seconds that question took, and roughly how many average questions that time would have covered.
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4 × 60 = 240 seconds. At 75 seconds each that is 240 ÷ 75 = 3.2, so about 3 other questions.
9 On a 35-question paper you answer 27 and guess the remaining 8 blindly, with 4 options each. On average, how many of those 8 guesses would be correct?
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8 ÷ 4 = 2 — which is why guessing beats leaving blanks.