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 Of the letters C E O P R S T, which contain only curved lines?
Show worked solution
C, O and S only. P has a straight stem, so it does not belong.
2 Using C E O P R S T, write how many letters contain both kinds of line, and how many contain only straight lines.
Show worked solution
Both: P and R, so 2. Only straight: E and T, so 2. The remaining three (C, O, S) are curved only.
3 How many of the letters C E O P R S T satisfy "either only curved or only straight, but not both"?
Show worked solution
C, O, S, E and T — 5 letters. P and R are excluded.
Level 2 · Core
4 A job needs at least 7 metres of cable. Rolls are sold in lengths of 3 m, 5 m, 8 m and 12 m. Which is the shortest roll that would do the job?
Show worked solution
3 m and 5 m are too short. Of 8 m and 12 m, the shorter is 8 m. (7 m is the requirement, not a roll on sale.)
5 Six cards lie face down: four have odd numbers and two have even numbers. Four cards are turned over and their sum is odd. Write how many of the four turned over must be odd, and how many cards are left face down.
Show worked solution
Four numbers sum to odd only when an odd number of them are odd, and with only two evens available that means 3 odd and 1 even. Six take four leaves 2 face down.
6 A tank needs at least 2.5 litres of fluid. Bottles hold 0.4 litres each. What is the smallest number of whole bottles that will fill it?
Show worked solution
2.5 ÷ 0.4 = 6.25, and six bottles give only 2.4 L, so 7 bottles are needed.
Level 3 · Challenge
7 Five cards lie face down: two even, three odd. Three are turned over and their sum is even.1 Exactly two of the three turned over are odd.
2 Both remaining cards are odd.
3 One remaining card is odd and one is even.
Which statements are correct?
2 Both remaining cards are odd.
3 One remaining card is odd and one is even.
Which statements are correct?
Show worked solution
Three numbers sum to even only when exactly two are odd (1 ✓). That uses 2 of the 3 odds and 1 of the 2 evens, leaving 1 odd and 1 even (3 ✓), so they are not both odd (2 ✗). 1 and 3.
8 Of the letters C E O P R S T, write how many satisfy "contains a curved line" and how many satisfy "contains a curved line but not a straight one".
Show worked solution
Contains a curve: C, O, S, P and R — 5. Excluding the ones that also have a straight line removes P and R, leaving C, O and S — 3.
9 A lift can carry at most 450 kg. Six people weigh 95, 90, 85, 80, 75 and 70 kg. What is the largest number of them that can ride together?
Show worked solution
All six weigh 495 kg, which is over the limit. Leaving out the heaviest gives 90 + 85 + 80 + 75 + 70 = 400 kg, so 5 can ride.