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.
35 questions · official format, shuffled order
1 In a year that is not a leap year, 1 March is a Tuesday. What day of the week is 1 May?
Show worked solution
31 + 30 = 61 days. 61 = 8 × 7 + 5, so five days on from Tuesday: Sunday.
2 In a hall, two fifths of the students are from Year 5, and one third of the rest are from Year 6. The remaining 24 students are from Year 4. How many students are in the hall?
Show worked solution
Year 6 is ⅓ of ⅗ = ⅕. Year 4 is ⅗ − ⅕ = ⅖, and that is 24. One fifth is 12, so 60 students.
3 The product of two consecutive whole numbers is 342. What is their sum?
Show worked solution
18 × 19 = 342, so the sum is 18 + 19 = 37.
4 This jug holds the water measured so far for a recipe that needs 1.8 L. If 350 mL more is poured in, how much more will still be needed?
Show worked solution
The jug holds 1 300 mL. 1 300 + 350 = 1 650. 1 800 − 1 650 = 150 mL.
5 Written in plain capitals, which of these words looks the same when it is reflected in a horizontal line through its middle (flipped top to bottom)?
Show worked solution
D, I, C and E all have a horizontal line of symmetry, so DICE is unchanged. M, A, T, V fail.
6 How many of the numbers from 1 to 100 are multiples of 4 or multiples of 6, or both?
Show worked solution
25 multiples of 4, 16 multiples of 6, 8 multiples of 12 counted twice. 25 + 16 − 8 = 33.
7 A rectangle 18 cm by 8 cm is cut into two pieces that fit together, with no gaps, to make a square. What is the perimeter of the square?
Show worked solution
18 × 8 = 144 = 12 × 12. Perimeter 4 × 12 = 48 cm.
8 A tap drips 3 mL every 10 seconds. How many litres does it drip in 24 hours?
Show worked solution
18 mL a minute, 1 080 mL an hour, 25 920 mL a day = 25.92 L.
9 Every ▲ has the same value and every ■ has the same value. What is ▲?
Show worked solution
3▲ = 2 × (12 + ▲) = 24 + 2▲, so ▲ = 24 (and ■ = 36: 72 = 72 ✓).
10 A path is tiled in the repeating pattern grey, grey, white, grey, white. What colour is the 83rd tile, and how many grey tiles are there among the first 83?
Show worked solution
16 full blocks (48 greys) and then tiles G, G, W: the 83rd is white, and the greys are 48 + 2 = 50. white, 50.
11 Two spinners, each with four equal sections numbered 1 to 4, are spun and the two numbers are multiplied. How many of the 16 equally likely outcomes give a square number?
Show worked solution
1 once, 4 three times (1 × 4, 2 × 2, 4 × 1), 9 once, 16 once: 6 outcomes.
12 60 students chose one sport each. Which statement is correct?
Show worked solution
3 + 15 = 18, so Netball was chosen by 18 students. Boys 15 beat girls 9 at soccer; 12 of 30 boys is not half; soccer (24) beat cricket (18); 6 of 30 girls is a fifth.
13 A number is tripled, then 14 is subtracted, then the result is halved. The answer is 20. What was the number?
Show worked solution
20 × 2 = 40. 40 + 14 = 54. 54 ÷ 3 = 18.
14 Two straight lines cross. One of the angles is four times the angle next to it. What is the smaller angle?
Show worked solution
5 parts = 180°, so one part is 36° (and the larger angle is 144°).
15 Which of these is not equal to 24 × 15?
Show worked solution
24 × 20 − 24 × 4 = 480 − 96 = 384. The others all make 360 (24 × 20 − 24 × 5 would have worked).
16 A square of side 10 cm has a 3 cm by 2 cm rectangle cut from one corner. What is the perimeter of the shape that is left?
Show worked solution
The notch's 3 and 2 replace the missing 3 and 2 of the square's edges, so the perimeter is unchanged: 40 cm. (The area changes; the perimeter does not.)
17 P and Q are marked on a number line from 0 to 1 divided into twentieths.1 P is less than 2/5.
2 Q − P = 9/20.
3 The number halfway between P and Q is 0.6.
Which statements are correct?
2 Q − P = 9/20.
3 The number halfway between P and Q is 0.6.
Which statements are correct?
Show worked solution
0.35 < 0.4 (1 ✓). 0.8 − 0.35 = 0.45 = 9/20 (2 ✓). Halfway is (0.35 + 0.8) ÷ 2 = 0.575, not 0.6 (3 ✗). 1 and 2.
18 In this magic square every row, column and diagonal has the same total. What number goes in the bottom-left cell?
Show worked solution
Total = 3 × 14 = 42. The diagonal 15, 14, ? gives 42 − 15 − 14 = 13. Check the left column: 17 + 12 + 13 = 42 ✓.
19 A bag holds 3 red and 5 blue counters. One red counter is taken out and not put back.1 The chance of red is now 2/7.
2 The chance of blue is now 5/7.
3 Blue is now less likely than it was before.
Which statements are correct?
2 The chance of blue is now 5/7.
3 Blue is now less likely than it was before.
Which statements are correct?
Show worked solution
2/7 (1 ✓) and 5/7 (2 ✓). 5/7 is more than 5/8, so blue is more likely now, not less (3 ✗). 1 and 2.
20 A full crate of 24 bottles weighs 15.6 kg. Each bottle weighs 0.55 kg. What does the empty crate weigh?
Show worked solution
24 × 0.55 = 12 + 1.2 = 13.2 kg of bottles. 15.6 − 13.2 = 2.4 kg.
21 A crowd rounded to the nearest thousand is 36 000, and rounded to the nearest hundred is 35 700. Which of these could be the exact crowd?
Show worked solution
Only 35 680 lies in both ranges. 35 750 rounds to 35 800; the others are above 36 000 and round to 36 300, 36 500 and 36 700.
22 The table shows how far a car had travelled at the end of each hour of a journey.1 The car was stopped for one whole hour.
2 The car went fastest in the third hour.
3 The car travelled 40 km in the last hour.
Which statements are correct?
2 The car went fastest in the third hour.
3 The car travelled 40 km in the last hour.
Which statements are correct?
Show worked solution
Hour 2 added nothing (1 ✓). Hour 3 added 90 km, the most (2 ✓). Hour 4 added 30 km, not 40 (3 ✗). 1 and 2.
23 A ribbon is 6 m long. Pieces of 1⅔ m, 2¼ m and ⅚ m are cut from it. How much ribbon is left?
Show worked solution
20 + 27 + 10 = 57 twelfths = 4¾ m cut off. 6 − 4¾ = 1¼ m.
24 Three parcels weigh 19.5 kg altogether. Parcel A is 1.5 kg heavier than parcel B, and parcel C is twice as heavy as B. How heavy is parcel C?
Show worked solution
4B + 1.5 = 19.5, so 4B = 18 and B = 4.5 kg. C = 2 × 4.5 = 9 kg.
25 A pyramid has 12 edges. How many faces does it have?
Show worked solution
2n = 12, so the base has 6 sides. Faces: 6 triangles + 1 base = 7.
26 In the number 4.025, the value of the 4 is how many times the value of the 5?
Show worked solution
4 ÷ 0.005 = 800 (0.005 × 800 = 4).
27 Auckland is 2 hours ahead of Sydney. A video call must take place between 9 am and 5 pm in both cities. What is the latest Sydney time at which the call can start?
Show worked solution
Auckland 5 pm is Sydney 3 pm. Any later and it is past 5 pm in Auckland.
28 A 10 by 10 square has a 4 by 4 square hole in its centre. Then a border one unit wide is trimmed off the outside. What area is left, in square units?
Show worked solution
8 × 8 = 64, minus the 4 × 4 hole: 64 − 16 = 48.
29 Four identical jars of honey sit on this scale, which is marked every 100 g. What is the mass of one jar?
Show worked solution
The scale reads 2 600 g. 2 600 ÷ 4 = 650 g.
30 A shape is turned 90° clockwise five times in a row. Which single turn would have put it in the same position?
Show worked solution
450° − 360° = 90° clockwise, so 90° clockwise.
31 This net folds into a cube. Which face ends up opposite face C?
Show worked solution
Down the column N, C, S, X: N is opposite S, and C is opposite X. E and W are the remaining pair.
32 A rectangle's length is 3 cm more than its width, and its perimeter is 38 cm. What is its area?
Show worked solution
2w + 3 = 19, so w = 8 and the length is 11. Area 8 × 11 = 88 cm².
33 In this sequence each term is double the previous term, minus 3. Which term is the first to be greater than 300?
Show worked solution
5, 7, 11, 19, 35, 67, 131, 259, 515. The 8th term is 259, still under 300; the 9th is 515.
34 What is the value of ♣?
Show worked solution
♦ = 8. 8 + ♣ = 3♣ − 2, so 10 = 2♣ and ♣ = 5. Check: 13 = 15 − 2 ✓.
35 How many two-digit numbers have digits that add to 9?
Show worked solution
18, 27, 36, 45, 54, 63, 72, 81, 90: 9 numbers. (09 is not a two-digit number.)