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 A clock shows 1945. What is this in 12-hour time, a quarter of an hour later?
Show worked solution
1945 + 15 min = 2000, and 20 − 12 = 8, so 8:00 pm.
2 Three fifths of a cake is eaten, and then half of what is left is eaten. What fraction of the whole cake remains?
Show worked solution
10 − 6 = 4 left, less half of 4 = 2, leaving 2 tenths, which is 1/5.
3 What is the smallest 4-digit number multiplied by the largest 2-digit number?
Show worked solution
1 000 × 99 = 100 000 − 1 000 = 99 000.
4 A scale reads 1 600 g with a jar on it. The empty jar weighs 350 g, and a recipe needs 1 500 g of flour. How many grams short is the flour?
Show worked solution
1 600 − 350 = 1 250 g of flour, and 1 500 − 1 250 = 250 g short.
5 Written plainly, which is the largest two-digit number with a horizontal line of symmetry?
Show worked solution
The allowed digits are 0, 1, 3 and 8, and the largest two-digit number from them is 88.
6 What is the difference between the largest multiple of 6 under 50 and the smallest even multiple of 9?
Show worked solution
48 − 18 = 30.
7 Rectangle P is 15 cm by 4 cm. Rectangle Q has the same area and is 5 cm wide. How long is Q?
Show worked solution
15 × 4 = 60, and 60 ÷ 5 = 12 cm.
8 A bottle holds 800 mL. Ana drinks 250 mL, then tops the bottle back up to the 600 mL mark. How many millilitres of the original drink are now in the bottle?
Show worked solution
800 − 250 = 550 mL of the original drink remain; the top-up is water.
9 In these two number sentences, 8 × □ = 96 and △ + □ = 40. What is the value of △?
Show worked solution
96 ÷ 8 = 12, so □ = 12, and △ = 40 − 12 = 28.
10 This row of 9 tiles must be symmetrical about its middle tile. What is the fewest number of tiles that still need colouring?
Show worked solution
Positions 6, 7, 8 and 9 are empty and must copy 4, 3, 2 and 1: 4 tiles.
11 The chances of four colours on a spinner add to 1. Red is 0.25 and blue is 0.15. Green and yellow share the rest, and green is twice as likely as yellow. What is the chance of green?
Show worked solution
1 − 0.4 = 0.6, split into three parts of 0.2. Green takes two: 0.4.
12 This graph shows rainfall in millimetres. Which statement is correct?
Show worked solution
120 mm is June had 12 cm of rain. June is exactly twice May, July had the least, and April had 90 mm not 9.
13 An amount of money is halved, then halved again, then halved once more, leaving $1.50. How much was there at the start?
Show worked solution
$1.50 → $3 → $6 → $12.
14 An isosceles triangle has an apex angle of 50°. One base angle is extended along a straight line. How big is the angle just outside the triangle?
Show worked solution
Base angles are 65° each, and 180 − 65 = 115°.
15 Which number sentence matches "95 shared between 12, with 11 left over"?
Show worked solution
95 ÷ 12 = 7 remainder 11, so 95 = 12 × 7 + 11.
16 What is the perimeter of this shape, in units?
Show worked solution
It fits in a 7 by 5 rectangle, so 2 × (7 + 5) = 24 units.
17 A strip is divided into 10 equal parts; 2 are red and 3 are blue.Which statement is correct?
Show worked solution
5 of 10 is a half, so Red and blue together are half the strip. Red is one fifth and blue is three tenths.
18 In this magic square every row, column and diagonal has the same total. What number goes in the shaded cell?
Show worked solution
The total is 8 + 1 + 6 = 15, and the middle column is 1 + 5 + ? = 15, so 9.
19 A spinner with 4 equal sections has landed on red on its first spin. Which statement about the second spin is correct?
Show worked solution
A spinner has no memory: Red is still 1 out of 4.
20 An empty crate reads 3 kg on a scale. With four identical bricks in it the scale reads 23 kg. How heavy is one brick?
Show worked solution
23 − 3 = 20 kg for four bricks, so one is 5 kg.
21 The number 3 682 471 is rounded to the nearest million, and the same number is rounded to the nearest hundred thousand. What is the difference between the two answers?
Show worked solution
4 000 000 − 3 700 000 = 300 000.
22 This graph shows rainfall in millimetres.1 June had the most rain.
2 April and May together had more than June.
3 March had more rain than May.
Which statements are correct?
2 April and May together had more than June.
3 March had more rain than May.
Which statements are correct?
Show worked solution
120 beats every month (1 ✓). 90 + 60 = 150 > 120 (2 ✓). March 40 is less than May 60 (3 ✗). 1 and 2.
23 Four pizzas are shared. Ana takes 1½, Ben takes ¾ and Cal takes ¾. How much is left?
Show worked solution
6 + 3 + 3 = 12 quarters used of 16, leaving 4 quarters: 1 pizza.
24 Three boxes are weighed two at a time: A + B = 32 kg, B + C = 40 kg, A + C = 36 kg. What is the total mass of the three boxes?
Show worked solution
32 + 40 + 36 = 108, and halving gives 54 kg.
25 For a pentagonal pyramid, what is the number of faces plus the number of edges plus the number of vertices?
Show worked solution
6 faces + 10 edges + 6 vertices = 22.
26 In the number 50 080, the value of the 5 is how many times the value of the 8?
Show worked solution
50 000 ÷ 80 = 625.
27 A flight leaves a city at 2200 on Friday and takes 18 hours. Sydney is 17 hours ahead of that city. What is the day and time in Sydney when it lands?
Show worked solution
Fri 2200 + 18 h = Sat 1600. Then + 17 h: 8 h to Sunday 0000 and 9 more, so Sunday 0900.
28 What is the total area of the two shaded rings between a 6 by 6 square, a 5 by 5 square and a 4 by 4 square?
Show worked solution
36 − 25 = 11 and 25 − 16 = 9, so 11 + 9 = 20 squares.
29 This jug is marked every 50 mL. Five times as much of a second liquid is added. What is the total, in millilitres?
Show worked solution
The jug holds 200 mL; five times that is 1 000 mL; the total is 1 200 mL.
30 A square is turned about its centre by three steps of its rotational symmetry. How many degrees has it turned altogether?
Show worked solution
One step is 90°, so three steps is 270°.
31 Which of these five-square arrangements can be completed into a cube net by adding one square?
Show worked solution
Only P has a band of four with one cap, so only it completes: P only.
32 A rectangle is w cm by 8 cm. An identical rectangle is joined to it along an 8 cm side, and the perimeter of the new shape is 14 cm more than the perimeter of one rectangle. What is w?
Show worked solution
One rectangle is 2w + 16; joined it is 4w + 16. The growth is 2w = 14, so w = 7.
33 In this sequence each term is the sum of the three terms before it. What is the missing term?
Show worked solution
3 + 4 + ? = 12, so the missing term is 5. Check: 4 + 5 + 12 = 21 ✓.
34 Each star has the same value and each heart has the same value.What is the value of one star?
Show worked solution
26 − 17 = 9, so a star is 9 (and a heart is 8).
35 How many multiples of 4 up to and including 100 are not multiples of 6?
Show worked solution
100 ÷ 4 = 25 multiples of 4. Multiples of 12 up to 100: 12, 24, 36, 48, 60, 72, 84, 96 — eight of them. 25 − 8 = 17.