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 train leaves at 2250 and the journey takes 1 hour 40 minutes. At what time does it arrive?
Show worked solution
2250 + 1 h 40 min = 0030, the next day.
2 A tank is three quarters full. A third of the water in it is used. What fraction of the whole tank is left?
Show worked solution
9 twelfths full, less a third of 9 = 3, leaves 6 twelfths, which is 1/2.
3 What is the largest 3-digit number multiplied by the smallest 2-digit number?
Show worked solution
999 × 10 = 9 990.
4 A dial is labelled every 2 kg with a mark every 0.5 kg. The pointer is on the mark just past 6 kg. What does it read?
Show worked solution
Each mark is 2 ÷ 4 = 0.5 kg, so one mark past 6 is 6.5 kg.
5 Written plainly, which of these numbers has a vertical line of symmetry?
Show worked solution
Only 0, 1 and 8 mirror vertically, and 88 also reads the same backwards.
6 How many numbers from 1 to 60 are multiples of 4 but not multiples of 5?
Show worked solution
60 ÷ 4 = 15 multiples of 4; the multiples of 20 are 20, 40 and 60 — three of them. 15 − 3 = 12.
7 A rectangle has an area of 72 cm² and one side of 8 cm. What is its perimeter?
Show worked solution
72 ÷ 8 = 9 cm, so the perimeter is 2 × (9 + 8) = 34 cm.
8 A jug holds 1 200 mL. Ben pours out 450 mL, then pours back 150 mL. How many millilitres are in the jug now?
Show worked solution
1 200 − 450 + 150 = 900 mL.
9 In these two number sentences, 7 × □ = 91 and △ − □ = 20. What is the value of △?
Show worked solution
91 ÷ 7 = 13, so □ = 13, and △ = 20 + 13 = 33.
10 A regular hexagon is turned about its centre. What is the smallest turn that makes it look exactly the same?
Show worked solution
360 ÷ 6 = 60°.
11 A bag holds 4 red, 6 blue and 10 green counters. One is taken without looking. What is the chance it is red?
Show worked solution
4 of 20 is 1 out of 5.
12 This pie graph shows how 800 people travel to work. How many more travel by car than walk?
Show worked solution
Car is half, 400; walking is a quarter, 200. The difference is 200.
13 A number is multiplied by 4, then 7 is added, and the result is 47. What was the number?
Show worked solution
47 − 7 = 40, and 40 ÷ 4 = 10.
14 Three angles meet at a point. Two of them are 145° and 80°. How big is the third?
Show worked solution
360 − 145 − 80 = 135°.
15 Which number sentence matches "83 shared between 9, with 2 left over"?
Show worked solution
83 ÷ 9 = 9 remainder 2, so 83 = 9 × 9 + 2.
16 What is the perimeter of this shape, in units?
Show worked solution
It fits in an 8 by 6 rectangle: 2 × (8 + 6) = 28 units.
17 A bar is divided into 12 equal parts; 3 are red and 4 are blue.Which statement is correct?
Show worked solution
7 of 12 is more than 6 of 12, so Red and blue together are more than half.
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 4 + 9 + 2 = 15, and the bottom row is 8 + ? + 6 = 15, so the cell holds 1.
19 A bag holds 5 red and 5 blue counters. A red one is taken out and kept. What is the chance the next counter taken is red?
Show worked solution
4 red remain of 9 counters: 4 out of 9.
20 An empty box reads 4 kg on a scale. With five identical tins in it the scale reads 24 kg. How heavy is one tin?
Show worked solution
24 − 4 = 20 kg for five tins, so one is 4 kg.
21 The number 8 461 209 is rounded to the nearest million and to the nearest hundred thousand. What is the difference between the two answers?
Show worked solution
8 500 000 − 8 000 000 = 500 000.
22 This graph shows how many children chose each sport.1 Hockey was the most popular.
2 Twice as many chose soccer as tennis.
3 More chose netball than soccer.
Which statements are correct?
2 Twice as many chose soccer as tennis.
3 More chose netball than soccer.
Which statements are correct?
Show worked solution
48 beats every other sport (1 ✓). Soccer is 36 and tennis 12, which is three times, not twice (2 ✗). Netball 24 is fewer than soccer 36 (3 ✗). 1 only.
23 Five pizzas are shared. Ana takes 1¾, Ben takes 1½ and Cal takes ¾. How much is left?
Show worked solution
7 + 6 + 3 = 16 quarters used of 20, leaving 4 quarters: 1 pizza.
24 Three parcels are weighed two at a time: A + B = 25 kg, B + C = 31 kg, A + C = 28 kg. How heavy is parcel B?
Show worked solution
25 + 31 + 28 = 84, halved is 42 kg altogether. B = 42 − 28 = 14 kg.
25 A solid has 8 faces, 18 edges and 12 vertices. How many sides does its end face have?
Show worked solution
2n = 12, so n = 6 — a hexagonal prism.
26 In the number 70 040, the value of the 7 is how many times the value of the 4?
Show worked solution
70 000 ÷ 40 = 1 750.
27 A flight leaves Sydney at 0900 on Monday and takes 13 hours. Los Angeles is 17 hours behind Sydney. What is the day and time in Los Angeles when it lands?
Show worked solution
Mon 0900 + 13 h = Mon 2200 Sydney. 17 h back: 22 − 17 = Monday 0500.
28 What is the area of the shaded ring between a 7 by 7 square and the 6 by 6 square inside it?
Show worked solution
49 − 36 = 13 squares.
29 A container holds 250 mL of juice. Four times as much water is added. How many millilitres are there altogether?
Show worked solution
4 × 250 = 1 000 mL of water, plus 250 mL of juice: 1 250 mL.
30 A regular pentagon is turned two steps of its rotational symmetry. How many degrees has it turned?
Show worked solution
One step is 72°, so two steps is 144°.
31 Two views of the same cube are shown. Every face carries a different number. Which number is opposite the 1?
Show worked solution
The 1 touches 2, 3, 4 and 5, so 6 is opposite it.
32 A rectangle is w cm by 5 cm. An identical rectangle is joined along a 5 cm side, and the perimeter grows by 18 cm. What is w?
Show worked solution
2w = 18, so w = 9 cm.
33 In this sequence each term is the sum of the three terms before it. What comes next?
Show worked solution
10 + 18 + 33 = 61.
34 Each square has the same value and each circle has the same value.What is the value of one circle?
Show worked solution
31 − 20 = 11, so a square is 11, and a circle is 20 − 11 = 9.
35 How many numbers from 1 to 100 are multiples of 6 but not multiples of 9?
Show worked solution
100 ÷ 6 = 16 multiples of 6. Multiples of 18 up to 100: 18, 36, 54, 72, 90 — five. 16 − 5 = 11.