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 film starts at 1915 and runs for 2 hours 48 minutes. Buses home leave every 25 minutes, starting at 2200. How many minutes after the film ends does the next bus leave?
Show worked solution
1915 + 2 h 48 min = 2203. The 2200 bus has gone; the next is 2225, which is 22 minutes later.
2 A tank is seven eighths full. One third of the water in it is used, and then 10 litres are added, which fills the tank exactly. How many litres does the tank hold?
Show worked solution
⅔ of ⅞ = 14/24 = 7/12 remains, so 5/12 of the tank is empty, and that is 10 L. One twelfth is 2 L, so the tank holds 24 L.
3 What is the difference between the largest three-digit number whose digits add to 20 and the smallest three-digit number whose digits add to 20?
Show worked solution
Largest: 9 + 9 + 2 → 992. Smallest: the first digit cannot be 1 (1 + 9 + 9 is only 19), so 2 + 9 + 9 → 299. 992 − 299 = 693.
4 A bowl of sugar sits on this scale. The empty bowl weighs 650 g. The recipe needs 1.8 kg of sugar. How many grams of sugar must be taken out?
Show worked solution
The scale reads 2 750 g. 2 750 − 650 = 2 100 g of sugar, which is 2 100 − 1 800 = 300 g too much.
5 Written plainly, the digits 0, 1 and 8 look the same in a mirror. How many three-digit numbers can be made from these digits so that the number reads the same in a mirror held beside it? (A number cannot start with 0.)
Show worked solution
First digit 1 or 8 (two choices), middle 0, 1 or 8 (three choices), last digit equal to the first: 2 × 3 = 6 numbers — 101, 111, 181, 808, 818, 888.
6 Pat's number is a multiple of 9 between 50 and 110. Quinn's number is an even multiple of 7 less than 60. What is the largest possible difference between Pat's number and Quinn's number?
Show worked solution
Largest multiple of 9 under 110 is 108. Smallest even multiple of 7 is 14. 108 − 14 = 94.
7 Rectangle P is 24 cm by 5 cm. Square Q has an area 1 cm² greater than P. What is the perimeter of Q?
Show worked solution
24 × 5 = 120, so Q has area 121 = 11 × 11. Perimeter 4 × 11 = 44 cm.
8 A 1.5 L bottle is three fifths full of juice. Ana pours out 400 mL, then tops the bottle up with water to the 1.2 L mark. How much juice is in the bottle now?
Show worked solution
⅗ of 1 500 = 900 mL of juice. 900 − 400 = 500 mL of juice remain; the top-up is water.
9 What is the value of ○?
Show worked solution
□ = 84 ÷ 7 = 12. △ = 60 ÷ 12 = 5. ○ = 19 − 5 = 14.
10 This row of 13 tiles must be symmetrical about its middle tile. What is the fewest tiles that still need colouring?
Show worked solution
Tiles 10, 11, 12 and 13 must copy tiles 4, 3, 2 and 1: 4 tiles.
11 A bag holds red, blue, green and yellow counters. The chance of red is 0.3. Blue and green are equally likely, and yellow is half as likely as blue. What is the chance of yellow?
Show worked solution
0.7 ÷ 2.5 = 0.28 for blue and for green. Yellow is half of that: 0.14. Check: 0.3 + 0.28 + 0.28 + 0.14 = 1.
12 This graph shows rainfall in millimetres. Which statement is correct?
Show worked solution
130 = 2 × 65, so May had exactly twice as much rain as January. February was 11 cm, March was 4.5 cm, April (85) is less than February (110), and the total is 435 mm.
13 Kai spends one third of his money, then spends $12, then gives away half of what is left. He has $9 left. How much did he start with?
Show worked solution
$9 × 2 = $18. $18 + $12 = $30, which is two thirds of the start. One third is $15, so he started with $45.
14 An isosceles triangle has an apex angle of 38°. One side of the base is extended in a straight line. How big is the angle just outside the triangle?
Show worked solution
Each base angle is 71°. 180 − 71 = 109°.
15 Which number sentence matches "134 shared equally among 15, with 14 left over"?
Show worked solution
15 × 8 = 120, and 134 − 120 = 14, which is less than 15: 134 = 15 × 8 + 14. (15 × 7 + 29 is true but 29 is not a remainder; 15 × 9 − 1 is true but describes no sharing.)
16 What is the perimeter of this T-shape, in units? It is 12 wide and 8 tall; the bar is 3 deep and the stem is 4 wide.
Show worked solution
12 + 3 + 4 + 5 + 4 + 5 + 4 + 3 = 40.
17 A strip is divided into 12 equal parts: 3 are red, 4 are blue, 2 are green and the rest are white.1 Red and green together make 5/12 of the strip.
2 Blue is one third of the strip.
3 White is less than a quarter of the strip.
Which statements are correct?
2 Blue is one third of the strip.
3 White is less than a quarter of the strip.
Which statements are correct?
Show worked solution
3 + 2 = 5 twelfths (1 ✓). 4/12 = 1/3 (2 ✓). White is 3/12, which is exactly a quarter, not less (3 ✗). 1 and 2.
18 In this magic square every row, column and diagonal has the same total. What number goes in the top-middle cell?
Show worked solution
The diagonal 13 + 12 + (bottom-left) and the middle column (top) + 12 + 16 share one total. With bottom-left 11 the total is 36 (left column 15 + 10 + 11 also works), so the top-middle cell is 36 − 12 − 16 = 8.
19 A spinner has five equal sections: two red, two blue and one green. The first spin lands on green. Which statement about the second spin is correct?
Show worked solution
A spinner has no memory. Two red and two blue sections: Red and blue are equally likely. Green is still 1 in 5.
20 A box holding 6 identical tins weighs 4.1 kg on a scale. With only 2 tins in it, the box weighs 2.5 kg. What does the empty box weigh?
Show worked solution
4.1 − 2.5 = 1.6 kg for 4 tins, so a tin is 0.4 kg. The box is 2.5 − 2 × 0.4 = 1.7 kg.
21 The number 5 449 999 is rounded to the nearest million, and the same number is rounded to the nearest ten thousand. What is the difference between the two answers?
Show worked solution
Nearest million: 5 000 000 (the 4 rounds down). Nearest ten thousand: 5 449 999 → 5 450 000 (the 9 rounds up). Difference 450 000.
22 Temperatures were recorded through one day.1 The biggest rise was between 9 am and 12 pm.
2 At 6 pm it was 2 °C warmer than at 6 am.
3 The temperature fell by 5 °C between 3 pm and 6 pm.
Which statements are correct?
2 At 6 pm it was 2 °C warmer than at 6 am.
3 The temperature fell by 5 °C between 3 pm and 6 pm.
Which statements are correct?
Show worked solution
Rises of 5 then 6, so 9–12 is biggest (1 ✓). 8 − 6 = 2 (2 ✓). 14 − 8 = 6, not 5 (3 ✗). 1 and 2.
23 Five pizzas are shared. Ana takes 1¾, Ben takes 1⅛ and Cal takes ⅞. How much pizza is left?
Show worked solution
14 + 9 + 7 = 30 eighths taken of 40, leaving 10 eighths: 1¼ pizzas.
24 Three boxes are weighed two at a time: A + B = 41 kg, B + C = 53 kg, A + C = 48 kg. What is the mass of box C?
Show worked solution
41 + 53 + 48 = 142, so A + B + C = 71. C = 71 − (A + B) = 71 − 41 = 30 kg.
25 A solid has two hexagonal faces and six rectangular faces. What is its number of faces plus edges plus vertices?
Show worked solution
8 faces + 18 edges + 12 vertices = 38.
26 In the number 806 040, the value of the 8 is how many times the value of the 4?
Show worked solution
800 000 ÷ 40 = 20 000.
27 A flight leaves Sydney at 2330 on Thursday and takes 14 hours 20 minutes. The destination city is 9 hours behind Sydney. What is the local day and time when it lands?
Show worked solution
Thu 2330 + 14 h 20 min = Fri 1350 Sydney time. Nine hours earlier is Friday 4:50 am.
28 Four squares with sides 9, 7, 5 and 3 units share a corner. The rings are shaded alternately from the outside. What is the total shaded area, in square units?
Show worked solution
81 − 49 = 32 and 25 − 9 = 16. 32 + 16 = 48.
29 This jug is marked every 25 mL. Three times as much of a second liquid is added, and then 200 mL is poured out. How much is in the jug now?
Show worked solution
The jug holds 325 mL. Three times that is 975 mL, giving 1 300 mL in all. 1 300 − 200 = 1 100 mL.
30 A regular hexagon is turned about its centre through four steps of its rotational symmetry, then back one step. Through how many degrees has it turned altogether, measured from the start?
Show worked solution
One step is 60°. Three net steps: 3 × 60 = 180°.
31 Which of these five-square arrangements can be completed into a cube net by adding one square?
Show worked solution
P only: a band of four with one cap, needing a cap on the other side. Q contains a 2 by 2 block, which overlaps when folded. R is five in a row, which also overlaps.
32 A rectangle is w cm by 10 cm. An identical rectangle is joined to it along a 10 cm side, and the perimeter of the new shape is 16 cm more than the perimeter of one rectangle. What is w?
Show worked solution
One rectangle: 2w + 20. The pair is 2w by 10: 4w + 20. The growth is 2w = 16, so w = 8.
33 In this sequence each term is the sum of the three terms before it. What is the missing term?
Show worked solution
2 + ? + 7 = 14, so the missing term is 5. Check: 5 + 7 + 14 = 26 ✓.
34 Each star has the same value and each heart has the same value. What is the value of one star?
Show worked solution
Star 9, heart 8: 27 + 8 = 35 ✓ and 9 + 16 = 25 ✓. One star is 9.
35 How many multiples of 6 up to and including 200 are not multiples of 9?
Show worked solution
200 ÷ 6 = 33 r 2, so 33 multiples of 6. 200 ÷ 18 = 11 r 2, so 11 of them are multiples of 18. 33 − 11 = 22.