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 Which number has a 6 in the hundreds place and a 3 in the tens place?
Show worked solution
8632: 8 thousands, 6 hundreds, 3 tens, 2 ones.
2 The clock shows the time now.What time was it 2 hours 45 minutes ago?
Show worked solution
Now is 1:10. Back 2 hours → 11:10; back 45 minutes → 10:25.
3 Which one of these numbers is closest to 5000?
Show worked solution
Distances from 5000: 410, 320, 290, 250, 380. The smallest is 250, so 4750.
4 Four marks on this number line are labelled with letters.Which letter marks 1⅗?
Show worked solution
Five gaps per whole, so the marks are fifths. 1⅗ is three marks after 1: R (Q is 1⅕, S is 1⅘).
5 Tiles are laid in a repeating pattern: square, square, circle, triangle, circle, square, square, circle, triangle, circle, …What shape is the 43rd tile?
Show worked solution
The pattern repeats every 5 tiles. 43 = 8 × 5 + 3, so the 43rd tile is the 3rd of a group: a circle.
6 Ravi buys 4 pens at $1.85 each and a notebook for $3.40. He pays with a $20 note. How much change does he get?
Show worked solution
4 × $1.85 = $7.40; plus $3.40 = $10.80. $20 − $10.80 = $9.20.
7 A jug holds 150 mL of water. Sam drops in 2 identical stones and they sink; the water rises to 210 mL.Sam then drops in 4 more identical stones. What is the new water level?
Show worked solution
2 stones raised the water 60 mL, so 30 mL each. 4 more: 120 mL. 210 + 120 = 330 mL.
8 A number pattern follows one rule: double the number before, then take away 4. It begins with 9. Which is the fifth term?
Show worked solution
9 → 14 → 24 → 44 → 84.
9 This letter F is made of straight lines.How many right angles can be counted in the letter?
Show worked solution
The top bar meets the stem at a corner: 1 right angle. The middle bar meets the middle of the stem: a right angle above it and one below it. 1 + 2 = 3.
10 Nine tokens numbered 1 to 9 are in a bag, and Lena pulls one out without looking.1 Odd and even are equally likely.
2 A number above 5 is more likely than a number below 5.
3 The 3 and the 8 have the same chance.
Which statement(s) is/are correct?
2 A number above 5 is more likely than a number below 5.
3 The 3 and the 8 have the same chance.
Which statement(s) is/are correct?
Show worked solution
Four even, five odd (1 ✗). Greater than 5: 6, 7, 8, 9 (four); less than 5: 1, 2, 3, 4 (four) — equal, so not more likely (2 ✗). One counter each (3 ✓).
11 Hayden chooses a number, subtracts 6, then multiplies the result by 3. He gets 42. What do you get if you add together the digits of his starting number?
Show worked solution
Undo: 42 ÷ 3 = 14; 14 + 6 = 20. Digits 2 + 0 = 2.
12 The thermometer shows the temperature at noon.By evening the temperature had fallen by 9 °C. What was the evening temperature?
Show worked solution
Each small tick is 2 °C. Noon: 3 ticks above 20 = 26 °C. 26 − 9 = 17 °C.
13 Here is part of a bus timetable from Elm to Oak.
Which trip takes the longest?
| leaves Elm | arrives Oak |
| 7:10 am | 8:55 am |
| 9:30 am | 11:20 am |
| 12:05 pm | 1:50 pm |
| 3:40 pm | 5:35 pm |
Show worked solution
Trip times: 1 h 45 min, 1 h 50 min, 1 h 45 min, 1 h 55 min. The 3:40 pm trip is longest.
14 This object is made from identical cubes. No cube is floating and there are no hidden gaps.How many cubes were used?
Show worked solution
A 2 × 2 base (4), two cubes on the back row (2), and one more on top (1): 7.
15 What fraction of a whole day is 8 hours?
Show worked solution
A day is 24 hours. 8 ÷ 24 = ⅓.
16 The column graph shows umbrellas sold at a shop on six days.On which day were twice as many umbrellas sold as on Tuesday?
Show worked solution
Tuesday: 8. Twice as many is 16, which is Friday.
17 The map shows two gates. A ruler in millimetres is laid between them.How far apart are the gates in real life?
Show worked solution
76 mm = 7.6 cm. 7.6 × 25 m = 190 m (7 × 25 = 175, plus 0.6 × 25 = 15).
18 A packet of 8 biscuits costs $3. How much do 40 biscuits cost?
Show worked solution
40 biscuits is 5 packets. 5 × $3 = $15.
19 This L-shape is made of squares.How will it look after a HALF turn?
Show worked solution
A half turn puts the shape upside down: the foot moves to the top and points the other way. C is the mirror image (not a turn), A and B are quarter turns, D is unchanged.
20 A square has a perimeter of 36 cm. What is its area?
Show worked solution
Each side is 36 ÷ 4 = 9 cm. Area 9 × 9 = 81 cm².
21 On these scales, two apples balance three bananas.Three fruit boxes are packed for delivery.
Box 1: 6 apples and 4 bananas.
Box 2: 4 apples and 7 bananas.
Box 3: 8 apples and 2 bananas.
Which is true about their weights?
Box 1: 6 apples and 4 bananas.
Box 2: 4 apples and 7 bananas.
Box 3: 8 apples and 2 bananas.
Which is true about their weights?
Show worked solution
Swap every 2 apples for 3 bananas. Box 1: 9 + 4 = 13 bananas. Box 2: 6 + 7 = 13. Box 3: 12 + 2 = 14. Boxes 1 and 2 match; Box 3 is heavier.
22 One tap alone fills a tub in 20 minutes. A second tap alone fills the same tub in 30 minutes. If both taps are turned on together, how long does the tub take to fill?
Show worked solution
In 60 minutes the first tap fills 3 tubs and the second fills 2 — 5 tubs together. One tub takes 60 ÷ 5 = 12 minutes.
23 The picture graph shows the goals four teams scored this season.How many goals were scored altogether?
Show worked solution
Each circle is 6 goals. Hawks 15, Owls 6, Bears 18, Foxes 3. Total 42.
24 12 May 2027 is a Wednesday. What day of the week is 3 June 2027?
Show worked solution
May has 31 days. From 12 May to 31 May is 19 days, plus 3 days into June: 22 days = 3 weeks and 1 day. Wednesday + 1 = Thursday.
25 Two squares of the same size are drawn. Square X is ruled into 16 equal small squares; square Y is cut by its diagonals into 4 equal triangles. Parts of each are shaded.How many extra small squares need shading on X to make its shaded area match Y's?
Show worked solution
One triangle = 16 ÷ 4 = 4 small squares. Two shaded triangles = 8 small squares. X has 5 shaded, so 3 more.
26 Which list shows the numbers in order from smallest to largest?
Show worked solution
Write them with two decimal places: 0.09, 0.40, 0.45, 0.50. Only C has them in that order.
27 This spinner has unequal sections: half red, a quarter blue, and an eighth each of green and yellow.1 Landing on red is as likely as not landing on red.
2 Blue is twice as likely as green.
3 Green is more likely than yellow.
Which statement(s) is/are correct?
2 Blue is twice as likely as green.
3 Green is more likely than yellow.
Which statement(s) is/are correct?
Show worked solution
Red is exactly half (1 ✓). A quarter is twice an eighth (2 ✓). Green and yellow are equal (3 ✗).
28 A wall is built one layer at a time, always finishing a layer before starting the next. Each layer uses 7 bricks. There are 45 bricks and all of them are used. Which layer is being built when the last brick is laid?
Show worked solution
45 ÷ 7 = 6 remainder 3. Six layers are complete and the last 3 bricks are on the 7th layer.
29 Each of the five shapes in Set 2 is meant to be a copy of one of the Set 1 shapes — rotated if necessary, but never flipped over.How many shapes in the second set are NOT true copies?
Show worked solution
L turned ✓, mirror L ✗, T turned ✓, T turned ✓, Z (not in Set 1) ✗. Two are not identical.
30 A hall has 28 rows with 16 chairs in each row. 375 people are seated, one per chair. How many chairs are empty?
Show worked solution
28 × 16 = 448 chairs. 448 − 375 = 73 empty.
31 Eight small cubes are glued into one 2 × 2 × 2 cube; turning it around, you can see 24 small-cube faces in total. The large cube is broken into two flat 2 × 2 slabs of 4 cubes.How many small-cube faces are visible now, counting both pieces?
Show worked solution
Each slab has 4 joins, hiding 8 of its 24 faces: 16 visible. Two slabs: 32. (Breaking the cube broke 4 joins, uncovering 8 faces: 24 + 8 = 32.)
32 Squares are made from matchsticks, joined in a row so that neighbours share a side.Pattern 1 uses 4 sticks, pattern 2 uses 7 and pattern 3 uses 10. How many sticks does pattern 12 use?
Show worked solution
Each new square adds 3 sticks: 3 × n + 1. Pattern 12: 3 × 12 + 1 = 37.
33 Cho's savings jar starts the week empty. Her running total is $15; when Monday finishes, $39 when Wednesday finishes and $85 when Friday finishes. Her Tuesday, Wednesday and Friday deposits are all equal. What did she deposit on Thursday?
Show worked solution
Tuesday + Wednesday = 39 − 15 = $24, so $12 each; Friday is $12. Thursday + Friday = 85 − 39 = $46, so Thursday = $34.
34 A regular hexagon is cut along the dashed line from one corner to the opposite corner.What two shapes are made?
Show worked solution
Each piece has the cut as one side plus three sides of the hexagon: two four-sided shapes (trapeziums).
35 A box holds 20 counters: 7 red, 9 blue and 4 green. Zoe wants it to be equally likely to pick a red counter or a blue counter. What is the smallest change she could make?
Show worked solution
Red 7, blue 9: the gap is 2. Adding 2 red (or removing 2 blue) closes it. Green counters do not affect red against blue.