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.
40 questions · official format, shuffled order
1 A square piece of paper is folded in half, and a corner is cut off as shown. What does the paper look like when it is unfolded?
Show worked solution
Unfolding mirrors the cut across the fold, giving a notch in both top corners.
2 Which 3D object has one curved surface and one flat circular face?
Show worked solution
A cone has one flat circular face and one curved surface. A cylinder has two circles.
3 Which of these is another way of writing 4 807?
Show worked solution
4 thousands, 8 hundreds, no tens and 7 ones: 4 × 1 000 + 8 × 100 + 7.
4 On this plan, the canteen is at B2. Which square is the library in?
Show worked solution
The library sits in the fourth column and the first row: D1.
5 The calendar shows one month. What is the date of the third Friday?
Show worked solution
Fridays fall on 3, 10, 17 and 24. The third is the 17th.
6 The arrow on this spinner is spun once. Which colour is it most likely to stop on?
Show worked solution
Blue covers half the spinner, more than any other colour.
7 Which number sentence has the same answer as 14 × 5?
Show worked solution
14 × 5 = (10 + 4) × 5 = 10 × 5 + 4 × 5 = 50 + 20 = 70.
8 What is 3 684 ÷ 4?
Show worked solution
3 684 ÷ 4 = 921. Check: 921 × 4 = 3 684.
9 Four jugs are shown. Each has a different scale. Which jug holds the least liquid?
Show worked solution
W holds 400 mL, X 350 mL, Y 600 mL and Z 300 mL, the least.
10 What fraction of this shape is shaded?
Show worked solution
6 squares of 16 are shaded, and 6 out of 16 is the same as three eighths.
11 Which of these nets folds up to make a cube?
Show worked solution
P only. Q is two columns of three, which folds into a box with faces doubled over, and R is a straight strip of six, which wraps round on itself.
12 Two pencils and a sharpener cost the same as three pencils. A pencil costs 60c. What does the sharpener cost?
Show worked solution
Two pencils are on both sides, so the sharpener costs the same as one pencil: 60c.
13 What is the area of this shape, in square units?
Show worked solution
6 × 4 = 24 squares, less the 2 × 2 = 4 cut out: 20 square units.
14 Which arrow points closest to one half?
Show worked solution
Halfway is 0.5, and Q at about 0.45 is the closest.
15 A runner follows this course from Start to Finish. At which marked corner does the runner change direction the most?
Show worked solution
J is a square corner and K is a gentle bend; at L the runner almost doubles back, which is a bigger change of direction than the turn at M.
16 The table shows the marbles in a bag. One marble is taken without looking.Which statement is correct?
Show worked solution
There are 10 red and 5 blue, so Red is twice as likely as blue.
17 Which flag has exactly one line of symmetry?
Show worked solution
C folds onto itself across the middle from top to bottom, and no other way: one line. A is symmetrical both across and down, so it has two, and B has a circle in one corner only, so it has none.
18 Which of these decimals is greater than 0.6?
Show worked solution
0.65 has 6 tenths and 5 hundredths, which is more than 0.60. The others all have fewer than 6 tenths.
19 A bus leaves the stop every 25 minutes, starting at 8:10 am. You arrive at the stop at 8:40 am. How long do you wait?
Show worked solution
The next bus after 8:40 is at 9:00, so the wait is 20 minutes.
20 Two views of the same cube are shown. Every face carries a different number. Which number is on the face opposite the 1?
Show worked solution
The 1 touches 2 and 3 in view 1, and 4 and 5 in view 2. That rules out four of the six numbers, leaving 6 on the face opposite.
21 How many metres are there in 2 500 centimetres?
Show worked solution
2 500 ÷ 100 = 25 metres.
22 Four identical tiles of which shape can be fitted together, with no gaps, to make a larger square?
Show worked solution
Four small squares make a bigger square, two along each side: the square. Regular pentagons and hexagons leave gaps.
23 Which shape has exactly one pair of parallel sides?
Show worked solution
X is a trapezium: its top and bottom are parallel, its slanting sides are not. W and Z have two pairs, and Y is a kite with none.
24 The large grid has 100 squares and 30 of them are shaded. The strip below it is divided into 10 equal parts. How many parts of the strip must be shaded to shade the same fraction?
Show worked solution
30 out of 100 is 3 out of 10, so 3 parts of the strip.
25 Which rectangle has an area of 8 square centimetres?
Show worked solution
2 cm by 4 cm gives 2 × 4 = 8 square centimetres.
26 The pie graph shows how 800 people travelled to work. About how many walked?
Show worked solution
The walking sector is a quarter of the circle: 800 ÷ 4 = 200 people.
27 The graph shows how many books four children read. How many more did Dana read than Ben?
Show worked solution
Dana read 12 and Ben read 5: 12 − 5 = 7 more.
28 What is 2 465 + 1 370?
Show worked solution
2 465 + 1 370 = 3 835.
29 How many dots are inside the square AND inside the triangle but NOT inside the circle?
Show worked solution
The dots at the left of the overlap pass all three tests: 2 of them.
30 $18 buys 3 identical notebooks. How many notebooks can be bought for $42?
Show worked solution
$18 ÷ 3 = $6 each, so $42 ÷ 6 = 7 notebooks.
31 94 eggs are packed into cartons of 12. How many cartons are needed to hold all the eggs?
Show worked solution
94 ÷ 12 = 7 remainder 10, and those 10 eggs need a carton: 8.
32 This rectangle has a perimeter of 26 cm. How many centimetres is the shorter side?
Show worked solution
26 − 18 = 8 for the two short sides, so each is 4 cm.
33 A number is divided by 5 and then 3.4 is added. The result is 9.8. What was the number?
Show worked solution
9.8 − 3.4 = 6.4, and 6.4 × 5 = 32.
34 These digit cards are used once each to make a 3-digit number. What is the largest odd number that can be made?
Show worked solution
The ones place must be 5, then the rest biggest first: 825.
35 This solid is made of centimetre cubes. How many cubes are there altogether?
Show worked solution
6 cubes in the bottom layer and 2 on top: 8 cubes.
36 One city has 3.8 million people and another has 1.25 million. How many million more people does the larger city have?
Show worked solution
3.80 − 1.25 = 2.55 million.
37 Opposite faces on a die add to 7. Two dice show 3 and 6 on top. What is the total of the two faces underneath?
Show worked solution
4 + 1 = 5.
38 A class of 32 children went to the museum. Three quarters of them brought a packed lunch. How many children brought a packed lunch?
Show worked solution
32 ÷ 4 = 8, so three quarters is 3 × 8 = 24 children.
39 A film starts at 10:25 pm and runs for 1 hour and 50 minutes. At what time does it finish? Write the answer in 24-hour time as four digits, like 0930.
Show worked solution
10:25 pm + 1 h 50 min = 12:15 am, which is 0015.
40 Three angles meet at a point. Two of them are 135° and 90°. How many degrees is the third?
Show worked solution
360 − 135 − 90 = 135°.