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 What number is 7 hundreds more than 39415?
Show worked solution
39415 + 700 = 40115. The hundreds go from 4 to 11, so a thousand is carried.
2 The clock shows the time a bus leaves. The trip takes 55 minutes.At what time does the bus arrive?
Show worked solution
The clock shows 7:35. Add 25 minutes → 8:00, then 30 more → 8:30.
3 Round every one of these numbers to the nearest ten. Which one stays exactly as it is?
Show worked solution
520 already ends in 0, so rounding to the nearest ten leaves it as 520. The others all move.
4 Part of a number line is drawn below; the curved arrow marks a single jump.Starting from 6, what value is reached after 8 of these jumps?
Show worked solution
One jump is ¾ to the left. 8 jumps = 24 quarters = 6. 6 − 6 = 0.
5 Beads are threaded in a repeating pattern: blue, green, green, red, red, red, blue, green, green, red, red, red, …What colour is the 50th bead?
Show worked solution
The pattern repeats every 6 beads. 50 = 8 × 6 + 2, so the 50th is the 2nd of a group: green.
6 Tristan has $20. He buys 3 juices at $2.75 each and 2 rolls at $4.10 each. How much money does he have left?
Show worked solution
3 × $2.75 = $8.25; 2 × $4.10 = $8.20; total $16.45. $20 − $16.45 = $3.55.
7 Two thermometers were read at the same moment, one outside a library.By how many degrees is the inside reading higher?
Show worked solution
Each small tick is 2 °C. Outside: 1 tick above 10 = 12 °C. Inside: 2 ticks above 20 = 24 °C. Difference 12 °C.
8 Shawn starts with the number 5 and follows this instruction four times: "Double the number, then subtract 3." What number does he end with?
Show worked solution
5 → 7 → 11 → 19 → 35.
9 A regular pentagon is cut along the dashed line from one corner to the middle of the opposite side.What two shapes are made?
Show worked solution
Each piece has the cut, part of the far side, and two whole sides of the pentagon: four sides each.
10 A tin holds 18 counters: 6 red, 3 green, 8 blue and 1 yellow. Without looking, Oliver takes one counter out.1 Oliver is certain to get a blue counter.
2 Getting blue and not getting blue are equally likely.
3 Oliver could get the yellow counter.
Which of the numbered statements are true?
2 Getting blue and not getting blue are equally likely.
3 Oliver could get the yellow counter.
Which of the numbered statements are true?
Show worked solution
8 of 18 is not all (1 ✗). Blue 8, not blue 10 — not equal (2 ✗). One yellow counter is enough for "possible" (3 ✓).
11 Ana thinks of a number. She adds 9, then halves the result, and gets 17. What do you get if you add together the digits of her starting number?
Show worked solution
Undo: 17 × 2 = 34; 34 − 9 = 25. Digits 2 + 5 = 7.
12 Priya is measuring water in a container with an unusual scale.How much water is in the container?
Show worked solution
Five gaps between 0 and 100 mL, so each gap is 20 mL. The water is at the second mark: 40 mL.
13 Buses leave the station every 25 minutes, starting at 7:05 am. Kim arrives at the station at 8:00 am. How long does she wait for the next bus?
Show worked solution
Buses: 7:05, 7:30, 7:55, 8:20. The next after 8:00 is 8:20 — a 20-minute wait.
14 Both of these solids are built from identical small cubes, with no hidden gaps.Andrea pulls them apart into single cubes. How many 4-cube models can she build from the pile?
Show worked solution
The objects have 6 and 7 cubes: 13 altogether. 13 ÷ 4 = 3 remainder 1, so 3 objects.
15 Which of these fractions is nearest to 3?
Show worked solution
Distances from 3: ½, ⅓, ⅕, ¼, ⅓. The smallest is ⅕, so 2⅘.
16 The column graph shows books read by Mia and Ken, but its scale is missing. The picture graph shows Mia's books; Ken's pictures have not been drawn yet.How many circles belong in Ken's row of the picture graph?
Show worked solution
Mia: 1½ circles = 6 books and 3 gridlines, so one gridline = 2 books. Ken: 5 gridlines = 10 books = 2½ circles.
17 The map shows two front doors. A ruler in millimetres is laid between them.How far apart are the doors in real life?
Show worked solution
95 mm = 9.5 cm. 9.5 × 40 m = 380 m (9 × 40 = 360, plus half of 40).
18 Two classes have 57 students altogether. Class A has 7 more students than class B. How many students are in class A?
Show worked solution
Take away the extra 7: 50, shared equally is 25 each. Class A has 25 + 7 = 32.
19 Three squares are shaded. The finished pattern must be symmetrical about the dashed line.Which three squares on the right need shading?
Show worked solution
Each square reflects to the same row, the same distance past the line: R4 → S4, Q1 → T1, P3 → U3.
20 Two identical rectangles, each 9 cm long and 4 cm wide, are joined along their long sides to make one larger rectangle. What is the perimeter of the larger rectangle?
Show worked solution
The larger rectangle is 9 cm by 8 cm. Perimeter 9 + 8 + 9 + 8 = 44 cm.
21 The shapes on each scale balance. Shapes that look the same weigh the same.What does one square weigh?
Show worked solution
Swap the square for 3 triangles on the second scale: 4 triangles = 12 kg, so a triangle is 3 kg and the square is 9 kg.
22 A machine makes 5 badges every 4 minutes. How many badges does it make in 20 minutes?
Show worked solution
20 minutes is 5 lots of 4 minutes: 5 × 5 = 25 badges.
23 A canteen recorded today's drink sales on this graph.How many drinks were sold altogether?
Show worked solution
Milk 35, juice 15, water 25, tea 45: 120 in total. Two bars end halfway between gridlines.
24 11 August 1999 was a Wednesday. What day of the week was 11 August 2000?
Show worked solution
The year 2000 was a leap year and 29 February 2000 lies between the two dates, so there are 366 days = 52 weeks and 2 days. Wednesday + 2 = Friday.
25 Each grid square is 1 cm². What is the area of the shaded shape?
Show worked solution
5 whole squares and 2 half squares (1 more): 6 cm².
26 Which one of these numbers is the largest?
Show worked solution
Compare tenths first: 0.7, 0.71, 0.68, 0.65 all have 6 or 7 tenths; 0.099 has none. Then 0.71 beats 0.70.
27 This spinner has 6 equal sections: 2 red, 1 blue and 3 green.Ana spins it 60 times. About how many times should she expect it to land on green?
Show worked solution
Green is 3 of 6 sections — half. Half of 60 is 30.
28 Thirty 250 g tins need carrying home in bags, and no bag may carry more than 2 kg. What is the fewest bags that will do?
Show worked solution
2000 ÷ 250 = 8 tins per bag. 30 ÷ 8 = 3 remainder 6, so 4 bags.
29 Each of the six 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 ✓, Z (mirror of S) ✗, S turned ✓, mirror L ✗, square ✗, L ✓. Three are not identical.
30 A factory packs 1200 stickers into packets of 35. How many stickers are left over after the last full packet?
Show worked solution
35 × 34 = 1190, so 34 full packets with 1200 − 1190 = 10 stickers left over.
31 Eight small cubes are glued into one 2 × 2 × 2 cube, which you may turn around and inspect from every side.How many small-cube faces are hidden inside the joins?
Show worked solution
The 8 small cubes have 48 faces. There are 12 glued joins, each hiding 2 faces: 24 hidden (and 24 visible).
32 Here are the first three patterns in a sequence made of squares.How many squares are in pattern 9?
Show worked solution
Pattern 1: 6, pattern 2: 10, pattern 3: 14 — four more each time, or 4 × n + 2. Pattern 9: 4 × 9 + 2 = 38.
33 Cho's savings jar starts the week empty. Her running total is $11; when Monday finishes, $31 when Wednesday finishes and $75 when Friday finishes. Her Tuesday, Wednesday and Friday deposits are all equal. What did she deposit on Thursday?
Show worked solution
Tuesday + Wednesday = 31 − 11 = $20, so $10 each; Friday is $10. Thursday + Friday = 75 − 31 = $44, so Thursday = $34.
34 Shape P covers 5 cm². Shape Q is the same shape with every side made twice as long.How much area does Shape Q cover?
Show worked solution
Doubling every side multiplies the area by 2 × 2 = 4. 5 × 4 = 20 cm². (10 cm² is the trap.)
35 A bag holds 24 counters: 9 red, 6 blue and 9 white. Rui 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 9, blue 6: the gap is 3. Adding 3 blue closes it. White counters do not affect red against blue.