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 die is rolled twice and the two numbers are added. How many of the 36 outcomes give a total that is a multiple of 5?
Show worked solution
Total 5: 1+4, 2+3, 3+2, 4+1 (four ways). Total 10: 4+6, 5+5, 6+4 (three ways). 7 outcomes.
2 On a standard die, opposite faces add to 7. Two dice are pressed together so that the touching faces are a 2 and a 6. What is the total of the two faces at the far ends — the ones opposite the touching faces?
Show worked solution
5 + 1 = 6.
3 Which of these fractions is closest to one half?
Show worked solution
As decimals: 0.467, 0.55, 0.52, 0.529, 0.455. The closest to 0.5 is 0.52, which is 13/25.
4 The hall clock is 6 minutes slow. Sam leaves when it shows 8:19. The walk to school takes 23 minutes and school starts at 8:45. Is Sam late or early, and by how much?
Show worked solution
Real time 8:25. Arrives 8:48, which is 3 min late.
5 A fund of $3 050 000 is shared into grants of $500 each. How many grants is that?
Show worked solution
3 050 000 ÷ 1 000 = 3 050, and × 2 = 6 100 grants.
6 A rectangle has an area of 60 cm² and whole-number sides. What is the smallest perimeter it could have?
Show worked solution
1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10. The 6 by 10 rectangle has perimeter 2 × 16 = 32.
7 Lee gives half of her stickers plus 3 more to Ava. She then gives half of what is left plus 2 more to Ben, and has 5 left. How many did Lee start with?
Show worked solution
Before Ben: (5 + 2) × 2 = 14. Before Ava: (14 + 3) × 2 = 34.
8 What is the smaller angle between the hands of this clock?
Show worked solution
Hour hand: 7 × 30 + 10 = 220°. Minute hand: 120°. Difference 100°.
9 This pie graph shows how 180 students travel to school. The bus sector is 150°, walking is 90° and bike is 30°. How many more students come by bus than by bike?
Show worked solution
Bus: 5/12 of 180 = 75. Bike: 1/12 of 180 = 15. 75 − 15 = 60.
10 In this sequence each term is double the one before, plus 1. Which term is 639?
Show worked solution
4, 9, 19, 39, 79, 159, 319, 639 — the 8th term.
11 A 2.4 m plank is cut into as many 35 cm pieces as possible. How long is the piece left over?
Show worked solution
6 × 35 = 210, and 7 × 35 = 245 is too long. 240 − 210 = 30 cm.
12 Every △ has the same value and every □ has the same value. What is △ + □?
Show worked solution
3△ + 3□ = 42, so △ + □ = 14. (△ = 6, □ = 8.)
13 A bag of rice that is three quarters full weighs 4.1 kg. When it is completely full it weighs 5.3 kg. What does the empty bag weigh?
Show worked solution
5.3 − 4.1 = 1.2 kg is a quarter of the rice, so the rice is 4.8 kg. The bag is 5.3 − 4.8 = 0.5 kg.
14 Written in plain capitals, how many of the letters in the word SYMMETRY have at least one line of symmetry?
Show worked solution
Y, M, M, E, T and Y each have a line of symmetry; S and R do not. 6.
15 What is the smallest whole number that leaves a remainder of 1 when divided by 2, by 3, by 4, by 5 and by 6?
Show worked solution
The LCM of 2, 3, 4, 5 and 6 is 60, so the number is 60 + 1 = 61.
16 The journey takes 33 minutes and Mia must arrive by 8:38. Which train should she catch, and how long before 8:38 will she arrive?
Show worked solution
8:06 + 33 = 8:39, which misses 8:38. So the 7:42, arriving 8:15: 7:42, 23 min early.
17 Three eighths of a class are boys. Two thirds of the girls wear glasses, and the 10 girls who do not wear glasses are the rest. How many students are in the class?
Show worked solution
10 girls are one third of the girls, so there are 30 girls, and 30 is ⅝ of the class. One eighth is 6, so 48 students.
18 A 12 by 9 rectangle has a 5 by 4 rectangle removed from one corner, leaving an L-shape. What is the area of the L-shape?
Show worked solution
12 × 9 = 108, minus 5 × 4 = 20: 88.
19 A spinner has 6 equal sections: 3 red, 2 blue and 1 green.1 The chance of red is 1/2.
2 The chance of not landing on blue is 1/3.
3 Blue is twice as likely as green.
Which statements are correct?
2 The chance of not landing on blue is 1/3.
3 Blue is twice as likely as green.
Which statements are correct?
Show worked solution
3/6 = 1/2 (1 ✓). Not blue is 4/6 = 2/3, not 1/3 (2 ✗). 2 sections against 1 (3 ✓). 1 and 3.
20 Bottles hold 750 mL each. How many bottles can be filled completely from a 20 L container, and how much is left over?
Show worked solution
26 × 750 = 19 500 mL, and one more would need 20 250. 20 000 − 19 500 = 500: 26 bottles, 500 mL left.
21 Three corners of a rectangle are at (1, 2), (7, 2) and (7, 6). What is its area, in square units?
Show worked solution
6 × 4 = 24.
22 Which calculation has an answer closest to 1 000?
Show worked solution
19 × 48 = 912, 12 × 84 = 1 008, 31 × 33 = 1 023, 24 × 44 = 1 056, 2 030 ÷ 2 = 1 015. The closest is 1 008.
23 A large cube is built from 4 × 4 × 4 small cubes and painted on all six faces. How many small cubes have paint on exactly one face?
Show worked solution
6 faces × 4 middle cubes = 24.
24 Five students' test scores are shown.1 Di scored more than Ali and Cy combined.
2 Three students scored above 75.
3 The difference between the highest and lowest scores is 27.
Which statements are correct?
2 Three students scored above 75.
3 The difference between the highest and lowest scores is 27.
Which statements are correct?
Show worked solution
91 is less than 136 (1 ✗). 85, 91 and 78 are above 75 (2 ✓). 91 − 64 = 27 (3 ✓). 2 and 3.
25 Which number makes this sentence true?
Show worked solution
54 ÷ 6 = 9, so □ − 4 = 9 and □ = 13.
26 An equilateral triangle and a square have the same perimeter. The square has sides of 9 cm. How long is each side of the triangle?
Show worked solution
4 × 9 = 36 cm. 36 ÷ 3 = 12 cm.
27 A shop is open from 0830 to 1215 and again from 1300 to 1745. How long is it open in the day?
Show worked solution
3 h 45 min + 4 h 45 min = 7 h 90 min = 8 h 30 min.
28 0.5 × 0.5 × 0.5 + 0.375 = ?
Show worked solution
0.125 + 0.375 = 0.5.
29 The point (3, 4) is reflected in the y-axis, and the image is then moved 2 units up. Where does it finish?
Show worked solution
(3, 4) → (−3, 4) → (−3, 6).
30 Six identical pumps empty a pool in 10 hours. How long would 4 of the pumps take?
Show worked solution
60 pump-hours ÷ 4 pumps = 15 h.
31 In this sequence each term is the sum of the two before it. What is the sum of the first eight terms?
Show worked solution
2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 = 141.
32 A model car is made at a scale of 1 : 24. The model is 18 cm long. How long is the real car?
Show worked solution
18 × 24 = 432 cm = 4.32 m.
33 A number between 125 and 150 is a multiple of both 8 and 12. What is the sum of its digits?
Show worked solution
24, 48, 72, 96, 120, 144, 168 — only 144 is between 125 and 150. 1 + 4 + 4 = 9.
34 Three friends share a bill equally, except that Ana also pays $4.50 extra for her dessert. The whole bill is $58.50. How much does each friend pay for the shared part?
Show worked solution
$58.50 − $4.50 = $54. $54 ÷ 3 = $18.
35 How many three-digit numbers have three different digits that are all odd?
Show worked solution
5 × 4 × 3 = 60.