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 school has 480 students, and 35% of them walk to school. How many students walk to school?
Show worked solution
30% is 144 and 5% is 24, so 35% is 168. (312 is the number who do NOT walk; 445 takes 35 away from 480 instead of 35%.)
2 A printer prints 18 pages in 45 seconds. Working at the same rate, how many pages does it print in 4 minutes?
Show worked solution
18 pages per 45 s is 6 pages per 15 s. 240 s is 16 lots of 15 s, so 16 × 6 = 96. (72 treats 45 seconds as if it were a whole minute.)
3 Tiles are laid in a cross pattern. Figure 1 uses 5 tiles, Figure 2 uses 9 and Figure 3 uses 13. The pattern continues. How many tiles does Figure 20 use?
Show worked solution
Figure n uses 4n + 1 tiles, so Figure 20 uses 80 + 1 = 81. (80 forgets the centre tile; 85 is Figure 21; 77 is Figure 19.)
4 Eve is taller than Ana. Ana is taller than Bo. Cy is shorter than Bo but taller than Dee. Who is the second shortest?
Show worked solution
Tallest to shortest: Eve, Ana, Bo, Cy, Dee. Dee is the shortest, so the second shortest is Cy. (Bo is third shortest.)
5 A 4 cm by 5 cm rectangle is cut from one corner of a 12 cm by 9 cm rectangle, leaving the shape below. What is the perimeter of the shape, in centimetres?
Show worked solution
The missing sides are 12 − 5 = 7 cm (top) and 9 − 4 = 5 cm (right). 12 + 9 + 7 + 4 + 5 + 5 = 42, the same as the full 12 by 9 rectangle. (50 adds the notch’s 4 cm sides twice; 88 is the area in cm2, and 108 is the area of the full rectangle.)
6 At an exchange booth, 4 euros can be swapped for 7 Australian dollars. How many euros are 63 Australian dollars worth?
Show worked solution
63 ÷ 7 = 9 lots, and each lot is 4 euros: 9 × 4 = 36. (110.25 multiplies by 7/4 instead of 4/7 — but euros must be the smaller number; 59 just takes away 4.)
7 The graph shows how many books each student in a class read last month. What is the median number of books read?
Show worked solution
In order: one 0, three 1s (up to the 4th), five 2s (up to the 9th), then seven 3s. The 10th and 11th are both 3, so the median is 3. (2 is just the middle label of the axis; 2.5 is the mean; 10 is the middle position, not the value.)
8 The sequence 5, 9, 13, 17, … continues by adding 4 each time. Which of these numbers is in the sequence?
Show worked solution
The terms are 4k + 1. 2024 is a multiple of 4, so 2025 is in the sequence. 2022 and 2023 leave remainders 2 and 3, and 2024 leaves 0.
9 In a school, 60% of the students are girls. 25% of the girls and 40% of the boys play cricket. What percentage of all the students play cricket?
Show worked solution
25% of 60 = 15 girls and 40% of 40 = 16 boys: 31 out of 100, so 31%. (32.5% averages 25% and 40% as if the groups were equal; 34% swaps the percentages; 65% adds them.)
10 A bag holds only red, blue and green marbles. A marble taken at random has a 1/4 chance of being red and a 1/3 chance of being blue. There are 10 green marbles. How many marbles are in the bag?
Show worked solution
Green is 1 − 1/4 − 1/3 = 5/12 of the bag. 5/12 is 10 marbles, so 1/12 is 2 and the bag holds 24. (14 is the red and blue marbles only; 12 is just the common denominator.)
11 What is the next number in this sequence?
Show worked solution
Each term is double the one before minus 1 (the gaps 2, 4, 8, 16 keep doubling): 2 × 33 − 1 = 65. (66 doubles without taking 1 away; 49 repeats the gap of 16.)
12 Tom’s mean score on 7 tests is 64. After his 8th test, his mean score is 66. What did he score on the 8th test?
Show worked solution
Totals: 7 × 64 = 448 and 8 × 66 = 528, so the 8th test was 528 − 448 = 80. (66 is the new mean, and 68 only adds the rise of 2 once — the 8th score has to lift all eight tests by 2.)
13 A fish tank has a rectangular base 50 cm by 30 cm, and the water in it is 20 cm deep. A rock is put in and sinks completely, and the water rises to 22 cm. What is the volume of the rock?
Show worked solution
The rock’s volume is the extra layer: 50 × 30 × 2 = 3 000 cm3. (1 500 forgets the 2 cm; 30 000 and 33 000 are the water volumes at 20 cm and 22 cm.)
14 A trapezium has parallel sides of 9 cm and 15 cm, and its area is 84 cm2. What is its perpendicular height h?
Show worked solution
½ × (9 + 15) × h = 12h = 84, so h = 7 cm. (3.5 cm forgets the ½ and divides 84 by 24; 5.6 cm divides by the 15 cm side alone.)
15 A clock with no numbers on its face is seen in a mirror. In the mirror the hands look like this, as if the time were 4:20. What time does the clock really show?
Show worked solution
The minute hand is reflected from 20 to 40 minutes. The hour hand, just past 4 in the mirror, is really just before 8 — two thirds of the way from 7 to 8. So the time is 7:40. Check: 4:20 + 7:40 = 12:00. (7:20 reflects only the hour hand; 4:40 only the minute hand; 8:20 rounds the hour the wrong way.)
16 Two phone plans charge as shown. For how many minutes of calls in a month do the two plans cost exactly the same?
Show worked solution
The $15 gap closes at 6c a minute: 1 500c ÷ 6c = 250 minutes. Check: X = 20 + 25 = $45, Y = 35 + 10 = $45. (150 divides by 10c and 375 by 4c, instead of the difference 6c.)
17 Both balances are level. All circles weigh the same and all squares weigh the same. How much does one circle weigh?
Show worked solution
Doubling the bottom balance: 2 squares + 2 circles = 30 g, and 2 squares = 3 circles, so 5 circles = 30 g and a circle is 6 g (a square is 9 g; check 3 × 6 = 2 × 9). (9 g is the square; 15 g is a square and a circle together.)
18 Ana, Ben and Cal share $150. Ben gets twice as much as Ana, and Cal gets $10 less than Ben. How much does Cal get?
Show worked solution
a + 2a + (2a − 10) = 150, so 5a = 160 and a = 32. Ben gets $64 and Cal gets $54. (Check: 32 + 64 + 54 = 150. $64 is Ben’s share; $60 forgets Cal’s $10 less.)
19 Each side of a square is made 20% longer. By what percentage does the area of the square increase?
Show worked solution
Area goes from 10 × 10 = 100 to 12 × 12 = 144, an increase of 44%. (40% adds 20% for each direction and misses the 4% corner; 4% is only that corner.)
20 A closed box is a rectangular prism. Three of its faces have the areas shown. What is the volume of the box, in cm3?
Show worked solution
Edges 3, 4 and 5 cm give faces 12, 15 and 20 (or: (ab)(bc)(ca) = 3 600 = (abc)2, so abc = √3 600). Volume = 3 × 4 × 5 = 60. (3 600 forgets the square root; 47 adds the areas.)
21 A leaking tap drips once every 2 seconds, and 20 drops make 1 mL. How much water does it waste in one day?
Show worked solution
86 400 ÷ 2 = 43 200 drops, ÷ 20 = 2 160 mL = 2.16 L. (4.32 L counts a drop every second; 43.2 L forgets that 20 drops make 1 mL.)
22 The sector graph shows the favourite sports of a group of students. 24 students chose swimming. How many chose tennis?
Show worked solution
Tennis is 360° − 150° − 90° − 60° = 60°. Swimming’s 90° is 24 students, so 60° is two thirds of that: 16. (60 is the angle, not the number of students.)
23 In a class, 40% of the students are boys. Then 10 more girls join the class, and now 30% of the students are boys. How many students are in the class now?
Show worked solution
0.4n = 0.3(n + 10) gives 0.1n = 3, so n = 30 at first (12 boys) and now there are 40. Check: 12 out of 40 is 30%. (12 is the number of boys; 30 is the class before the girls joined.)
24 Lee drives the first 120 km of a trip at 60 km/h. How fast must he drive the next 120 km so that his average speed for the whole 240 km is 80 km/h?
Show worked solution
At 80 km/h, 240 km takes 3 hours. The first half took 2 hours, so 120 km must be done in 1 hour: 120 km/h. (100 km/h averages the two speeds, but Lee spends longer at the slow speed, so that gives less than 80 km/h overall.)
25 The counting numbers are written in rows like this, with one more number in each row. What is the first number in Row 20?
Show worked solution
Rows 1 to 19 hold 1 + 2 + … + 19 = 19 × 20 ÷ 2 = 190 numbers, so Row 20 starts at 191. (210 is the last number of Row 20 and 211 starts Row 21.)
26 A farmer builds a rectangular pen against a long straight wall, so fencing is needed on only three sides. She uses exactly 40 m of fencing, and the side parallel to the wall is twice as long as each of the other two sides. What is the area of the pen, in m2?
Show worked solution
4x = 40, so x = 10 m and the pen is 10 m by 20 m: area 200 m2. (400 is 20 × 20, taking both sides as 20 m; 100 is 10 × 10, taking both sides as 10 m.)
27 What is the value of 1 − 2 + 3 − 4 + 5 − 6 + … + 99 − 100?
Show worked solution
There are 50 pairs and each pair is −1, so the sum is −50. (50 forgets the sign: each pair is minus 1, not plus 1.)
28 A rectangle is cut into four smaller rectangles by one line across and one line down. Three of the small rectangles have the areas shown, in cm2. What is the area of the fourth one?
Show worked solution
In the top row 18 is 1.5 times 12, so the right column is 1.5 times as wide as the left. The bottom row has the same widths, so the fourth area is 1.5 × 30 = 45. (36 treats the areas as if they add: 30 + 18 − 12; 20 uses the ratio the wrong way round, 30 × 12 ÷ 18.)
29 A large cube is built from 27 small cubes. A square tunnel one cube wide is cut straight through the centre from each face to the opposite face — three tunnels in all. How many small cubes are left?
Show worked solution
The tunnels remove the 6 face-centre cubes and the 1 centre cube: 7 cubes, leaving 20. (18 takes away 3 × 3 = 9, counting the centre cube three times; 24 removes only one tunnel.)
30 Two trains start 300 km apart on the same track and travel towards each other at 70 km/h and 80 km/h. At the start, a bird flies from the front of one train at 100 km/h, back and forth between the trains, until they meet. How far does the bird fly altogether?
Show worked solution
The trains close the gap at 70 + 80 = 150 km/h, so they meet after 300 ÷ 150 = 2 hours. The bird flies for 2 hours at 100 km/h: 200 km. (300 km is the starting gap, not the bird’s distance.)
31 Five positive whole numbers have a mean of 10 and a median of 12. Their only mode is 15. What is the sum of the two smallest numbers?
Show worked solution
The middle number is 12, and 15 must appear at least twice, so the two largest are 15 and 15. The total is 5 × 10 = 50, so the two smallest add to 50 − 12 − 30 = 8 (for example 3, 5, 12, 15, 15). (23 uses only one 15; 10 is the mean.)
32 Five books — an atlas, a cookbook, a dictionary, a maths book and a novel — stand in a row on a shelf.
• The atlas is at one end.
• The cookbook is immediately to the right of the novel.
• The dictionary is somewhere to the left of the maths book.
• Neither the dictionary nor the maths book is next to the atlas.
• The maths book is not at an end.
Which book is in the middle?
• The atlas is at one end.
• The cookbook is immediately to the right of the novel.
• The dictionary is somewhere to the left of the maths book.
• Neither the dictionary nor the maths book is next to the atlas.
• The maths book is not at an end.
Which book is in the middle?
Show worked solution
The atlas’s neighbour is the novel or the cookbook, and the cookbook comes just after the novel. Atlas on the left: atlas, novel, cookbook, then the dictionary and maths book — but the maths book would have to be last, which is not allowed. So the atlas is on the right: dictionary, maths, novel, cookbook, atlas. The middle book is the novel. (The maths book is second, not third.)
33 A sequence starts 2, 5. Each term after that is the term just before it minus the term before that (so the 3rd term is 5 − 2 = 3). What is the sum of the first 100 terms?
Show worked solution
The terms are 2, 5, 3, −2, −5, −3, then 2, 5, … again: a block of 6 that adds to 0. 100 = 16 × 6 + 4, so the sum is the first four terms: 2 + 5 + 3 − 2 = 8. (0 forgets the 4 terms left over after the 16 full blocks.)
34 If Ana gives Ben $5, they will have the same amount. If instead Ben gives Ana $10, Ana will have twice as much as Ben. How much does Ana have?
Show worked solution
a − 5 = b + 5, so a = b + 10. Then a + 10 = 2(b − 10) gives b + 20 = 2b − 20, so b = 40 and Ana has $50. Check: 60 is twice 30. ($40 is Ben’s amount; $45 uses a gap of $5 instead of $10.)
35 Two candles are the same length. One burns down completely in 4 hours and the other in 6 hours, each at a steady rate. Both are lit at the same time. After how long is one candle exactly twice as long as the other?
Show worked solution
1 − t/6 = 2(1 − t/4) gives t/2 − t/6 = 1, so t/3 = 1 and t = 3 h. Check: after 3 hours one has ¼ left and the other ½. (2 h 24 min is 4 × 6 ÷ 10, the time if the two candles burned one shared length together — a different question.)