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.
26 questions · official format, shuffled order
1 Expand and simplify 3(2x − 5) − 2(x − 4).
Show worked solution
6x − 15 − 2x + 8 = 4x − 7. (4x − 23 writes −2 × −4 as −8; 8x − 7 adds the x-terms instead of subtracting.)
2 What is the next number in this series?
Show worked solution
Each term is double the one before plus 1 (the gaps 3, 6, 12, 24 double too): 47 × 2 + 1 = 95. (71 repeats the gap of 24; 141 triples.)
3 After a 20% discount, a jacket costs $120. What was its price before the discount?
Show worked solution
80% of the price is $120, so 10% is $15 and 100% is $150. ($144 adds 20% of $120 — but the 20% was taken from the original, not from $120. $96 takes 20% off again.)
4 In a code, CODE is written as EQFG. How is FISH written in the same code?
Show worked solution
Every letter moves 2 places on: F → H, I → K, S → U, H → J, giving HKUJ. (GJTI moves each letter only 1 place.)
5 Solve (x + 4)/3 = x − 2.
Show worked solution
x + 4 = 3x − 6, so 10 = 2x and x = 5. Check: 9/3 = 3 = 5 − 2 ✓. (3 comes from x + 4 = 3x − 2, multiplying only the x by 3; 10 forgets to halve.)
6 The same rule links the three numbers in each row. Which number replaces the question mark?
Show worked solution
The third number is double the sum of the first two: 2(2 + 8) = 20, 2(5 + 3) = 16. So 2(4 + ?) = 22, 4 + ? = 11 and ? = 7. (11 halves 22 but forgets to take away the 4; 18 takes away the 4 but forgets to halve.)
7 What is the gradient of the line through (−2, 5) and (4, −7)?
Show worked solution
Rise −12, run 6: gradient = −12 ÷ 6 = −2. (−1/2 divides run by rise; 2 loses the sign — the line falls from left to right.)
8 A farmer has enough feed for 30 cows for 20 days. After 8 days he sells 6 of the cows. For how many more days will the remaining feed last?
Show worked solution
Feed = 30 × 20 = 600 cow-days. After 8 days, 600 − 240 = 360 are left, shared by 24 cows: 360 ÷ 24 = 15 days. (12 ignores the sale; 25 is how long the feed would last 24 cows from the very start.)
9 A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. What is its area?
Show worked solution
262 − 102 = 676 − 100 = 576 = 242, so the base is 24 cm. Area = ½ × 24 × 10 = 120 cm2. (130 cm2 uses the hypotenuse as a base; 240 cm2 forgets the half.)
10 In each row the same rule turns a, b and c into d. Which number replaces the question mark?
Show worked solution
d = a × b − c: 24 − 5 = 19 and 21 − 8 = 13. So 45 − ? = 29 and ? = 16. (74 adds 29 to 45 instead of subtracting.)
11 Simplify (2x3)2 × 3x4 ÷ 6x5.
Show worked solution
4x6 × 3x4 = 12x10, and 12x10 ÷ 6x5 = 2x5. (x5 forgets to square the 2; 2x4 adds the indices in the bracket instead of multiplying, giving x5.)
12 A clock gains 3 minutes every hour. It is set to the correct time at 9:00 am. What time does it show when the correct time is 5:00 pm the same day?
Show worked solution
9 am to 5 pm is 8 hours, so the clock gains 8 × 3 = 24 minutes and shows 5:24 pm. (4:36 pm takes the minutes off — the clock is fast, not slow; 5:27 pm counts 9 hours.)
13 The stem-and-leaf plot shows nine scores. Leaving the median out of both halves, what is the interquartile range?
Show worked solution
Scores: 12, 15, 18, 20, 23, 23, 27, 31, 34. Lower half 12, 15, 18, 20 gives Q1 = 16.5; upper half 23, 27, 31, 34 gives Q3 = 29. IQR = 29 − 16.5 = 12.5. (9 puts the median into both halves; 22 is the range; 23 is the median.)
14 What is the next number in this series?
Show worked solution
Two series take turns: 4, 7, 10, 13 goes up 3 and 20, 17, 14 goes down 3. The next number belongs to the second series: 14 − 3 = 11. (The gaps +16, −13, +10, −7, +4, −1, −2 shrink by 3 each time and give 11 as well. 16 continues the wrong series.)
15 Solve 5 − 2x > 11.
Show worked solution
−2x > 6, and dividing by −2 reverses the sign: x < −3. Check x = −4: 5 + 8 = 13 > 11 ✓. (x > −3 forgets to reverse the sign; x < 3 loses the negative in 6 ÷ −2.)
16 Each shape stands for a number. What is ●?
Show worked solution
Adding: 2(▲ + ■ + ●) = 44, so ▲ + ■ + ● = 22. Then ● = 22 − 13 = 9 (and ▲ = 5, ■ = 8). (8 is ■.)
17 A map has a scale of 1 : 25 000. Two towns are 6 cm apart on the map. How far apart are they really?
Show worked solution
6 × 25 000 = 150 000 cm = 1 500 m = 1.5 km. (0.15 km and 15 km slip a power of ten when converting cm to km.)
18 Pipe A alone fills a tank in 6 hours. Pipe B alone fills it in 3 hours. How long do both pipes take together?
Show worked solution
Together they fill 1/6 + 1/3 = 1/2 of the tank each hour, so the tank takes 2 hours. (4.5 hours averages the times; 9 hours adds them — together must be faster than B alone.)
19 What is the volume of this cylinder? Leave π in the answer.
Show worked solution
π × 32 × 10 = 90π cm3. (60π is 2πrh, the curved surface area; 360π uses the diameter 6 as the radius.)
20 The symbol # stands for the same rule each time. What is 6 # 3?
Show worked solution
a # b = a × b + a + b: 12 + 7 = 19, 10 + 7 = 17, 6 + 7 = 13. So 6 # 3 = 18 + 9 = 27. (18 is the product only; 9 is the sum only.)
21 Factorise x2 − x − 12.
Show worked solution
−4 × 3 = −12 and −4 + 3 = −1, so (x − 4)(x + 3). ((x + 4)(x − 3) gives +x in the middle; (x − 6)(x + 2) gives −4x.)
22 Two trains leave at 10:30 am from stations A and B, 420 km apart, and travel towards each other. At what time do they meet?
Show worked solution
The gap closes at 140 km/h, so they meet after 420 ÷ 140 = 3 hours, at 1:30 pm. (3:45 pm uses only the faster train, 420 ÷ 80; 4:30 pm uses the average speed of one train, 70 km/h.)
23 Two fair six-sided dice are rolled. What is the probability that the total is 8?
Show worked solution
(2, 6), (3, 5), (4, 4), (5, 3), (6, 2): 5 of the 36 outcomes, so 5/36. (1/9 = 4/36 leaves out (4, 4); 1/12 = 3/36 counts (2, 6) and (6, 2) as one outcome.)
24 In this square, every row, column and diagonal has the same total. Which number replaces the question mark?
Show worked solution
The diagonal 13 + 11 + 9 = 33, so every line totals 33. The other diagonal: 17 + 11 + ? = 33, so ? = 5. (Check the right column: 13 + 15 + 5 = 33 ✓.)
25 Adult tickets cost $12 and child tickets cost $7. A group buys 25 tickets for $230 altogether. How many child tickets did they buy?
Show worked solution
$230 − $175 = $55 = 11 swaps, so 11 adult tickets and 25 − 11 = 14 child tickets. Check: 132 + 98 = 230 ✓. (11 is the number of adult tickets.)
26 What is the next number in this series?
Show worked solution
The multipliers go ×2, ×3, ×4, ×5, so next is ×6: 120 × 6 = 720. (240 doubles; 480 repeats ×4; 600 repeats ×5.)