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.
15 questions · official format, shuffled order
1 Solve 4(2x − 3) − 3(x − 5) = 23.
Show worked solution
8x − 12 − 3x + 15 = 23, so 5x + 3 = 23 and x = 4. (10 comes from writing −3 × −5 as −15.)
2 Solve (3x − 1)/5 − (x + 2)/3 = 1.
Show worked solution
3(3x − 1) − 5(x + 2) = 15, so 9x − 3 − 5x − 10 = 15, 4x = 28 and x = 7. (2 comes from −5(x + 2) written as −5x + 10.)
3 Solve 5 − 2x ≤ 3x − 20.
Show worked solution
25 ≤ 5x, so 5 ≤ x: x ≥ 5. (Collecting on the left gives −5x ≤ −25, and dividing by −5 reverses the sign to the same answer.)
4 How many integers x satisfy −4 < 3 − x ≤ 6?
Show worked solution
−7 < −x ≤ 3, so −3 ≤ x < 7. The integers −3, −2, …, 6 number 10.
5 Make r the subject of A = P(1 + rt).
Show worked solution
A − P = Prt, so r = (A − P)/(Pt). (r = A/(Pt) − 1 subtracts the 1 after dividing by t, which is too late.)
6 T = 2(a + b) − ab. Find T when a = −3 and b = 4.
Show worked solution
2(1) − (−12) = 2 + 12 = 14. (−10 subtracts 12 instead of −12.)
7 Ana is 4 times as old as Ben. In 10 years she will be twice as old as Ben. How old is Ana now?
Show worked solution
4b + 10 = 2b + 20, so b = 5 and Ana is 4 × 5 = 20. (5 is Ben’s age.)
8 Adult tickets cost $12 and child tickets $7. Thirty tickets were sold for $290 in total. How many adult tickets were sold?
Show worked solution
5a + 210 = 290, so a = 16. (14 is the number of child tickets.)
9 Kai cycles to a town at 15 km/h and walks back the same way at 5 km/h. The whole trip takes 4 hours. How far away is the town?
Show worked solution
d/15 + 3d/15 = 4d/15 = 4, so d = 15 km. (20 km uses the average of the two speeds, which is wrong because more time is spent walking.)
10 Solve x/4 + x/6 = 5.
Show worked solution
3x + 2x = 60, so 5x = 60 and x = 12. (60 forgets to divide by 5.)
11 Three statements about the inequality −2x + 7 > 1:
1 x = 3 is a solution.
2 The solution is x < 3.
3 x = −10 is a solution.
Which statements are correct?
1 x = 3 is a solution.
2 The solution is x < 3.
3 x = −10 is a solution.
Which statements are correct?
Show worked solution
−2x > −6 gives x < 3 (2 ✓). At x = 3 the left side is 1, and 1 > 1 is false (1 ✗). At x = −10 it is 27 > 1 (3 ✓). 2 and 3.
12 Three consecutive multiples of 5 add to 285. What is the largest of them?
Show worked solution
3n + 15 = 285, so n = 90 and the largest is 100. (95 is the middle one, 285 ÷ 3.)
13 A rectangle’s length is 3 cm more than twice its width, and its perimeter is 54 cm. What is its area?
Show worked solution
6w + 6 = 54, so w = 8 and the length is 19: area 8 × 19 = 152 cm2.
14 Make x the subject of y = (2 − 3x)/4.
Show worked solution
4y = 2 − 3x, so 3x = 2 − 4y and x = (2 − 4y)/3. (x = (4y − 2)/3 loses the minus sign in front of 3x.)
15 The equation 3(x − 4) = 2x + k has the solution x = 7.
1 k = 5.
2 k = −5.
3 If k = 0 instead, the solution is x = 12.
Which statements are correct?
1 k = 5.
2 k = −5.
3 If k = 0 instead, the solution is x = 12.
Which statements are correct?
Show worked solution
3 × 3 = 14 + k, so k = −5 (2 ✓, 1 ✗). With k = 0: 3x − 12 = 2x gives x = 12 (3 ✓). 2 and 3.