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.
Level 1 · Warm-up
1 The nth term of a sequence is T = a + (n − 1)d. Find T when a = 40, n = 9 and d = −6.
Show worked solution
T = 40 + (8)(−6) = 40 − 48 = −8. −14 uses n instead of n − 1 (40 − 54); 88 drops the negative on d; −288 adds 40 + 8 before multiplying.
2 The distance travelled is s = (u + v)t/2. Find s when u = 4, v = 16 and t = 7. Then find t when s = 60, u = 4 and v = 16.
Show worked solution
s = 20 × 7 / 2 = 70. Then 60 = 20t/2 = 10t, so t = 6.
3 Find the value of Q = a2 − 3ab for the values in the table.
Show worked solution
a2 = (−2)2 = 4. 3ab = 3 × (−2) × 5 = −30, so Q = 4 − (−30) = 34.
Level 2 · Core
4 The angle sum of a polygon with n sides is S = 180(n − 2). Make n the subject.
Show worked solution
÷ 180: S/180 = n − 2. + 2: n = S/180 + 2. Check: n = 5 gives S = 540, and 3 + 2 = 5 ✓. S/180 − 2 subtracts instead of adding; (S − 2)/180 undoes the steps in the wrong order; 180S + 2 multiplies instead of dividing.
5 The formula v2 = u2 + 2as links speeds and distance. Find v (positive) when u = 3, a = 4 and s = 2. Then find s when v = 13, u = 5 and a = 8.
Show worked solution
v2 = 9 + 16 = 25, so v = 5. Then 169 = 25 + 16s, so 16s = 144 and s = 9.
6 Find x when y = −4.
Show worked solution
−4 = (4 − 3x)/2, so −8 = 4 − 3x. Then 3x = 12 and x = 4. Check: (4 − 12)/2 = −4.
Level 3 · Challenge
7 Three rearrangements:
1 If F = ma + k, then a = F/m − k.
2 If T = 2(p + q), then q = T/2 − p.
3 If w = 5 − 3(x + 1), then x = (2 − w)/3.
Which statements are correct?
1 If F = ma + k, then a = F/m − k.
2 If T = 2(p + q), then q = T/2 − p.
3 If w = 5 − 3(x + 1), then x = (2 − w)/3.
Which statements are correct?
Show worked solution
F − k = ma, so a = (F − k)/m; F/m − k divides before subtracting (1 ✗). T/2 = p + q, so q = T/2 − p (2 ✓). w = 5 − 3x − 3 = 2 − 3x, so 3x = 2 − w and x = (2 − w)/3 (3 ✓). 2 and 3.
8 A ball is thrown straight up at 30 m/s. Its velocity after t seconds is v = u + at with u = 30 and a = −10. Find v when t = 4, and find t when v = −15.
Show worked solution
v = 30 + (−10)(4) = 30 − 40 = −10 m/s. Then −15 = 30 − 10t, so 10t = 45 and t = 4.5 s.
9 Make x the subject of y = 3(x − 4)/2 + 5, then find x when y = −4.
Show worked solution
x = 2(y − 5)/3 + 4. With y = −4: 2(−9)/3 + 4 = −6 + 4 = −2. Check: 3(−6)/2 + 5 = −9 + 5 = −4.