Module 1 · Answers
Answers & working
Workings shown so you can see where each answer comes from.
Section A — Easy
01
−7, −3, −1, 0, 2, 5
02
(a) −4 > −9 (b) −2 < 1 (c) 0 > −5
Remember: on a number line, further right = bigger.
03
−8°C
−2 − 6 = −8
04
(a) 3 (b) −5 (c) −9 (d) 9
(c) −6 + (−3) = −6 − 3 = −9
(d) 7 − (−2) = 7 + 2 = 9
(d) 7 − (−2) = 7 + 2 = 9
05
(a) −6 (b) 4 (c) −6 (d) −10
(b) −3 − (−7) = −3 + 7 = 4
(c) 2 + (−8) = 2 − 8 = −6
(c) 2 + (−8) = 2 − 8 = −6
06
(a) −20 (b) 18 (c) −6 (d) 3
Same signs → positive (b, d). Different signs → negative (a, c).
07
(a) −8 (b) 25
(a) −2 × −2 = +4, then +4 × −2 = −8
(b) (−5)² = (−5) × (−5) = 25
(b) (−5)² = (−5) × (−5) = 25
08
21, 25, 29
Common difference is +4, so keep adding 4.
09
−3 (it's going down by 3 each time)
Section B — Medium
10
−10
(−3) + (−5) − (−2) − 4
= −3 − 5 + 2 − 4
= −10
= −3 − 5 + 2 − 4
= −10
11
23°C
8 − (−15) = 8 + 15 = 23
12
−8
−24 ÷ (−6) = +4 (same signs)
+4 × (−2) = −8 (different signs)
+4 × (−2) = −8 (different signs)
13
nth term = 4n + 3
Common difference = 4, so start with 4n.
When n = 1: 4(1) = 4, but term 1 is 7, so add 3.
Check: 4(2) + 3 = 11 ✓
When n = 1: 4(1) = 4, but term 1 is 7, so add 3.
Check: 4(2) + 3 = 11 ✓
14
nth term = −3n + 33 (or 33 − 3n)
Common difference = −3, so start with −3n.
When n = 1: −3(1) = −3, but term 1 is 30, so add 33.
Check: −3(2) + 33 = 27 ✓
When n = 1: −3(1) = −3, but term 1 is 30, so add 33.
Check: −3(2) + 33 = 27 ✓
15
3, 8, 13, 18
n = 1: 5(1) − 2 = 3
n = 2: 5(2) − 2 = 8
n = 3: 5(3) − 2 = 13
n = 4: 5(4) − 2 = 18
n = 2: 5(2) − 2 = 8
n = 3: 5(3) − 2 = 13
n = 4: 5(4) − 2 = 18
16
Yes — 100 is the 32nd term.
Set 3n + 4 = 100
3n = 96
n = 32
Since n = 32 is a whole number, 100 IS in the sequence.
3n = 96
n = 32
Since n = 32 is a whole number, 100 IS in the sequence.
17
(a) Geometric (×2): 32, 64 (b) Square numbers: 25, 36 (c) Fibonacci: 8, 13
Section C — Hard
18
−205m
Start: −180
Rises 45m: −180 + 45 = −135
Dives 70m: −135 − 70 = −205
Rises 45m: −180 + 45 = −135
Dives 70m: −135 − 70 = −205
19
−19
(−2)³ = −8
(−3)² = 9
(−4) × (−5) = 20
So: −8 + 9 − 20 = −19
(−3)² = 9
(−4) × (−5) = 20
So: −8 + 9 − 20 = −19
20
51
2(5)² + 1 = 2(25) + 1 = 50 + 1 = 51
21
n = 4 (both give 19)
Set 4n + 3 = 6n − 5
3 + 5 = 6n − 4n
8 = 2n
n = 4
Check: 4(4) + 3 = 19, and 6(4) − 5 = 19 ✓
3 + 5 = 6n − 4n
8 = 2n
n = 4
Check: 4(4) + 3 = 19, and 6(4) − 5 = 19 ✓
22
(a) d = 4 (b) first term = 3 (c) nth term = 4n − 1
From term 3 to term 7 is 4 steps. Value goes from 11 to 27, increase of 16.
Common difference = 16 ÷ 4 = 4.
First term = 11 − 2 × 4 = 3.
nth term: 4(1) − 1 = 3 ✓
Common difference = 16 ÷ 4 = 4.
First term = 11 − 2 × 4 = 3.
nth term: 4(1) − 1 = 3 ✓
23
After 10 weeks
Need to go from 50 to −30, a change of −80.
At £8 per week: 80 ÷ 8 = 10 weeks.
At £8 per week: 80 ÷ 8 = 10 weeks.