Book 1
Algebra
N1t
1. Answer 14 so Ben is correct. 2. Answer 2 so Mike is correct.
3. Answer 19 so Iain is correct.
4. (a) 10 (b) 3 (c) 4 (d) 12 (e) 13 (f) 50
(g) 2 (h) 44
5. (a) Correct (b) Correct (c) Correct (d) Wrong, should be 3
(e) Wrong, should be 0 (f) Correct
6. (a) 69 (b) 49 (c) 42 (d) 20 (e) 153 (f) 20
(g) 530 (h) 11 (i) 89 (j) 105
N2t
1. (a) 2𝑃 (b) 5𝑃
(c) 7𝑃 is seven times the number
(d) 10𝑃 = 60; 𝑃 = 6 so the last digit of the password is 6
2. (a) 5𝑥 (b) 7𝑡 (c) 6𝑎 + 10 (d) 2𝑝 + 3𝑞 (e) 5𝑟 + 8
(f) 4𝑢 + 3𝑣
3. Examples: 2𝑝 + 6𝑞 or 3𝑏 + 7𝑐 or 4𝑑 + 2𝑒, etc
4. Examples: 6𝑧 + 4 or 9𝑓 + 4 or 7𝑒 + 8, etc
5. Examples: 6𝑧 + 4 or 9𝑓 + 4 or 7𝑒 + 8, etc
6. Examples: 7𝑎 + 2𝑏 + 3𝑐 or 9𝑓 + 4 or 8𝑚 + 3𝑛 + 4𝑝, etc
7. (a) 4𝑝 (b) 10𝑦 (c) 3𝑝 (d) 5𝑧 (e) 𝑝𝑞
(f) 𝑏𝑐𝑑 (g) 5𝑟𝑠 (h) 𝑝2
8. (a) 7𝑦 (b) 10𝑝 (c) 4𝑥 (d) 4𝑦 (e) 4𝑑
(f) 4𝑝 + 2𝑞
9. (a) 7𝑝 + 7𝑞 (b) 13𝑦 + 9𝑣 (c) 4𝑥 + 7𝑦 (d) 5𝑐 + 4𝑑
(e) 7𝑥 + 7 (f) 7𝑦 + 3 (g) 5𝑥 + 7𝑦 (h) 11𝑥 + 10
10. (a) 6𝑥 (b) 5𝑎 (c) 6𝑝 (d) 4𝑡 (e) 7𝑟
(f) 3𝑥 (g) 5𝑝 (h) 7𝑟 (i) 8t (j) 4𝑎
11. (a) 8𝑥 (b) 8𝑟 (c) 17𝑝 (d) 5𝑡 (e) 13𝑠
(f) 4𝑥 (g) 22𝑟 (h) 8𝑝 (i) 11𝑠 (j) 0
(k) 19𝑠 − 3 (l) 15𝑟 + 12 (m) 3𝑥 + 9 (n) 8 (o) 5𝑡 + 9
(p) 11 + 𝑝 (q) 10𝑟 − 2 (r) 3𝑡 + 9𝑦 (s) 2𝑠 + 6𝑡
(t) 7𝑝 − 3 (u) 12
12. (a) 8𝑥 + 10𝑦 (b) 7𝑠 + 15𝑡 (c) 22𝑝 (d) 12𝑢 + 9𝑣 (e) 3𝑥 + 13𝑦
(f) 6𝑝 + 5𝑞 (g) 7𝑥 + 16 (h) 7𝑦 + 5 (i) 10𝑥 + 5𝑦 (j) 13𝑥 + 8
(k) 2𝑥 + 𝑦 (l) 10𝑥 + 11
13. (a) 7𝑥 + 3– 4𝑥 = (7𝑥– 4𝑥) + 3 = 3𝑥 + 3
(b) Add (or subtract) the like terms but not unlike terms
N3t
1. 𝐴 = 20 2. 10 3. 𝑘 = 11 4. 8
5. 𝑝 = 5 6. 40 7. 𝑅 = 36 8. 31
9. 𝐿 = 42 10. 22
N4s
1. (a) ÷ 𝟔 (b) +𝟖 (c) × 𝟖 (d) −𝟕
(e) −𝟗 (f) +𝟏𝟐 (g) ÷ 𝟏𝟔 (h) × 𝟓
2. (a) 𝟑 (b) 𝟓
3. (a) 𝟒 (b) 𝟏𝟒 (c) 𝟏𝟏 (d) 𝟓
4. (a) 𝟔 (b) 𝟑𝟐 ÷ 𝟔 = 𝟓 ∙ 𝟑𝟑.. (c) 𝟏𝟓 (d) 𝟒𝟎
N5s
1. (a) 𝑦 = 7𝑥 + 4 (b) 𝑏 = 3𝑎 + 1 (c) 𝑞 = 5𝑝 − 2
(d) 𝑣 = 2𝑢 − 7 (e) 𝑡 = 8𝑠 + 7
2. (a) 𝑦 = 2𝑥 + 1 (b) 𝑦 = 21 (c) 21
(c) Yes, the two answers are the same.
3. (a) 𝑏 = 3𝑎 − 15 (b) 𝑏 = 15 (c) 15
(c) Yes, the two answers are the same.
14 7 9
9
7
8 9 9 8
10
10
11
N6s
1. (a) 𝑥 = 6 (b) 𝑥 = 5 (c) 𝑥 = 14 (d) 𝑥 = 7
2. (a) + (b) ÷ (c) × (d) −
3. (a) 𝑥 = 4 (b) 𝑥 = 4 (c) 𝑥 = 5 (d) 𝑥 = 3
(e) 𝑦 = 5 (f) 𝑥 = 3 (g) 𝑥 = 18 (h) 𝑥 = 45
4. (a) 𝑎 = 4 (b) 𝑏 = 1 (c) 𝑐 = 12 (d) 𝑑 = 7
(e) 𝑒 = 4 (f) 𝑓 = 7 (g) 𝑔 = 670 (h) ℎ = 21
5. (a) 𝑝 = 7 (b) 𝑞 = 1 (c) 𝑟 = 13 (d) 𝑠 = 2
(e) 𝑡 = 8 (f) 𝑢 = 10 (g) 𝑣 = 50 (h) 𝑤 = 56
6. (a) 𝑖 = 11 (b) 𝑗 = 10 (c) 𝑘 = 20 (d) 𝑥 = 10
(e) 𝑚 = 7 (f) 𝑛 = 4 (g) 𝑦 = 800 (h) 𝑧 = 45
7. 𝑥 = 11, so Sandy is correct.
Whole Numbers
N7
1. (a) 0, 2, 7, 28 (b) 2, 7, 28 (c) 2, 7, 28 (d) 2, 28
(e) 2, 7 (f) 2, 28
2. (a) 6, 8, 17 (b) 2, 19 (c) 6, 8 (d) 2, 22
N8s
1.
3 5 4 5
3
3
5 7 6 4
6
6
6 14 13 8
16
7
12 6 11 3
17
7
11 14 8
13
5
12 9 16 7
16
6
9
2.
3.
4.
5. (a) 52 (b) 84 (c) 83 (d) 87
(e) 110 (f) 49 (g) 52 (h) 15
(i) 46 (j) 103 (k) 373 (l) 176
N9s
1. 6 2. 54 3. 143 4. 399 5. 306
6. 674 7. 1216 8. 55 9. 265 10. 2923
11. 2416 12. 4446 13. 6076 14. 6247 15. 1828
16. 1400g 17. 333g
18. (a) 283 (b) 230 (c) 441 (d) 107
19. (a) 612 (b) 512 (c) 432 (d) 1140
20. Yes, 2548 is more than the 2500 required.
N10s
1. 135 2. 567 3. 340 4. 184 5. 584
6. 576 7. 459 8. 161 9. 116 10. 116
11. 283 12. 224 13. 107 14. 121 15. 28
16. (a) 190 (b) 246 (c) 192 (d) 84
(e) 168 (f) 1300 (g) 115 (h) 432
17. (a) 50 (b) 2188 (c) 968 (d) 1580
(e) 1358 (f) 1513 (g) 838 (h) 1136
18. (a) 450 (b) 2188 (c) 78 408 (d) 1580
(e) 33 750 (f) 1513 (g) 838 (h) 1136
19. Yes, Eva will have 2 candles left over.
20. No, Cara needs 10 more candles.
21. Yes, there will be 2 chocolates left over.
22. Yes, Cara will have 10 mm of wood left over.
23. No, Eva needs another 20 mins to complete the course.
N11s
1. £ 5355 million 2. £74 166 666∙67 million per month
3. £13∙50 per person 4. 8 505 000 kg of CO2 5. 3248 bikes
6. (a) £4404 (b) £1486
7. 0∙7 litres more required (or 20 km short)
8. 6 trips 9. £64
N12s
1. 370 2. 6760 3. 43 950 4. 6500
5. 78 900 6. 549 000 7. 18 000 8. 223 000
9. 6 128 000 10. 4 11. 78∙3 12. 546∙8
13. 0∙42 14. 9∙45 15. 74∙12 16. 0∙021
17. 0∙565 18. 9∙664 19. 640 20. £96∙80
21. £12∙50 22. 36 500 passengers
23. (a) 40 mm (b) 1050 mm (c) 320 mm (d) 32 mm
(e) 126 mm (f) 1035 mm
24. (a) 3 cm (b) 76 cm (c) 107 cm (d) 3∙5 cm
(e) 53∙6 cm (f) 115∙5 cm
25. Yes, as 620 mm is between 600 mm and 650 mm.
26. Yes, Eva can get pieces of 4∙5 cm which will all be longer than 4 cm.
27. (a) 3000 ml (b) 25 000 ml (c) 180 000 ml (d) 500 ml
(e) 1500 ml (f) 12 300ml
28. (a) 5 l (b) 12 l (c) 1∙4 l (d) 0∙33 l
(e) 0∙5 l (f) 0∙75 l
29. Pranav needs to add 250 ml.
30. Yes, Sandy has 170 ml more than required.
31. (a) 5000g (b) 200g (c) 12 000g (d) 1200g
(e) 3600g (f) 10 200g
32. (a) 2kg (b) 8kg (c) 1∙5kg (d) 0∙5kg
(e) 0∙2kg (f) 0∙05kg
33. Cara must remove 200g of flour.
34. Yes, Jamie has 800g of flour more than required.
35. (a) 300p (b) 1500p (c) 20 000p (d) 550p
(e) 380p (f) 90p
36. (a) £4 (b) £32 (c) £7 (d) £2∙56
(e) £4∙20 (f) £0∙23
37. Yes, Ben has 20p more than required.
38. No, John needs an extra £6.
Negative Numbers
N13s
1. 3, −4, 0, 8 2. 21
2, 5 ∙ 1, −1 ∙ 2,
3
4
3. a 4. a, b, c 5. None
N14s
1. (a) −3, 1, 4 (b) −10, −2, 6 (c) −15, 0, 25 (d) −24, −8, 8
N15s
1. (a) 3 (b) 1 (c) 0 (d) 5 (e) 2 (f) 1
2. (a) 2 (b) −3
3. −5, −3, 0, 1, 2, 4
4. (a) −6 (b) −4 (c) −3 (d) 6
5. (a) −2, −1, 0, 3, 7 (b) −15, −8, 8, 12
6. (a) −8℃, −6℃, −4℃, −1℃, 2℃
(b) −15℃, −11℃, 6℃, 10℃, 14℃
(c) −25℃, −23℃, −13℃, 12℃, 16℃, 18℃, 20℃
N16s
1. (a) −14℃ (b) 29℃ (c) 22℃ (d) −16℃ (e) −2℃
2. (a) 2℃ (b) −2℃ (c) −4℃ (d) −3℃
3. (a) 5℃ (b) −3℃ (c) −1℃ (d) −1℃
N17t
1. (a) 10℃ (a) −4℃ (a) −35℃ (a) −20℃ (a) −7℃
2. (a) 8 − (−6) (b) 14℃
3. (a) −3 − 5 (b) −8℃
4. (a) −15 + 7 (b) −8℃
5. (a) −14 − 9 (b) −23℃
6. (a) −7 + 11 (b) 4℃
7. (a) 4℃ (b) −6℃
8. −16℃ 9. Rise of 16℃ 10. −6℃
11. (a) UK (b) Netherlands (c) 2℃ Netherlands
(d) −5℃ UK (e) −1 + 7 = 6℃
Book 4
M5s
1. 2m 2. 7 to 8m 3. 40 to 50m
4. 90-110m 5. 20cm, 16cm 6. 120cm, 60cm
7. 15-19cm 8. 15cm
M6s
1. Trundle wheel 2. Measuring tape 3. Measuring tape
4. Ruler 5. Ruler 6. Trundle wheel
M7s
Results of Practical Activity
M8s
1. (a) 70mm (b) 120mm (c) 86mm
(d) 34mm (e) 591mm (f) 7020mm
2. (a) 6cm (b) 40cm (c) 25cm
(d) 0.3cm (e) 400cm (f) 50cm
(g) 1700cm (h) 890cm (i) 908cm
(j) 360cm (k) 2cm (l) 175cm
3. (a) 3m (b) 50m (c) 14m
(d) 5.9m (e) 0.6m (f) 0.71m
4. (a) 19.3km (b) 8.65km (c) 0.45km
(d) 9km (e) 0.2km (f) 0.014km
5. (a) 24mm (b) 3200m (c) 1.8m
(d) 106cm (e) 0.76km (f) 3cm
(g) 56mm (h) 720m (i) 0.6935m
(j) 3425.6cm (k) 0.501km (l) 194cm
6. (a) 313mm (b) 201m (c) 0.503cm
(d) 4.3cm (e) 0.034km (f) 8.4681m
(g) 0.62mm (h) 1500m (i) 0.0002m
(j) 34.267cm (k) 0.000089km (l) 4300cm
7. (a) 7.1mm (b) 7800m (c) 8940cm
(d) 0.667cm (e) 0.231km (f) 0.0908m
(g) 8.02mm (h) 1050m (i) 0.27m
(j) 0.934cm (k) 0.0009091km (l) 20200cm
M9s
1. Metres 2. Millimetres 3. Kilometres
4. Metres 5. Centimetres
M10s
1. 120cm 2. 12cm 3. 7.2m
4. 120mm 5. 19.4cm or 194mm 6. 31.2cm
7. 28cm or 280mm
M11s
1. (a) 28.5m (b) No as 22 < 28.5
2 (12+9.5)=43m so no as 42 < 43
3. 30mm
4. Yes as 100cm > 90cm
5. (a) 19.2m (b) No as 45<48
M12t
Check accuracy of scale drawings
M13s
1. (a) 20 sq cm (b) 12 sq cm (c) 36 sq cm
(d) 12 sq cm (e) 16 sq cm (f) 38 sq cm
(g) 18 sq cm
2. 1x36, 2x18, 3x12, 4x9, 6x6
3. (a) 10 sq cm (b) 32 sq cm (c) 12 sq cm
(d) 18 sq cm (e) 18 sq cm (f) 20 sq cm
4. Check areas are 20,24,32
M14s
1. (a) 60 sq cm (b) 300 sq cm (c) 4 sq m
(d) 160 sq m
2. £2295
3. £148.65
M15t
1. (a) 15000 sq mm or 150 sq cm (b) 18 sq cm
(c) 270 sq m (d) 120 sq cm (e) 36 sq m
(f) 6 sq cm
2. 33 sq cm 3. 12.65 sq m
S16s
1. Check diagram
2. C=377m, D=120m and r=60m
3. r=32.5cm, D=65cm and C=204cm
4. r=40cm, D=80cm and C=250cm
S17t
1. Check diagrams r=4cm,r=36mm,d=9cm and d=60mm
2. Check diagram
S18t
1. Check diagram
2. Check diagram
S19s
1. 7cm 2. 12.3cm
S20s
1. 15700cm
2. 51000cm or 510m
3. (a) 257cm (b) 2570cm or 25.7m
Book 5
Volumes
M15s
1. 9 cubic cm 2. 8 cubic cm 3. 5 cubic cm
4. 6 cubic cm 5. 9 cubic cm 6. 9 cubic cm
7. (a) 45cm3 (b) 24cm3 (c) 24cm3
M16s
1. (a) 2 litres (b) 1∙4 litres (c) 0∙35 litres
(d) 0∙005 litres (e) 0∙568 litres (f) 0∙15 litres
(g) 0∙5 litres (h) 0∙75 litres (i) 3∙5 litres
(j) 160 litres (k) 5 litres (l) 0∙33 litres
2. (a) 160000 ml (b) 50000 ml (c) 2000 ml
(d) 333 ml (e) 4000 ml (f) 500 ml
(g) 568 ml (h) 750 ml (i) 50 ml
3. Examples could be
(a) oil drum (b) large storage box (c) bottle of water
(d) can of juice (e) milk carton (f) bottle of juice
(g) pint of beer (h) bottle of wine (i) travel toiletries
M17t
1. (a) 𝑉 = 𝑙𝑏ℎ (b) 55000cm3
(c) An extra 55000cm3
2. (a) 125cm3 (b) 72cm3
3. ℎ = 20cm
4. (a) 72cm3 (b) 162cm3 (c) 105cm3
(d) 100cm3
5. (a) 𝑉 = 𝑙𝑏ℎ (b) 20000cm3
6. (a) 216cm3 (b) 200cm3
7. ℎ = 2cm
8. (a) 72cm3 (b) 50m3 (c) 2500cm3
(d) 520m3 (e) 2150cm3 (f) 96m3
9. (a) 12cm3 (b) 144cm3
10. (a) 3m3 (b) 15m3
M18t
1. (a) 248cm3 (b) 5103cm3
2. 17982cm3 3. 2800cm3
4. 2560cm3 – shape is not a prism; it does not have a constant cross section.
3D Shapes
S21s
1. (a) 5 Faces (b) 6 Vertices (c) 9 Edges
2. (a) 5 Faces (b) 5 Vertices (c) 8 Edges
S22s
1. a) 2. b) 3. c)
4. c) 5. b) 6. a)
S23s
Worksheets
S24s
1. Various answers
2. (b), (c), (f), (g) are nets of cubes.
Book 6
Percentages
N25f
Revision
(a) 1
20 (b)
1
5 (c)
2
5
(d) 1
2 (e)
3
4 (f)
3
10
(g) 4
5 (h)
1
10 (i)
1
4
1. (a) 1
4= 0.25 (b)
1
2= 0.5 (c)
1
5= 0.2
(d) 7
10= 0.7 (e)
1
100= 0.01 (f)
1
10= 0.1
2. (a) 3
4= 0.75 (b)
1
20= 0.05 (c)
7
20= 0.35
(d) 3
20= 0.15 (e)
3
10= 0.3 (f)
17
20= 0.85
3. (a) 4
5= 0.8 (b)
2
5= 0.4 (c)
11
20= 0.55
(d) 1
2= 0.5 (e)
19
20= 0.95 (f)
13
20= 0.65
4. See Worksheet
5. (a) 50% (b)10% (c) 25%
(d) 20% (e) 5% (f) 75%
6. (a) 0.3 (b) 0.4 (c) 0.35
(d) 0.7 (e) 0.15 (f) 0.6
7. (a) 1
2= 50% (b)
1
4= 25% (c)
1
5= 20%
(d) 1
20= 5% (e)
1
10= 10% (f)
3
10= 30%
8. (a) 7
10= 70% (b)
3
20= 15% (c)
3
4= 75%
(d) 9
10= 90% (e)
13
20= 65% (f)
3
5= 60%
N26s
Section A
1. 60 2. 35ml 3. 68p 4. 18m2 5. 35g
Section B
6. £304 7. 243g 8. £245 9. £112.50 10. £252
Section C
11. £13.33 12. 65 13. 800 14. £504 15. £45
N27t
1. $423750 2. £23000 3. £71200 4. £984 5. £140800
Statistics and Graphs
D4s
1. Holiday Inn, Ibis, NH Hotel 2. All Round, Ultimate, Brand New
D5s
1. (a) 0.5 Billion (b) 6 Billion (c) 10 Billion
2. (a) 375 (b) 225
(c) Downward trend. Less people drink driving.
D6s
1. (a) Upwards (b) Lowered, as graph shows it decreasing at this
time
2. (a) Downwards (b) Approximately 1548
3. (a) Approximately 780 (b) Approximately 120
(c) Pedestrian – downward, Cycling – no change
D7t
1. (a) Banana (b) Grape (c) None
(d) 4 (e) 3 (f) 24
(g) Banana, Apple, Orange, Strawberry, Grape
2. (a)
(b)
(c) woodlice (d) wood ant
3.
(a) 10 (b) 5 (c) 5 (d) 1
(e) 7 (f) 6 (g) 27 (h) 2,1,3,4,5
4. (a)
(b) 3
D8t
1.
2.
3.
4. (a)
(b)
5. (a)
(b)
(c) Main theme – clothes shopping
Vast majority of those surveyed highlighted this as is what they liked
most.
D9t
1. (a)
(b)
Score Tally frequency
10-19
3
20-29
3
30-39
5
40-49
1
50-59 2
Total = 14
2. (a)
(b)
Score Tally frequency
1-10 1
11-20
3
21-30
5
31-40
6
41-50
3
Over 50
2
Total = 20
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