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