A triangle has side lengths of (10a+9)(10a+9) centimeters, (8a-3)(8a−3) centimeters, and (10b+7)(10b+7) centimeters. Which expression represents the perimeter, in centimeters, of the triangle

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1.1 Multiplication and Division

1. (a) 20 (b) 21 (c) 36 (d) 42 (e) 45 (f) 18

(g) 28 (h) 49 (i) 40 (j) 8 (k) 9 (l) 4

(m) 7 (n) 7 (o) 9 (p) 0 (q) 0 (r) 0

2. (a) 3 (b) 7 (c) 4 (d) 8 (e) 3 (f) 4 (g) 9

(h) 7 (i) 3 (j) 7 (k) 4 (l) 5 (m) 2 (n) 4

(o) 7 (p) 0 (q) 0 (r) 0

3. 24

4. 27

5. (a) 16 (b) 28 (c) 32

6. (a) 6 (b) 3 (c) 4

7. 8

8. (a) 35 (b) 14 (c) 42

9. (a) Daniel 70p, Joel 56p (b) Daniel has 14p more than Joel

10. (a) 80 (b) 64 (c) 40

11. £6

12. (a) 9 (b) 7, with 1 left over

13. Team A: 7, Team B: 21, Team C: 14, Team D: 14 14. (a) 7 (b) 5

1.2 Squares, Cubes, Square Roots and Cube Roots

1. (a) 25 (b) 36 (c) 1 (d) 49 (e) 6 (f) 1 (g) 7

(h) 5

2. (a) 27 (b) 64 (c) 216 (d) 1000 (e) 3 (f) 10

(g) 6 (h) 4

3. (a) 100 (b) 4 (c) 16 (d) 49 (e) 64 (f) 81

(g) 1 (h) 343 (i) 512 (j) 0 (k) 0 (l) 8

4. (a) 10 (b) 2 (c) 9 (d) 8 (e) 4 (f) 3

5. (a) 144 (b) 121 (c) 3375 (d) 2197 (e) 169 (f) 225

(g) 400 (h) 1331 (i) 11 (j) 20 (k) 13 (l) 15

(m) 15 (n) 13 (o) 12 (p) 11

6. (a) 52 (b) 5 (c) 116 (d) 25 (e) 16 (f) 72

(g) 1001 (h) 100

MEP Pupil Text 1-6 Answers

252

1.3 Index Notation

1. (a) 45

(b) 33

(c) 67

(d) 74

(e) 183

(f) 192

(g) 46 (h) 75

(i) 106

(j) 1005

2. (a) 81 (b) 625 (c) 2401 (d) 10 000 (e) 1 (f) 729

(g) 128 (h) 2 (i) 4096 (j) 4 (k) 1 (l) 25

3. (a) 211 (b) 39

(c) 313 (d) 45

(e) 54

(f) 55

(g) 42 (h) 53

(i) 32 (j) 74

(k) 172 (l) 94

(m) 45

(n) 416 (o) 36 (p) 3 1 0 = (q) 3 3 1 =

(r) 35 (s) 37

(t) 47 (u) 50

4. (a) 22 (b) 23

(c) 24 (d) 26

(e) 33

(f) 52

(g) 43

(h) 34

(i) 53

5. (a) 313 (b) 28

(c) 411 (d) 310 (e) 29

(f) 210

(g) 35 (h) 37

(i) 35 (j) 810 (k) 73

(l) 92

(m) 2 4 4 2 or (n) 23

(o) 23

6. (a) 23

(b) 103

(c) 24 (d) 33

(e) 34

(f) 104

(g) 54

(h) 43

(i) 64

(j) 20 (k) 62

(l) 50

7. (a) 26

(b) 34

(c) 66

(d) 56

(e) 28

(f) 46

(g) 38

(h) 58

(i) 36

8. (a) 28

(b) 24 (c) 310 (d) 53

(e) 105 3

( ) (f) 75 4

( )

9. (a) 36 (b) 214 (c) 512 (d) 73

(e) 74

(f) 27

(g) 3 1 0 = (h) 4 4 1 = (i) 2 2 1 =

10. (a) a5

(b) a10 (c) x9 (d) x2 (e) y3

(f) p3

(g) q3

(h) x8

(i) b3

(j) b6

(k) c3

(l) x5

(m) y2

(n) x 0 = 1 (o) x8

(p) p4 (q) x3

(r) y4

(s) x 0 = 1 (t) x x 1 = (u) x12 (v) x8

(w) x15

(x) x54

11. (a) p = 3 (b) q = 0

12. 2 4 x

MEP Pupil Text 1-6 Answers

253

1.4 Factors

1. (a) 1, 2, 7, 14 (b) 1, 3, 9, 27 (c) 1, 2, 3, 6 (d) 1, 3, 5, 15

(e) 1, 2, 3, 6, 9, 18 (f) 1, 5, 25 (g) 1, 2, 4, 5, 8, 10, 20, 40

(h) 1, 2, 4, 5, 10, 20, 25, 50, 100 (i) 1, 3, 5, 9, 15, 45

(j) 1, 2, 5, 10, 25, 50 (k) 1, 2, 3, 4, 6, 9, 12, 18, 36 (l) 1, 2, 4, 7, 14, 28

2. (a) 1 10 2 5 5 2 10 1 × ×× × ,,, (b) 1 82 44 28 1 ×× × × ,,,

(c) 1 77 1 × × , (d) 1 93 39 1 ××× , ,

(e) 1 16 2 8 4 4 8 2 16 1 × ××× × (f) 1 22 2 11 11 2 22 1 ×× ×× ,,,

(g) 1 11 11 1 × × ,

(h) 1 24 2 12 3 8 4 6 6 4 8 3 12 2 × × ×××× × , , 24 1 ×

3. (a) 4 (b) 3 (c) 3 (d) 4 (e) 5 (f) 4 (g) 11

(h) 1

4. (a) 6, 10, 20, 8, 2, 24, 4 (b) 10, 20, 15, 55

5. (a) (i) 20, 22, 24, 26 (ii) 21, 24, 27 (iii) 20, 25

(b) prime numbers

6. (a) (i) 16 (ii) 18 (b) (i) 25 (ii) 27

1.5 Prime Factors

1. 2, 3, 5, 7, 13, 19, 23

2. 53, 59

3. (a) 2 5 × (b) 237 × × (c) 2 17 2 × (d) 2 37 3 × ×

(e) 2 53 × (f) 23 5 3 × × (g) 3 11 13 × × (h) 3 5 11 2 × ×

(i) 7 11 13 × ×

4. (a) 32 25 = and 56 2 7 3 = × (b) 2 8 3 (= )

5. (a) 236 × = (b) 236 × = (c) 3 5 15 × = (d) 2

(e) 2 5 10 × = (f) 5 7 35 × = (g) 2 3 24 3 × =

(h) 2 3 13 78 ×× = (i) 3 7 147 2 × =

6. (a) 45 3 5 2 = × , 99 3 11 2 = × , 135 3 5 3 = ×

(b) (i) 3 9 2 = (ii) 3 9 2 = (iii) 3 5 45 2 × = (c) 3 9 2 =

7. (a) 5 (b) 3 5 45 2 × = (c) 2 8 3 = (d) 2 5 10 × =

(e) 2 3 24 3 × = (f) 2 3 5 30 ××= (g) 2 3 108 2 3 × =

(h) 2 11 44 2 × = (i) 2 3 7 252 2 2 × ×=

MEP Pupil Text 1-6 Answers

254

1.6 Further Index Notation

1. (a) 1

16 (b) 1

8

(c) 1

6

(d) 1

7

(e) 3 (f) 8 (g) 2

(h) 3 (i) 1 (j) 1

25 (k) 8 (l) 32 (m) 2187

(n) 125 (o) 1

2

2. (a) – 4 (b) – 1 (c) – 3 (d) 1

2

(e) − 1

2

(f) 2

(g) 3 (h) – 1 (i) 1

3

(j) – 1 (k) – 2 (l) – 2

(m) – 3 (n) 1

2

(o) – 2 (p) 1

3

(q) 2

3

(r) 2

5

3. (a) 0.125 (b) 0.05 (c) 2 (d) 4 (e) 1

225 = 0 004444 . ...

(f) 0.000125 (g) 729 (h) 27 (i) 1

2

(j) 1728

(k) 62748517 (l) 1331

4. (a) 1

a

(b) a10 (c) a4 (d) 1

6 a

(e) 1

2 a

(f) 1

6 a

(g) a8

(h) a

5

2 (i) 1

3

2 a

(j) a2 (k) 1

3 a

(l) a3

(m) a

b

2

2 (n) a

b

6

12 (o) a b 12 2 (p) b

a

4

4 (q) a

b

8

12

(r) m

n

2

6 (s) a

b

3

5 (t) m

a

2

(u) c

a b

3

4 (v) x

m2

(w) z

x y

12

8 4 (x) b

a

16

3

2

5. (a) 1

9

(b) a4 (c) y = 5

2

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