Cambridge Essentials Mathematics Extension 9 A4.2 …essentials.cambridge.org/media/CEMKS3_E9_A4_2_WS_ANS.pdfCambridge Essentials Mathematics Extension 9 A4.2 Answers A4.2 Answers

Cambridge Essentials Mathematics Extension 9 A4.2 Answers

A4.2 Answers

1 a i

x –3 –2 –1 0 1 2 3

y –10 –7 –4 –1 2 5 8

ii

x –3 –2 –1 0 1 2 3

y –1 1 3 5 7 9 11

iii

x –3 –2 –1 0 1 2 3

y 4.5 5 5.5 6 6.5 7 7.5

iv

x –3 –2 –1 0 1 2 3

y 4 5 6 7 8 9 10

v

x –3 –2 –1 0 1 2 3

y –15 –12 –9 –6 –3 0 3

Original Material © Cambridge University Press 2010 1


b i (0, –1)

ii (0, 5)



iii (0, 6)

iv (0, 7)



v (0, –6)

2 a i

x –3 –2 –1 0 1 2 3

y 8 7 6 5 4 3 2

ii

x –3 –2 –1 0 1 2 3

y 12 10 8 6 4 2 0

iii

x –3 –2 –1 0 1 2 3

y 16.5 15 13.5 12 10.5 9 7.5

iv

x –3 –2 –1 0 1 2 3

y 35 30 25 20 15 10 5

v

x –3 –2 –1 0 1 2 3

y 18 14 10 6 2 –2 –6



b i (0, 5)

ii (0, 6)



iii (0, 12)

iv (0, 20)



v (0, 6)

3 a (0, 1) and (–13

, 0)



b (0, 3) and (–32

, 0)



c (0, 52

) and (–5, 0)

d (–3, 0) and (0, 2)



e (0, 3) and (32

, 0)



f (0, –6) and (–4, 0)

4

The lines are all parallel.



5 a 4, (0, –3) b –2, (0, 6) c 6, (0, 1)

d 6, (0, –12) e 12

, (0, 5) f 3, (0, 8)

g 0.3, (0, 2) h 23

, (0, –8) i 34

, (0, –14

)

6 a y = 52

x – 2, 52

, (0, –2) b y = 2x + 3, 2, (0, 3)

c y = 7 – 3x, –3, (0, 7) d y = 2x + 5, 2, (0, 5)

e y = 2 – 53

x, –53

, (0, 2) f y = 4.5 – 3x, –3, (0, 4.5)

g y = 54

x, 54

, (0, 0) h y = 5x – 7, 5, (0, –7)

i y = 25

– 25

x, –25

, (0, 25

)

7 a, c and e are parallel lines and all have gradient of 3.

8 a y = 3x – 1 b y = x + 3 c y = 3x – 6 d y = 13

x + 2

e y = –2x + 6 f y = –4x + 2

9 (1, 2.5)

10 a (0, 3.5) b (–1, 2.5)

11 a (–0.5, 2.5) b (4, 1) c (3, 0) d (2.5, –0.25)

12 a (1, –0.5) b (1.5, –0.5) c (–5, 4)

13 For example: (5, 3) and (1, 1); (0, 0) and (6, 4); (4, 3) and (2, 1)

14 a –15

b –14

c 16

d –5 e –74

15 a –12

b –14

c –3 d 1 e 12

f –43

g 52

h –1



16 c y = 6 – 14

x

17 a y = –2x b y = –2x + 7 c y = –2x – 3

18 a y-changex-change

= 0 − 68 − 0

= –68

= –34

b y = –34

x + 6

c i y = 43

x + 6 ii y = 43

x – 73

19 a y = x3

b y = 4x c y = x – 5 d y = x + 2

e y = x − 2

3 f y =

x + 52

g y = x − 1

5 h y = 3(x + 4)

20 a i y = 6 – x

ii y = 6 – x (the inverse of the function is the same as the original function)

b i y = 8 – x

ii y = 8 – x or x + y = 8 (the inverse of the function is the same as the original function)

c i y = 6 – 2x ii y = 6 − x

2

d i y = 12 – 3x ii y = 12 − x

3

e i y =8 − 3x

4 ii y =

8 − 4x3

f i y = 2x − 12

3 ii y =

12 + 3x2

g i y = 20 − 5x

2 ii y =

20 − 2x5



21 a

b

c



22 reflection in the line y = x

23 a i

x –3 –2 –1 0 1 2 3

y 13 8 5 4 5 8 13

ii

b i

x –3 –2 –1 0 1 2 3

y 13 3 –3 –5 –3 3 13



ii

c i

x –3 –2 –1 0 1 2 3

y –5 0 3 4 3 0 –5



ii

d i

x –3 –2 –1 0 1 2 3

y –8 2 8 10 8 2 –8

ii



e i

x –3 –2 –1 0 1 2 3

y 1 –2 –3 –2 1 6 13

ii

f i

x –3 –2 –1 0 1 2 3

y 15 9 5 3 3 5 9



ii

g i

x –3 –2 –1 0 1 2 3

y –4 –6 –6 –4 0 6 14



ii

h i

x –3 –2 –1 0 1 2 3

y 20 13 8 5 4 5 8



ii

24 a minimum is 4, at x = 0 b minimum is –5, at x = 0

c maximum is 4, at x = 0 d maximum is 10, at x = 0

e minimum is –3, at x = –1 f minimum is 2.75, at x = 0.5

g minimum is –6.25, at x = –1.5 h minimum is 4, at x = 1

25 a minimum, –7, at x = 0 b maximum, 5, at x = 0

c minimum, 12, at x = 0 d maximum, 7, at x = 0



26 a

t 0 1 2 3 4

h 0 9 12 9 0

b

c 12 metres

d about 2.3 seconds (accept answers 2.2 seconds to 2.4 seconds)

27 a i

x –3 –2 –1 0 1 2 3

y –27 –8 –1 0 1 8 27



ii

b i

x –3 –2 –1 0 1 2 3

y –22 –3 4 5 6 13 32

ii



Original Material © Cambridge University Press 2010

c i

x –3 –2 –1 0 1 2 3

y 29 10 3 2 1 –6 –25

ii

d i

x –3 –2 –1 0 1 2 3

y 37 18 11 10 9 2 –17

ii

28 a (0, 0) b (0, 5) c (0, 2) d (0, 10)

29 graph 1 d graph 4 c

graph 5 a graph 2 f

graph 6 b graph 3 e

24

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Cambridge Essentials Mathematics Extension 9 A4.2 …essentials.cambridge.org/media/CEMKS3_E9_A4_2_WS_ANS.pdfCambridge Essentials Mathematics Extension 9 A4.2 Answers A4.2 Answers