Topic test AnswersTopic test 1

1 D 2 B 3 A 4 D

5 C 6 C 7 C 8 A

9 C 10 A 11 D 12 A

13 D 14 C 15 B 16 C

17 B 18 C 19 C 20 D

21 36, 37, 38 or 39 22 a 12.62 b 10

23 Teacher to check 24 a 12

b 6 120

25 Roundedffiffiffi8p

too early103:8232:8284...¼ 36:7069 36:71

26 32

27 1115

28 2.32� 108

29 $3.50

30 40

31 3:1

32 $2820

33 a 1 : 200 000 b 16 km

34 112.5 g

35 a 7.5 m b scaled height 1.6 cm

36 a 24.64 L b 580 km

37 a 50 km/h b stopped c 45 mins

d increase e 12:15 pm f 12:45 pm

g 160 km

38 a $3455/month b 38 mL/min

Topic test 21 C 2 C 3 B 4 D

5 D 6 D 7 D 8 D

9 C 10 A 11 C 12 C

13 B 14 C 15 B 16 A

17 A 18 A 19 C 20 B

21 a 314.16 cm2 b 523.60 cm3

22 42 cm3

23 a 5 cm b 120 cm3

c 184 cm2

24 264 m3 25 605 cm2

26 94.25 m2

27 4 : 25

28 1897.52 cm 29 a 0.64 m3

b 4.02 m2

30 1250 cm2

31 a 1231.50 cm3b 729.80 cm2

32 a 40 cm b 3392.92 cm3 c 1413.72 cm2

34 19.10 cm

35 23

Topic test 31 B 2 A 3 C 4 D

5 C 6 A 7 B 8 D

9 A 10 A 11 D 12 A

13 C 14 B 15 D 16 C

17 B 18 B 19 B 20 B

21 a 50 b 6ffiffiffi2p

c 12ffiffiffi2p

d 10ffiffiffi1p

0 e 12 f 11ffiffiffi2p

gffiffiffi5p

h 6ffiffiffi3p

i 4ffiffiffiffiffi14p

� 2

22 affiffiffi2p

b iffiffiffi3p

ii 1.732

23 a -7 b 13

c 12a d

8

27k3

e -27w6f 64 a3

g 49 h 56

24 affiffiffiffiffih23p

orffiffiffih3p� �2

25 a 1þ 2ffiffiffi2p

b 105� 20ffiffiffi5p

c 9þ 2ffiffiffiffiffi14p

26 a 7ffiffi3p

4b 2

ffiffi5p�ffiffiffiffi10p

5

cffiffiffi2pþ

ffiffiffi3p

Topic test 41 B 2 B 3 A 4 D

5 D 6 A 7 B 8 B

9 B 10 B 11 C 12 D

13 D 14 C 15 A 16 A

17 B 18 C 19 C 20 B

21 a M = ± 9 b x = ± 5

c b = 0, - 14

22 a k = 12 311

b t = 5

23 a a = 12� 8b

b a = 2Ah � b or a = 2A�bh

h

24 a x = -4�ffiffi6p

2

b y = -1 23

or 3

c z = 2 12

25 a 21 cm by 7 cm

b 18 cm by 6 cm

26 Teacher to check

27

2

1

0 1 2 3

(3, 1)

x

y

x = 3, y = 1

-1

-1-2

-2

-3

-4

-5

188 NEW CENTURY MATHS 10: STAGES 5.2/5.3

28 x = -2, y = 1

29 7 years old

30 x = ± 1, ± 4

31 x = - 4 or 5

32 4 pigs, 92 chickens

Topic test 51 B 2 B 3 A 4 B

5 C 6 C 7 C 8 C

9 C 10 C 11 D 12 B

13 D 14 D 15 A 16 A

17 C 18 D 19 A 20 D

21 a = 228 (angle sum of a quadrilateral)

22 Proof by alternate angles

23 y = 105�

24 2xþ 2y = 180� (angle sum of DCAB)

25 r = 50

26 a exterior angle of triangle

b y = aþ c, z = aþ b

c xþ yþ z = 2(aþ bþ c) = 2� 180

27 e = 22, f = 68

28 a Proof by AA b 6 67

cm

29 Proof by AAS

30 a rhombus b diagonals bisect the angles

of a rhombus

31 Proof by SSS

32 2xþ 2y = 180 (angles on a straight line)

33 a AA bAC

AD=

AB

ACc CB2 = AB� DB

Topic test 61 B 2 A 3 A 4 D

5 D 6 A 7 B 8 A

9 A 10 B 11 D 12 C

13 C 14 C 15 B 16 C

17 B 18 C 19 B 20 D

21 a $294 b $1260

22 1.825%

23 a $16 882.29 b $2882.29

24 Monthly, because interest compounded more frequently

earns more money

25 a $15 438.30 b $12 561.70

26 a $163.50 b $926.50 c $34.74

d $961.24 e $36.97

27 $2552.90, $127.65

28 a $4926.96 b $4174.92

29 $812.78 30 $2108

31 a $2806.92 b $311.92 c 6.25% p.a.

32 $1800� $1350 = $450

33 7.1% p.a. 34 $495.22

35 a $720 b $92 800

Topic test 71 C 2 B 3 D 4 C 5 B 6 D

7 B 8 B 9 B 10 D 11 C 12 A

13 C 14 B 15 D 16 B 17 B 18 D

19 A 20 D 21 y ¼ 1

3xþ 2

22

x

y

x = -3

3

2

1

-1

-2

-3

4321-1-2-3-4 0

23 y = x� 7

24 Prove both pairs of opposite sides are parallel (or

diagonals bisect each other)

25 x-intercept 4, y-intercept 2

26 a Prove RS ’ TS

b RS ¼ ST ¼ffiffiffiffiffiffiffiffi125p

c 62.5 units2

27 7xþ 8y� 21 = 0 28 y ¼ -5

2x� 7

29 y ¼ 1

2x

30

3

4

2

1

-1

-2

-3

4321-1-2-3-4 0

y

x

31 2x� 5y� 5 = 0

32 a gradient 32, y-intercept -1

189ANSWERS

b

3

4

2

1

-1

-2

-3

-4

4321-1-2-3-4 0

y

6x – 4y – 4 = 0

x

33 a HJ ¼ IK ¼ffiffiffiffiffiffiffiffi145p

units

b Both midpoints�

4 12

,2�

c Rectangle, equal diagonals bisect each other

34 y: 0, -3, -4, -3, 0, 5

3

4

2

1

-1

-2

-3

-4

-5

321-1-2-3 0

y

y = x2– 4

x

Topic test 81 D 2 D 3 D 4 B 5 A

6 A 7 C 8 D 9 A 10 A

11 C 12 D 13 D 14 B 15 B

16 B 17 C 18 B 19 D 20 A

21 a 35� 180 b 108� 540 c 55� 510

22 50� 23 52�

24 a

b r2 = p2þ q2� 2pq cos R

25 37� 26 15.7 km 27 42�, 138�

28 129� 29 15.40 km 30 57�

31 -ffiffiffi3p

32 6 cm2 33 4.24 m

34 b 72 m 35 40�, 140� 37 b 21.2 m

Topic test 91 D 2 A 3 A 4 B 5 C

6 C 7 D 8 B 9 D 10 D

11 B 12 D 13 C 14 D 15 A

16 B 17 D 18 A 19 B 20 A

21 a 65 b 48 c 36.5 d 31

22 a Skewed b 6

c Around 1 to 2 days

23 a

c 3 d 2 24 85%

pRQ

P

rq

Score f cf

0 4 4

1 3 7

2 6 13

3 4 17

4 7 24

5 6 30

0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Cum

ulat

ive

freq

uenc

y

Number of calls per minute

b

190 NEW CENTURY MATHS 10: STAGES 5.2/5.3

25 a

b 100–109 c 98.75

26 a 25.86 b 2.28 c 4 d 25.5 e 25

27 a 53 b 74.5 c 12.5 d 38 e 12

f 10Z : higher median, box-and-whisker plot is further to

the right, i.e. towards higher rates.

g 10Y : the box and whiskers are wider.

Topic test 101 D 2 C 3 B 4 C 5 A 6 B

7 C 8 B 9 B 10 D 11 B 12 C

13 D 14 C 15 A 16 B 17 D 18 C

19 B 20 D 21 red, amber, green 22 12

23 a 1stdigit

1

4 14

15

41

45

51

54

5

1

1

5

4

4

5

2nddigit

Outcomes

b i 13

ii 13

iii 13

24 a No, there are two 4s so it’s more likely

b i 16

ii 13

iii 23

iv 56

25 Teacher to check

26 a 16

b 112

c 118

d 1136

27 a 1320

b 19 or 20

28 a 42% b 110

c 3750

d Choosing a student who doesn’t walk to school

e 256

29 a 25

b 23

30 a 1stchild

2ndchild

3rd child

BB

G

B BBBBBGBGBBGGGBB

GBGGGBGGG

GBGB

GBG

B

G

G

Outcomes

b 38

31 a i 111320

ii 310

b 311

Topic test 111 B 2 D 3 B 4 D 5 C

6 B 7 A 8 C 9 D 10 B

11 A 12 D 13 C 14 D 15 D

16 D 17 D 18 B 19 A 20 C

21 a Time of day

b 1000

c 3�4 am, 4�5 am or 2�3 pm

d 6 pm

e 7–8 am

22

6

8

10

12

14

4

2

-2

-4

-6

-8

-10

-12

321-1-2-3 0

y

x

(2, 2)

23 y ¼ 6x

24 a F b E c A d D

25 a 13

, 12

, 1, 2, -2, -1, - 12

, - 13

b -1� 0 has no value/meaning

Class

centre, X f f X

74.5 2 149

84.5 8 676

94.5 9 850.5

104.5 13 1358.5

114.5 8 916

Total 40 3950

191ANSWERS

c

3

2

1

-1

-2

-3

321-1-2-3 0

y

x

26 a concave down

b The coefficient of x2 is -1 (negative), so the parabola is

concave down.

c x = -1 d 3 e -3 and 1

27 a C b E c B d F

28

Temperature

Time

29

2

1

-1

-2

21-1-2 0 x

y

(-1, -2)

Topic test 121 A 2 A 3 A 4 B 5 B 6 B

7 D 8 B 9 C 10 A 11 D 12 A

13 C 14 D 15 B 16 C 17 A 18 C

19 A 20 B 21 k = 40 22 y = 145

23 r = 65 24 56 cm

25 ffCBD = ffDEB = ffEBD

26 x = 12 27 Proof by RHS

28 m = 48 29 x = 3

30 ffOPA = ffAPT = 45�, [ ffOAP = ffAPT

31 a ffOCB = 90� (angle between tangent and radius)

b ffCOD = 180�� 2(90�� x) = 2x

c ffDEC ¼ 12ð2xÞ ¼ x ¼ ffDCB

d The angle between a tangent and a chord is equal to the

angle in the alternate segment.

32 ffTAO = ffTBO = ffAOB = 90�, TA = TB

Topic test 131 C 2 D 3 C 4 B 5 B 6 B

7 B 8 C 9 A 10 A 11 B 12 C

13 a x3þ 2x2� xþ 5 b 97

c x4� 2x3� 8x2þ x� 4 d 1

14 y

x-6 20

a

y

x-4 -2 3

24b

15 (x� 3)2þ y2 = 25

16

y

x-2

12

a

192 NEW CENTURY MATHS 10: STAGES 5.2/5.3

y

x-1

b

17

y

x-1-1

4

5

3

2

1

-2

-2

-3

-3

-4

-4(-2, -3)

18 a P(-5) = 0 b (xþ 4)(xþ 5)(2x� 1)

c x = -4, -5 or 12

19 Centre (-10, 6), radius 1

20

y

y = A(x)

x

a

12

y = A(x) + 2

y = -A(x)

y

x

b

y

x

y = A( -x)

c

21 x = 2, y = 4

22 a H(1) = 0 b - (xþ 2) (x� 1) (x� 6)

y = H(x)

y

x

c

-2 1 6

-12

Topic test 141 C 2 C 3 C 4 B 5 A 6 A

7 B 8 B 9 B 10 A 11 C 12 D

13 C 14 A 15 A 16 C 17 C 18 B

19 D 20 D 21 a -3 b 13

c x = 27

22 a x „ 2 b y „ 0

23

y

x

y = f (x + 2)

-2

24 a y = x � 68

b y = - 3x

25 a 0 b 5 c - 2 d 13

26 log5 15 625 = 6

27 3y = x

193ANSWERS

28 Teacher to check

29 a 7 b 1 c loga 100 d logx 14

30 a logu 3 þ 12

logu 5 b loga 4þ 3

31 a xþ y b 12

y

32 a 4.755 b - 3.17 c 2.585

33

y

x1

(2, 1)

34 a k J 7.36 b x = 1296 c x J 1.89

194 NEW CENTURY MATHS 10: STAGES 5.2/5.3