Cambridge International Mathematics

694 ANSWERS

9 b=¡ 3

10 a AB=BC=5units b X(^12 ,^12 )

c gradient BX£gradient AC=7£¡^17 =¡ 1

REVIEW SET 12B

1a(¡ 3 ,3) b

p

58 units c ¡^32

2a b

c

3 m=2§ 3

p

5 4 Bis(5,¡4) 5a¡ 1 bundefined

6aThe value of 60 at A indicates that the plumber charges a

call-out fee of$60.

bAB has gradient 50 ; BC has gradient 40

These gradients indicate the average hourly charge for the

time intervals 06 h 63 (AB) or h> 3 (BC).

c AC has gradient 46 which means that the plumber charges an

average of$46per hour for a job lasting 5 hours.

7aD(4,¡3) b 5 units 8 c=20 9 a=¡ 8

10 a gradient AB=gradient DC=^15

bgradient AD=gradient BC=¡ 2

c ABkDC and ADkBC) ABCD is a parallelogram.

d(^12 ,^12 ); diagonals bisect each other

CHALLENGE

1a

p

(b+a)^2 +c^2 units b

p

(b¡a)^2 +c^2 units

dThe perpendicular bisector of the base of an isosceles triangle

passes through its apex.

2aBis(a+b,c) bmidpoint of AC is

³a+b

2

,c

2

́

midpoint of OB is

³a+b

2

,

c

2

́

c The diagonals of a parallelogram bisect each other.

3aax+cy=a^2 +c^2 and (b¡a)x¡cy=b^2 ¡a^2 ¡c^2

bx-coord. of S isb c RS is a vertical line.

dThe perpendicular bisectors of the sides of a triangle are

concurrent.

EXERCISE 13A

1acategorical b numerical c categorical

dnumerical e numerical f categorical

gcategorical h numerical

2amale, female

bsoccer, gridiron, AFL, rugby league, rugby union, Gaelic

c black, blond, brown, grey, red

3asample bcensus c sample d census esample

f sample

5aquantitative discrete bquantitative continuous

c quantitative discrete dquantitative discrete

equantitative discrete f quantitative continuous

gquantitative discrete h quantitative continuous

i quantitative continuous j quantitative discrete

EXERCISE 13B.1

1anumber of pets in a household

b Discrete, since you can’t have part of a pet.

c

d positively skewed e30% f 15%

2a 45 shoppers b 18 shoppers c 15 :6%

d positively skewed

3anumber of toothpicks in a box b discrete

c No. of toothpicks Tally Freq.

47 j 1

48 ©jjjj© 5

49 ©jjjj©©©jjjj 10

50 ©©jjjj©©jjjj©©jjjj©jjjj©jjj 23

51 ©jjjj©©©jjjj 10

52 ©jjjj©jjjj 9

53 jj 2

d

e approximately symmetrical f 38 :3%

4aNo. of accidents/month Tally Freq.

3 jj 2

4 jjjj 4

5 jjj 3

6 ©©jjjjj 6

7 ©©jjjj©jjjj© 10

8 ©©jjjjjjj 8

9 jjj 3

b Yes, negatively skewed.

c

d The distribution seems to have shifted towards the lower end.

Before there were 11 times when 9 or more accidents/month

occurred, now only 3.

y

x

5 y¡=¡5

O

y

x

O

y

x

-3

x¡=¡-3

O

0

2

4

6

8

01234

no. of pets

frequency

Number of household pets

Toothpicks in a box

0 5 10 15 20 25

47

48

49

50

51

52

53

number oftoothpicks

frequency

0

5

10

23456789101112

no. of accidents/month

frequency

before upgrade

after upgrade

Comparison of number of accidents

IB MYP_3 ANS

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\694IB_IGC1_an.CDR Thursday, 20 November 2008 4:10:26 PM PETER