Cambridge International Mathematics

722 ANSWERS

eThere appears to be a weak, positive correlation between

minutes spent preparingandtest score. This means that as

the time preparing increases, the score increases.

f/g On the graph above. h¼ 31 marks

2ax¼ 6 : 88 , y=83: 5

b

c A moderate, positive correlation between the variables.

d/e On the graph above. f About 95 thefts per day.

3ax¼ 23 : 3 , y¼ 78 : 8

b

c There is a moderate, positive correlation betweennumber of

dinersandnoon temperature.

d/e On the graph above. fi 68 diners ii 93 diners

EXERCISE 22C

1aw¼ 0 : 903 h¡ 81 : 0 b 99 : 7 kg

2aspray concentration

b

c y¼ 7 : 66 x+40: 1

dThe slope indicates that an increase in concentration of

1 ml/ 2 litres will increase the yield by approximately 7 : 66

tomatoes per bush. The vertical intercept indicates that a bush

can be expected to produce 40 : 1 tomatoes when no spray is

applied.

e 94 tomates/bush. Even though this is an interpolation this

seems low compared with the yield at 6 and 8. Looking at

the graph it would appear that the relationship is not linear.

3anumber of lawn beetles

b

c y¼¡ 0 : 967 x+10: 8

d The slope indicates that an increase in chemical of 1 gram

will decrease the number of lawn beetles by 0 : 967 per square

metre of lawn. The vertical intercept indicates that there are

expected to be 10 : 8 beetles per square metre of lawn when

no chemical is applied.

e 4 beetles. This is an interpolation and since the correlation

is strong, the prediction is reasonable.

4a

b Y¼ 0 : 371 n+23: 1. A very strong, positive association.

ci¼ 34 : 6 ii¼ 38 : 7

d “......, thegreaterthe yield of cherries.”

5a

The linear model seems to fit exactly.

b C=0: 8 t+ 313 c 335 parts per million

d 361 parts per million

6a

The most likely model is linear.

b t¼ 0 : 0322 v+0: 906 ci 2 : 68 secs ii 4 : 44 secs

d 55 lies within the poles,)cishould be reasonably reliable.

110 lies outside the poles,) ciicould be unreliable.

e The vertical intercept is the reaction time, i.e., the time taken

for the driver to respond to the red light when the car is

stationary.

f A three second margin should allow sufficient time to avoid

a collision with the car in front, taking into consideration that

the car is slowing down as it comes to a stop.

REVIEW SET 22A

1aThe independent variable isWeeks of experience.

The dependent variable isDefective items.

biweak iinegative

2a

0

50

100

150

012345 67891011

no. of thefts per day,y

unemployed adults (%),x

()xy,¡

0

20

40

60

80

100

120

15 20 25 30

no. of diners

temperature (°C)

()xy,¡

0

50

100

150

0 5 10 15

x(ml/2 litres)

y(tomatoes/bush)

0

5

10

15

024 6810

x(g)

y

38

36

34

32

30

28

18 20 22 24 26 28 30 32 34 36 38

Yield,Y

Frosty morn ( )n

310

320

330

340

350

0 10203040

t(years)

C(ppm)

0

1

2

3

4

5

0 20406080100

v(km/h)

t(s)

0

10

20

30

0 5 10 15 20 25 30

x

y(km/h)

()xy,¡

IB MYP_3 ANS

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100 100
Y:\HAESE\IGCSE01\IG01_an\722IB_IGC1_an.CDR Wednesday, 19 November 2008 4:27:48 PM PETER