Cambridge International Mathematics

ANSWERS 723

bx=13: 6 , y=14: 6 c/d On the graph.

ei 21 km/h ii 31 km/h

3a

bThere is a strong, positive correlation between spray

concentrationandyield of strawberries.

cThis suggests that the higher the spray concentration, the

higher the yield of strawberries.

dy¼ 3 : 45 x+5: 71

ei 16 strawberries/plant ii 40 strawberries/plant

fAs 10 lies outside the data range, this involves extrapolation

and therefore may not be a reliable prediction.

4aThe width of the whorl is the dependent variable, the position

of the whorl is the independent variable.

b

cThere is a very strong, positive association between the

variables.

dw¼ 0 : 381 p+0: 336

e 5 : 67 cm Asp=14is outside the poles, this prediction

could be unreliable.

REVIEW SET 22B

1aThe independent variable isage. b No association exists.

cIt is not sensible to find it as the variables are not linearly

related.

2a

A linear model does seem appropriate.

bn=6: 5 , d=81: 2 c/d On the graph.

eAbout 210 diagnosed cases.

Very unreliable as is outside the poles. The medical team

have probably isolated those infected at this stage and there

could be a downturn which may be very significant.

3a

bR¼¡ 0 : 106 I+9: 25 c 4 : 48 per 1000 people

dE100 000gives a rate of¡ 1 : 35 which is meaningless,

i.e.,E100 000is outside the data range of this model.

eiI=25, R =7: 3 This goes against the trend of

decrease inRfor increase inI.

ii b R¼¡ 0 : 104 I+9: 08 c 4 : 4 per 1000 people

4a

bA moderate, positive association exists betweenxandV.

cV¼ 305 x¡ 3050 dollars

dThe points clearly lie on a curve and not on a straight line.

Also, when x=0,V¼¡ 3050 dollars.

eAs we cannot use the model inc, we need to draw a smooth

curve through the points and extend it tox=50.

A reasonable estimate is V ¼$28 000 (if the trend

continues).

EXERCISE 23A.1

1af(x)=x^3 ¡ 7 x+6 b f(x)=2x^3 +9x^2 +x¡ 12

cf(x)=2x^3 +3x^2 ¡ 12 x¡ 20

df(x)=x^3 +3x^2 +3x+3

2a

b

c

0

10

20

30

40

024 6810

x(ml/litre)

y(strawberries/plant)

0

1

2

3

4

02 46 810

p

w(cm)

0

50

100

150

0246 81012

n(days)

d

()nd,¡

200

250

14

0

2

4

6

8

10

0 20 40 60 80 100

I(€ ’000)

R

0

5000

10000

15000

20000

0 1020304050

V($)

x

0

5000

10000

15000

20000

0 1020304050

V($)

x

25000

30000

y

x

-1

6

23

@=(!+1)(!-2)(!-3)

O

@ = -2(! + 1)(! - 2)(! -Qw_)

y

-1 x

-2

Qw_ 2

O

@=Qw_!(!-4)(!+3)

y

x

-3 4

O

IB MYP_3 ANS

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\723IB_IGC1_an.CDR Wednesday, 19 November 2008 4:34:32 PM PETER