Cambridge International Mathematics

ANSWERS 693

EXERCISE 12D.2

1a 114 b Tan walks at 114 metres per second.

cConstant as the gradient is constant.

2a 105 km/h bi 115 km/h ii 126 : 7 km/h

cFrom time 2 hours until time 5 hours.

3aThey-intercept(0,40)indicates that taxi drivers earn a base

rate ofE 40 before doing any work.

bThe gradient of 18 means that a taxi driver earnsE 18 per

hour of work.

ciE 148 iiE 310 d E 23 per hour

4aA has gradient^35029 ¼ 12 : 1 ; B has gradient^32033 ¼ 9 : 70

bA travels 12 : 1 km per litre of fuel; B travels 9 : 70 km per

litre of fuel.

c$28: 38

5a$3base charge

bAB has gradient 112 ; BC has gradient 1. These gradients

indicate the charge per kilometre travelled.

cAC has gradient 115 which means that the average charge is

$1: 20 per kilometre travelled.

EXERCISE 12E.1

1a¡ 2 b¡^52 c ¡^13 d¡^17 e^52 f^37 g^15

h 1

2c,d,fandhare perpendicular.

3aa=9 ba=1 ca=6^13

4at=^15 bt=5 ct=3^35

5at=4 bt=4 ct=14 dt=3^17

EXERCISE 12E.2

1anot collinear bcollinear c not collinear dcollinear

2ac=3 bc=¡ 5

EXERCISE 12F

1a bgradient of MN=¡^34

gradient of AC=¡^34

c MN=2^12 units

and AC=5units

2a bKL=KM=2

p

5 units

) ¢KLM is isosceles

c P(5,4)

dgradient of KP=¡^13

gradient of LM=3, etc.

3a

bigradient of AB=2

gradient of DC=2, ) ABkDC

ii gradient of BC=¡^38

gradient of AD=¡^38 , ) BCkAD

ca parallelogram

dAB=DC=2

p

5 units

BC=AD=

p

73 units

eimidpoint of AC is(8, 412 )

ii midpoint of BD is(8, 412 )

fDiagonals bisect each other.

4a

bAB=BC=DC=DA=5units

) ABCD is a rhombus.

cmidpoint of AC is(4,3); midpoint of DB is(4,3)

dgradient of AC=¡ 2 ; gradient of DB=^12 , etc.

5aiP(¡ 1 , 712 )

iiQ(2^12 ,4)

iii R(¡ 112 ,¡^12 )

iv S(¡ 5 ,3)

bi¡ 1 ii^98 iii¡ 1 iv^98

cOpposite sides are parallel and so it is a parallelogram.

6aOB=radius=10, ) OC=10also.

Using the distance formula,

p

62 +a^2 =10

) a=8 fasa> 0 g

bi^12 ii ¡ 2

cAC and CB are perpendicular ) AbCB is a right angle.

REVIEW SET 12A

12a 5 units b

p

13 units

3 (5,¡1)

4a^25 b¡ (^334)
5a i 40 km/h ii 90 km/h iii 20 km/h
bi 40 ii 90 iii 20
The gradients are the same as the average speeds ina.
c 60 km/h
6 AB=BC=
p
65 units, AC=
p
26 units
) ¢ABC is isosceles
7ak=¡ 412 b k=¡ 15
8 gradient of AB=gradient of BC=2and B is common
O
y
x
M
A N
B
C
5
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5
5
K
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M
P
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5
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AB
D C
y
O x
2 4 6
2
4
6
8
-4-2
-6
-2
B
Q
C
D
S
A P
R
y
-2 x
-2
2
2
A
D
C
B
O
y
x
O^10
A
B
C
D
2 4 6 8
2
4
6
8
10
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\693IB_IGC1_an.CDR Tuesday, 18 November 2008 3:32:04 PM PETER