Cambridge Additional Mathematics

Answers 469

10 a 100 g

bi¼ 173 g

ii 300 g

iii ¼ 1397 g

d 20 hours

c

11 a 32 amps

bi 8 amps

ii 2 amps

d 3 seconds

c

12 a i 22 ±C

ii 6 ±C

iii ¡ 2 ±C

iv ¡ 6 ±C

b

cThe temperature will not reach ¡ 10 ±C according to

this model, as the model has a horizontal asymptote at

T=¡ 10.

EXERCISE 4H

1 The graph ofy=ex

lies between y=2x

andy=3x.

2 One is the other

reflected in

they-axis.

3 a

4aex> 0 for allx

bi 0 :000 000 004 12 ii 970 000 000

5a¼ 7 : 39 b¼ 20 : 1 c¼ 2 : 01 d¼ 1 : 65

e¼ 0 : 368

6ae

(^12)
be
¡^12
ce¡^2 de
(^32)
7
Domain off,g, andhis fx:x 2 Rg
Range offis fy:y> 0 g, Range ofgis fy:y> 0 g
Range ofhis fy:y> 3 g
8
Domain off,g, andhis fx:x 2 Rg
Range offis fy:y> 0 g, Range ofgis fy:y< 0 g
Range ofhis fy:y< 10 g
9ae^2 x+2ex+1 b 1 ¡e^2 x c 1 ¡ 3 ex
10 ax=^12 b x=¡ 4
11 afg(x)=e^3 x+2, gf(x)=3ex+2 bx=¡ 1
12 a bDomain off¡^1 is
fx:x> 0 g,
Range off¡^1 is
fy:y 2 Rg
REVIEW SET 4A
1a¡15 + 20
p
3 b 86 ¡ 60
p
2
2a^2
p 3
3 b
p 35
5 c
p 7
28
3aa^6 b^7 b
2
3 x
c
y^2
5
4a i 81 ii^13 b k=9
5a
1
x^5
b
2
a^2 b^2
c
2 a
b^2
6a 33 ¡^2 a b 3
(^52) ¡ (^92) x
7a 4 b^19
8a
m
n^2
b
1
m^3 n^3
c
m^2 p^2
n
d
16 n^2
m^2
9a 9 ¡ 6 ex+e^2 x b x¡ 4 c 2 x+1
10 x= 349 + 341
p
13
11 ax=¡ 2 b x=^34 cx=¡^14
12 aC bE c A dB e D
13 a 3 b 24 c^34
14 aRange offis fy:y>¡ 3 g b¡ 2 c x=^12
4 8 12 16 20 24 28
250
500
750
1000
1250
1500
(5 173),
(10 300),
(24 1397),
W(t) ( )g
t(hours)
W(t) = 100 30.1t
0
100
123
5
10
15
20
25
30
32
t
()seconds
(2 2),
(1 8),
I(t) = 32 4-t
0
I(t) (amps)
x
y y=ex
y=2x
y=3x
O
10 20 30
T = -10
t(minutes)
(5 6),
(10 -2), (15 -6),
0
-10
10
20
22 T(t) (°C)
T(t) = -10 + 32 * 2-0.2t
y
x
y=x
y = f(x)^1
1
y = f-1(x)
O
y
x
f(x) = ex
y=10
h(x) = 10 - ex
g(x) = -ex
OO
1
9
-1
y
x
1
h(x) = e + 3x
f(x) = ex
g(x) = ex-2
y=3
O
4
x
y
y=e-x y=ex
O
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 IB HL OPT
Sets Relations Groups
Y:\HAESE\CAM4037\CamAdd_AN\469CamAdd_AN.cdr Tuesday, 8 April 2014 8:32:16 AM BRIAN