Cambridge Additional Mathematics

1_Qw t

• 
  
  
  
  • 0
  
  
  
  

a(t)

-5 -1 0 s

t=0

t=2

t=1

1 2 3 4

4

3

2

1

x

y

y=Rv

O

x

+

0

f'(x)

t

v(t)ms-1

-48

-40

O

Answers 497

5 decreasing at 0 : 16 m^3 per minute 6 203 cm per minute

7 25

p 3

6 ¼^7 :^22 cm per minute

8 decreasing at^25013 ¼ 19 : 2 ms¡^1

9a 0 : 2 ms¡^1 b 454 ms¡^1

10 decreasing at

p 2

100 radians per second

11 increasing at 0 : 12 radians per minute

REVIEW SET 14A

1ay=4x+2 b y=4x+ 4 ln 2¡ 4 c y=e^2

2 a=^52 ,b=¡^32

3aa=¡ 6

blocal max.(¡

p

2 , 4

p

2), local min.(

p

2 ,¡ 4

p

2)

c

4ay=^15 x¡^115 (or x¡ 5 y=11) b y=¡ 4 x+14

5 3267152 units^26 a=64 7 P(0, 7 :5),Q(3,0)

93 x¡ 4 y=¡ 5

10 ax> 0

bSign diagram off^0 (x)

f(x)is increasing

for all x> 0.

dnormal is x+2y=3

c

11 a by=¡

4

k^2 x+

8

k

cA(2k,0),B

³

0 ,^8

k

́

dArea=8units^2

ek=2

12 av(t)=(6t^2 ¡ 18 t+12)cm s¡^1 ,a(t) = (12t¡18)cm s¡^2

b s(0) =¡ 5 cm ( 5 cm to the left of origin)

v(0) = 12cm s¡^1 towards origin

a(0) =¡ 18 cm s¡^2 (reducing speed)

cAt t=2, particle is 1 cm to the left of the origin,

is stationary and is accelerating towards the origin.

dt=1,s=0 and t=2,s=¡ 1

e

f 16 t 6112 and t> 2

13 bk=9

14 ax(0) = 3cm, x^0 (0) = 2cm s¡^1 , x^00 (0) = 0cm s¡^2

bt=¼ 4 s and^34 ¼s c 4 cm

15 6 cm from each end

16 ay=^1

x^2

, x> 0

cbase is 1 : 26 m square, height 0 : 630 m

17 a v(t) = 15 +

120

(t+1)^3

cm s¡^1 , a(t)=

¡ 360

(t+1)^4

cm s¡^2

bAt t=3, particle is 41 : 25 cm to the right of the origin,

moving to the right at 16 : 88 cm s¡^1 and decelerating at

1 : 41 cm s¡^2.

cspeed is never increasing

18 A

³ 1

2

,

1

e

́

19 20

p 10

3 ¼^21 :^1 m per minute

20 aV(r)=^89 ¼r^3 m^3

b

dr

dt

=¡ 3758 ¼¼¡ 0 :006 79m min¡^1

REVIEW SET 14B

1ax=1 bex¡ 2 y=e¡^2

e

c y=16x¡^1272

2 a=¡ 14 ,b=21

3af(3) = 2,f^0 (3) =¡ 1 bf(x)=x^2 ¡ 7 x+14

4a 2 x+3y=^23 ¼+2

p

3 b

p

2 y¡ 4 x=1¡ 2 ¼

5 p=1,q=¡ 8 6 (¡ 2 ,¡25) 7 a=^12

8alocal minimum at(0,1) cf^00 (x)=ex

9 (0,ln 4¡1)

10 ay-intercept=¡ 35 bx=1,^72 , 5

clocal maximum at (2,9), local minimum at(^133 ,¡^10027 )

d

11 BC=^8

p 10

3 units

12 a 60 cm bi 4 : 24 years ii 201 years

ci 16 cm per year ii 1 : 95 cm per year

13 av(t)=¡ 8 e¡

10 t

¡ 40 ms¡^1

a(t)=^45 e¡^10 t ms¡^2 ft> 0 g

bs(0) = 80m

v(0) =¡ 48 ms¡^1

a(0) = 0: 8 ms¡^2

dt=10ln2seconds

c

14 a i $ 535 ii$ 1385 : 79

bi¡$ 0 : 267 per km h¡^1 ii$ 2 : 33 per km h¡^1

c 51 : 3 km h¡^1

12 t

++-

0

v(t)

y

x

y=x -6x 3

O

(-~`2_ 4~`2),

(~`2_ -4~`2),

(1 1),

x

y

O

y=x+lnx

y

x

-35

1

Uw 5

local max.

(2 9),

local min.

(-)QdE, QsPjP

y = 2x - 19x + 52x - 35 32

O

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 IB HL OPT
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Y:\HAESE\CAM4037\CamAdd_AN\497CamAdd_AN.cdr Tuesday, 8 April 2014 8:39:59 AM BRIAN