Cambridge Additional Mathematics

CARD GAME

Surds, indices, and exponentials (Chapter 4) 125

4 Consider y=2ex.

a Explain whyycan never be< 0. b Findyif: i x=¡ 20 ii x=20.

5 Find, to 3 significant figures, the value of:

a e^2 b e^3 c e^0 :^7 d

p

e e e¡^1

6 Write the following as powers ofe:

a

p

e b p^1

e

c^1

e^2

d e

p

e

7 On the same set of axes, sketch and clearly label the graphs of:

f:x 7 !ex, g:x 7 !ex¡^2 , h:x 7 !ex+3

State the domain and range of each function.

8 On the same set of axes, sketch and clearly label the graphs of:

f:x 7 !ex, g:x 7 !¡ex, h:x 7! 10 ¡ex

State the domain and range of each function.

9 Expand and simplify:

a (ex+1)^2 b (1 +ex)(1¡ex) c ex(e¡x¡3)

10 Solve forx:

a ex=

p

e b e

1

2 x=^1

e^2

11 Suppose f:x 7 !ex and g:x 7! 3 x+2.

a Find fg(x) and gf(x). b Solve fg(x)=

1

e

.

12 Consider the function f(x)=ex.

a On the same set of axes, sketch y=f(x), y=x, and y=f¡^1 (x).

b State the domain and range off¡^1.

Activity #endboxedheading

Click on the icon to run a card game for exponential functions.

Review set 4A

1 Simplify:

a 5

p

3(4¡

p

3) b (6¡ 5

p

2)^2

2 Write with integer denominator:

a

2

p

3

b

p

7

p

5

c

1

4

p

7

3 Simplify using the laws of exponents:

a a^4 b^5 £a^2 b^2 b 6 xy^5 ¥ 9 x^2 y^5 c

5(x^2 y)^2

(5x^2 )^2

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_04\125CamAdd_04.cdr Tuesday, 14 January 2014 10:28:43 AM BRIAN