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C3 Algebraic fractions and Exp/Logs
Contributed by: Razaq
C3 Algebraic fractions and Exponential/Log functions

Find the value of the constants, A, B, C and D in the

following identity:

 

 

x3-6x2+11x+2≡(x-2)(Ax2+ Bx+ C)+ D

A
B

C

D

Find the vlaue of the constants, A, B, C and D where:

 

 

4x3-6x2+8x-5  can be written as Ax2+Bx+c+  D

2x+1
A
B

C

D
2x+1
If logx y=2 :

x=2y

x=y2

y=2x

 x2=y
x3-3x2+6x-2 has remainder 2 when divided by:

x+1

x

x-1

x+2

The graph of y= ex +1 crosses the y-axis at y=
The graph of y= 4e-2x crosses the y-axis at y=
The graph of y= -ex +1 crosses the y-axis at y=
The horizontal asymptote is at y =

The graph of y= 3ex +2 crosses the y-axis

 

 

at y=

The graph of y= 50ex -5   crosses the y-axis

 

 

at y=

The horizontal asymptote is at y =
C3 Algebraic fractions and Exponential/Log functions

The graph of y= 20e-x +10 crosses the y-axis

 

 

at y=

The horizontal asymptote is at y =

Find A to the nearest pound:

 

Find the investment value after 10 years:

The value of an investment varies according

to the formulae

 

V=Ae(t/12)

with the investment worth £8000 after 3 years

(answers to nearest pound)

The graph of y= ln(x) crosses the x-axis

 

 

at x=

The vertical asymptote is at x =

The graph of y= ln(-x) crosses the x-axis

 

 

at x=

The vertical asymptote is at x =

The graph of y= ln(x-2) crosses the x-axis

 

 

at x=

The vertical asymptote is at x =

Solve the equation ln(3x+2) = 1,

giving your answer to 2dp

Solve the equation ex +e-x =2, (giving your answer

to the nearest whole number).

Solve the equation ln 2 +ln x = 4, (giving your answer

to the nearest whole number).

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