Read Mathematics Paper I Answer Sheet Marking Guidelines (2010) text version

NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 2010

MATHEMATICS: PAPER I MARKING GUIDELINES Time: 3 hours 150 marks

ANSWER SHEET

QUESTION 5 (a) Given p ( x) = - 3x 2 Determine the equation of the inverse of p stating its domain and range. Inverse :

y2

(5)

x = - 3y 2

= - x 3

M

A

Changing subject of formula

Must be shown Domain : Range :

y = ± -

x 0 y R

x 3

A

A

A

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-1

(b)

Given (1)

f ( x) = 2 x ,

g ( x) =

f ( x - 2) and h( x) =

f

( x) (2)

Write down the equations of g and h in the form y = ...

g : y = 2 x -2 h : y = log 2 x (2)

A A

On the set of axes where f is already drawn for you, add the graphs for g and h. Label your graphs clearly. y

(4)

5 4 3 2

A

f g

A A

h

Exp g: shape (2; 1) or (3; 2) or (4; 4) Log h: shape (1; 0) 5 x (2; 1) or (4; 2)

1

A

­3 ­2 ­1 ­1 ­2 ­3

(3)

1

2

3

4

All

exp: crossing x-asis Shape mark or log crossing y-axis not given

Solve for x if g(x) = h(x).

(1)

x = 2

CA

[12]

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