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NATIONAL CERTIFICATE

APRIL EXAMINATION

MATHEMATICS N3

1 APRIL 2016

This marking guideline consists of 10 pages.

MARKING GUIDELINE

MARKING GUIDELINE -2- T950(E)(A1)T MATHEMATICS N3

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QUESTION 1 1.1 1.1.1

(4) 1.1.2

(2) 1.2

(5)

2 2

2 2

(3 2) (3 2)3 2 3 23( ) 2( )3( )( ) 2( )( )[3( ) 2]( )[3 3 2]

x x y yx x y yx y x yx y x y x yx y x yx y x y

- - +

= - - -

= - - += - + - += + - -= + - -

4 2

2 2

4 3 1( 1)(4 1)

p p

p p

n nn n+ -

= + -

3 2

3 2

2

3 2

3 2

2

2

( ) 2 5 2(1) 2(1) (1) 5(1) 2

=2 1 5 2 =0

-1 is a factor of f ( ) 2 3 2

x-1 2 5 22 2

3 5 3 3

f x x x xf

x xx x

x x xx x

x xx x

= + - +

\ = + - ++ - +

\

+ -+ - +

-

-

-

2

- 2 2 -2 2 . .

( ) ( 1)(2 3 2) = ( 1)(2 1)( 2)

xx

f x x x xx x x

++

\ = - + -- - +

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MARKING GUIDELINE -3- T950(E)(A1)T MATHEMATICS N3

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1.3

üü

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(6)

[17]

)3)(1(1772

312

11 2

-+--

+--

++-

=xxxx

xx

xx

)3)(1(1772)1)(12()3)(1( 2

-+--++-+--

xxxxxxxx

)3)(1(17721234 222

-+--+-+++-

xxxxxxxx

)3)(1()32(5 2

-+--

=xxxx

MARKING GUIDELINE -4- T950(E)(A1)T MATHEMATICS N3

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QUESTION 2 2.1

(4) 2.2

(4) 2.3 2.3.1

(4) 2.3.2

(4)

[16]

32

32

12

1 32 2

2

12

32 1 322 1 1

2 32 16

xx

xx xxx

x xxx

-

-= ÷

-= ´

-=

0,5

2

2

72

12

2

2

log 128log 128

1log2

log 2log 27 log 21log 27

-

=

=

=-

= -

( )

2

22

2 2

16 3 3 2

16 3 3 2

16 3 3 4.3 412 4.33 3

1TEST : If 1 then LHS=RHS=5

x x

x x

x x x

x

x

xx

+ = +

\ + = +

\ + = + +

\ =

\ =\ =

=

0

2

(log 2) log( 2) 0log 2 0 or log( 2) 0 log 2 2=10 10 2 1 100 3

x xx xx x

x xx x

- ´ - =\ - = - =

\ = -

\ = - =\ = =

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MARKING GUIDELINE -5- T950(E)(A1)T MATHEMATICS N3

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QUESTION 3 3.1

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(4) 3.2

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(4)

bxbxD

-+

=2

MARKING GUIDELINE -6- T950(E)(A1)T MATHEMATICS N3

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3.3

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(3)

3.4 Deposit is

Total price is Total amount for 9 instalments=

Each monthly instalment =

(4) [15]

dsptw

e =log

dseptw

=

dsetpw =

R3xR33x

R30x

\ 30 10R9 3x xR=

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MARKING GUIDELINE -7- T950(E)(A1)T MATHEMATICS N3

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QUESTION 4 4.1 4.1.1

(2) 4.1.2

(4) 4.1.3

(3) 4.1.4

(3)

( ) ( )

( ) ( )

2 22 1 2 1

2 2

AB

= 4 2 5 1

= 4 16

= 20

=2 5

x x y y= - + -

- + -

+

( ) ( )( )

( )

2 2

2

2

BC=2 5

0 4 5 20

16 5 = 20

5 = 4 5 = 2 5 2 5 2 7 3

k

k

kk

k or kk k

\ - + - =

\ + -

\ -

\ - ±\ - = - = -\ = =

5 1 24 27 5 10 4 2

1 therefore CB AB

AB

CB

AB CB

M

M

M M

-\ = =

--

\ = = --

´ = -^

2

1Area of ΔABC = × base × height 2

1 =21 = 20 20 2

=10 units

AB BC´

´

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MARKING GUIDELINE -8- T950(E)(A1)T MATHEMATICS N3

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4.2

(4) 4.3

(5) [21] QUESTION 5 5.1 Y 3 ü -3 0 3 ü X -3 (2)

1 2 1 2coordinates of M ;2 2

2 4 1 7 = ;2 2

=(1;3) Equation =1

x x y y

x

+ +æ ö= ç ÷è ø- + - +æ ö

ç ÷è ø

\

o o

o o o

1 3tan 1 tan =3

=45 =71,565 ˆBAC = = 71,565 45 = 26,565

AB ACM Mq a

q a

a q

= =

\ = \

\ \

- -

2733 22 =+ yx

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MARKING GUIDELINE -9- T950(E)(A1)T MATHEMATICS N3

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5.2.1 5.2.2

(5)

(3) 5.3

(4) [14]

3 2

2

2

2

3 2

3 2

6 9

3 12 9

Let 0 3 12 9 0

3( 4 3) 0( 1)( 3) 0

1 or 3( 1) ( 1) 6( 1) 9( 1) 4( 3) ( 3) 6( 3) 9( 3) 0

Turningpoints ( 3;0) and ( 1;4)

y x x xdy x xdxyx x

x xx xx xff

= + +

= + +

=

\ + + + =

+ + =+ + == - = -

- = - - - - - - =

- = - - - - - - =- -

11 2

12 2

2

1 2

2

2(0,5)

1 1

y xx

y x x

dy x xdxdydx x x

-

--

= +

= +

= - +

= - +

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MARKING GUIDELINE -10- T950(E)(A1)T MATHEMATICS N3

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QUESTION 6 6.1

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(4) 6.2

(5) 6.3 6.3.1

6.3.2

(3)

(3)

2

2

2

o o

o

sin 1 cossin sinsin sin 0sin (sin 1) 0sin 0 or sin 1

0 or 90or 180

q q

q q

q qq qq q

q q

q

= -

\ =

\ - =\ - =\ = =

\ = =

=

o o

o

o

o

o

o

:30

sin 70 sin 4530sin 70sin 45

39,868

:

cos 25

cos 2539,868 cos 2536,133

In ABCAB

AB

m

In ABDADABAD AB

m

D

=

\ =

=

D

=

\ =

= ´=

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MARKING GUIDELINE -11- T950(E)(A1)T MATHEMATICS N3

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6.4

(2) [17]

TOTAL: 100

22

ap==

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