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T960(E)(A7)T

APRIL EXAMINATION

NATIONAL CERTIFICATE

MATHEMATICS N4

(16030164)

7 April 2016 (X-Paper)

09:00¨C12:00

Scientific calculators may be used.

This question paper consists of 5 pages and 1 formula sheet.

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T¡­(E)(A¡­)T

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T960(E)(A7)T

DEPARTMENT OF HIGHER EDUCATION AND TRAINING

REPUBLIC OF SOUTH AFRICA

NATIONAL CERTIFICATE

MATHEMATICS N4

TIME: 3 HOURS

MARKS: 100

INSTRUCTIONS AND INFORMATION

1.

Answer ALL the questions.

2.

Read ALL the questions carefully.

3.

Number the answers according to the numbering system used in this question paper.

4.

Show ALL intermediate steps and simplify where possible.

5.

ALL final answers must be rounded off to THREE decimal places (unless indicated

otherwise).

6.

Questions may be answered in any order, but subsections of questions must be kept

together.

7.

Use only BLUE or BLACK ink.

8.

Write neatly and legibly.

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T960(E)(A7)T

QUESTION 1

1.1

1.1.1

Draw the graph of y ? 2 cos ecx,0 0 ? x ? 2?

(3)

1.1.2

Is the graph of y ? 2 cosecx in QUESTION 1.1.1 above a function or a

relation?

(1)

Is the graph of y ? 2 cosecx in QUESTION 1.1.1 above symmetrical or

asymmetrical about the X-axis?

(1)

1.2.1

Draw the graph of the inverse of y ? 11x

(3)

1.2.2

What is the domain of the graph of the inverse of

QUESTION 1.2.1 above?

1.1.3

1.2

1.3

y ? 11x in

(2)

Given:

a?b ? c?3

2a ? c ? 3 ? b

c

? b ? ? ?a

2

Solve the value of 'a' by using Cramer's rule only.

1.4

(8)

Given:

1

2

0

?1

1

3

Calculate the value of the determinant.

(2)

[20]

QUESTION 2

2.1

Calculate the value of sin 2 A if cos A ?

2.2

Solve for the value of 'A' if:

24

and A is in the first quadrant.

25

(3)

5 cos 2 A ? 4 ? 3 cos A;0 0 ? A ? 1800

2.3

(5)

Prove that:

2 sin A ? 1

? sec A

cos A ? sin 2 A

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(3)

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2.4

-4-

Simplify:

?

? ?

?

?

? ?

sin 1800 ? a tan 1800 ? a sin 900 ? a

tan 1800 ? a cos?? a ?. sin?? a ?

2.5

2.6

T960(E)(A7)T

?

(2)

3

12

and sin y ?

and both 'x' and 'y' are acute angles, determine without

13

5

the use of a calculator the value of cos?x ? y ? .

If cos x ?

(4)

Prove that:

2 ? 2 cos 2 A ? 2 cos A

(3)

[20]

QUESTION 3

3.1

The perimeter of a field in the form of a right-angled triangle is 60 m. The length of

the hypotenuse is 25 m.

Calculate the lengths of the other two sides.

3.2

(5)

Solve for 'x' if:

4.4 x ? 29

3.3

(3)

Make 'c' the subject of the formula if:

t

?

?

?

i ? ? 0 ??1 ? e Rc ??

?

?

3.4

Solve for 'x' if:

x?

3.5

(3)

7

?5?0

x

(4)

Rationalise:

1

cos? ? j sin?

3.6

(3)

Given:

z ? 3 ? j6

Convert z into polar form. The argument may only be positive.

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(2)

[20]

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