NATIONAL SENIOR

CERTIFICATE

GRADE 10

MATHEMATICS P1

EXEMPLAR 2012

MARKS: 100

TIME: 2 hours

This question paper consists of 6 pages.

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INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

This question paper consists of 7 questions.

2.

Answer ALL the questions.

3.

Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in

determining your answers.

4.

Answers only will NOT necessarily be awarded full marks.

5.

You may use an approved scientific calculator (non-programmable and nongraphical), unless stated otherwise.

6.

If necessary, round off answers to TWO decimal places, unless stated otherwise.

7.

Diagrams are NOT necessarily drawn to scale.

8.

Number the answers correctly according to the numbering system used in this

question paper.

9.

Write neatly and legibly.

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QUESTION 1

1.1

Simplify the following expressions fully:

1.1.1

1.1.2

1.2

(m − 2n )(m 2 − 6mn − n 2 )

(3)

x3 + 1

4 x 2 − 3x − 1

−

4x + 1

x2 − x +1

(5)

Factorise the following expressions fully:

1.2.1

1.4

(2)

1.2.2

1.3

6 x 2 − 7 x − 20

a 2 + a − 2ab − 2b

(3)

Determine, without the use of a calculator, between which two consecutive integers

51 lies.

Prove that 0,245 is rational.

(2)

(4)

[19]

QUESTION 2

2.1

Determine, without the use of a calculator, the value of x in each of the following:

2.1.1

x 2 − 4 x = 21

2.1.2

96 = 3 x 4

(3)

2.1.3

R=

2 x

3S

(2)

(3)

5

2.2

Solve for p and q simultaneously if:

6q + 7 p = 3

2q + p = 5

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(5)

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QUESTION 3

3.1

3x + 1 ; 2x ; 3x – 7….. are the first three terms of a linear number pattern.

3.1.1

(3)

3.1.2

Determine the formula for T n , the general term of the sequence....