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TIME: 3 hours

This question paper consists of 9 pages, 1 diagram sheet and 1 information sheet.

MATHEMATICS P1

FEBRUARY/MARCH 2012

NATIONAL

SENIOR CERTIFICATE

GRADE 12

Mathematics/P1 2 DBE/Feb.– Mar. 2012

NSC

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INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

This question paper consists of 12 questions.

Answer ALL the questions.

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

determining your answers.

Answers only will not necessarily be awarded full marks.

You may use an approved scientific calculator (non-programmable and non-

graphical), unless stated otherwise.

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

Diagrams are NOT necessarily drawn to scale.

ONE diagram sheet for answering QUESTION 12.2 is attached at the end of this

question paper. Write your centre number and examination number on this sheet in

the spaces provided and insert the page inside the back cover of your ANSWER

BOOK.

An information sheet, with formulae, is included at the end of the question paper.

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

question paper.

Write neatly and legibly.

Mathematics/P1 3 DBE/Feb.– Mar. 2012

NSC

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QUESTION 1

1.1 Solve for x:

1.1.1 253 2 =− xx (3)

1.1.2 5

2 =−

x

x (4)

1.1.3 12)3)(1( >−+ xx (4)

1.2 Solve simultaneously for r and p in the following set of equations:

6r + 5rp – 5p = 8

r + p = 2

(7)

1.3 The volume of a box with a rectangular base is 3 072 cm3. The lengths of the sides are

in the ratio 1 : 2 : 3. Calculate the length of the shortest side.

(4)

[22]

QUESTION 2

Given the arithmetic series: – 7 – 3 + 1 + … + 173

2.1 How many terms are there in the series? (3)

2.2 Calculate the sum of the series. (3)

2.3 Write the series in sigma notation. (3)

[9]

QUESTION 3

3.1 Consider the geometric sequence: 4 ; – 2 ; 1 …

3.1.1 Determine the next term of the sequence. (2)

3.1.2 Determine n if the nth term is

64

1 .

(4)

3.1.3 Calculate the sum to infinity of the series 4 – 2 + 1 … (2)

3.2 If x is a REAL number, show that the following sequence can NOT be geometric:

1 ; x + 1 ; x – 3 …

(4)

[12]

Mathematics/P1 4 DBE/Feb.– Mar. 2012

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QUESTION 4

An athlete runs along a straight road. His distance d from a fixed point P on the road is

measured at different times, n, and has the form cbnannd ++= 2)( . The distances are

recorded in the table below.

Time (in seconds) 1 2 3 4 5 6

Distance (in metres) 17 10 5 2 r s

4.1 Determine the values of r and s. (3)

4.2 Determine the values of a, b and c. (4)

4.3 How far is the athlete from P when n = 8? (2)

4.4 Show that the athlete is moving towards P when n < 5, and away from P

when n > 5.

(4)

[13]

Mathematics/P1 5 DBE/Feb.– M...

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