Mathematics Paper 1 November
NATIONAL SENIOR CERTIFICATE
GRADE 12
MATHEMATICS P1 NOVEMBER 2008
MARKS: 150 TIME: 3 hours
This question paper consists of 10 pages, an information sheet and 2 diagram sheets.
Copyright reserved
Please turn over
Mathematics/P1
2 NSC
DoE/November 2008
INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 3. 4. 5. 6. This question paper consists of 11 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. TWO diagram sheets for answering QUESTION 5.1, QUESTION 5.2, QUESTION 11.2 and QUESTION 11.3 are included at the end of this question paper. Write your examination number on these sheets in the spaces provided and hand them in together with your ANSWER BOOK. Number the answers correctly according to the numbering system used in this question paper. It is in your own interest to write legibly and to present the work neatly.
7. 8.
Copyright reserved
Please turn over
Mathematics/P1
3 NSC
DoE/November 2008
QUESTION 1 1.1 Solve for x, rounded off to TWO decimal places where necessary: 1.1.1 1.1.2
x2 = 5x − 4 x(3 − x) = −3
(3)
(5) (5)
1.1.3 1.2
3 − x < 2x2
Determine the values of x and y if they satisfy both the following equations simultaneously:
2x + y = 3 x2 + y + x = y2
1.3 Given x = 999 999 999 999, determine the exact value of
(8)
x2 − 4 . x−2
Show ALL your calculations. 1.4 Explain why the equation x4 + 1 1 = has no real roots. x4 2
(3)
(2) [26]
Copyright reserved
Please turn over
Mathematics/P1
4 NSC
DoE/November 2008
QUESTION 2
2.1
Consider the sequence: 2.1.1 2.1.2
GRADE 12
MATHEMATICS P1 NOVEMBER 2008
MARKS: 150 TIME: 3 hours
This question paper consists of 10 pages, an information sheet and 2 diagram sheets.
Copyright reserved
Please turn over
Mathematics/P1
2 NSC
DoE/November 2008
INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 3. 4. 5. 6. This question paper consists of 11 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. TWO diagram sheets for answering QUESTION 5.1, QUESTION 5.2, QUESTION 11.2 and QUESTION 11.3 are included at the end of this question paper. Write your examination number on these sheets in the spaces provided and hand them in together with your ANSWER BOOK. Number the answers correctly according to the numbering system used in this question paper. It is in your own interest to write legibly and to present the work neatly.
7. 8.
Copyright reserved
Please turn over
Mathematics/P1
3 NSC
DoE/November 2008
QUESTION 1 1.1 Solve for x, rounded off to TWO decimal places where necessary: 1.1.1 1.1.2
x2 = 5x − 4 x(3 − x) = −3
(3)
(5) (5)
1.1.3 1.2
3 − x < 2x2
Determine the values of x and y if they satisfy both the following equations simultaneously:
2x + y = 3 x2 + y + x = y2
1.3 Given x = 999 999 999 999, determine the exact value of
(8)
x2 − 4 . x−2
Show ALL your calculations. 1.4 Explain why the equation x4 + 1 1 = has no real roots. x4 2
(3)
(2) [26]
Copyright reserved
Please turn over
Mathematics/P1
4 NSC
DoE/November 2008
QUESTION 2
2.1
Consider the sequence: 2.1.1 2.1.2