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Mathematics Task. Consists Of A Memo Lens High Assignment

1862 words - 8 pages

Copyright reserved Please turn over
MARKS: 150
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
Copyright reserved Please turn over
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
Copyright reserved Please turn over
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
NSC
Copyright reserved Please turn over
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.– Mar....

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