This Question Paper Consists of 6 Pages and a 2-Page Formula Sheet

EXEMPLAR-1-NC(V)/2009

MATHEMATICS

PAPER 1

NQF LEVEL 4

2009

(********)

November (X-Paper)

09:00 – 12:00

EXEMPLAR

REQUIREMENTS

Scientific calculator.

Graph paper

This question paper consists of 6 pages and a 2-page formula sheet.

TIME: 3 HOURS
MARKS: 200
______

INSTRUCTIONS AND INFORMATION

1.
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3.
4.
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6. / Answer ALL the questions.
Read ALL the questions carefully.
Number the answers correctly according to the numbering system used in this question paper.
Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers.
If necessary, answers should be rounded off to THREE decimal places, unless stated otherwise.
Diagrams are NOT drawn to scale.

QUESTION 1

1.1 / During a class exercise Simon correctly constructed the graph of. This is the graph he drew.

1.1.1 / Write the equation of the axis of symmetry for the graph of . / (1)
1.1.2 / Determine the equation of the inverse of the function . / (1)
1.1.3 / Sketch the inverse of the function . / (4)
1.1.4 / Is the inverse function continuous or discontinuous? / (1)
1.2 / Prove that is a factor of the expression:
/ (3)
1.3 / A retailer wishes to buy a maximum of 20 guitars. He/She can buy either type A for
R1 500 each or type B for R3 000 each. R45000 has been set aside for the purchase of the guitars. However, at least 6 of each type must be purchased.
1.3.1 / If the retailer buys guitars of type A and guitars of type B, write FOUR inequalities which satisfy the above conditions. / (4)
1.3.2 / Represent the inequalities graphically and indicate the feasible region. Scale: 1cm = 2 guitars / (5)
1.3.3 / If the retailer makes a profit of R400 on each guitar of type A and R1 000 on each guitar of type B, write an equation for the profit (P) and hence determine how many of each type he/she should buy to make a maximum profit. / (4)
[23]

QUESTION 2

2.1 / Determine from first principles if . / (5)
2.2 / Determine the derivatives of the following:
2.2.1 / / (4)
2.2.2 / / (3)
2.2.3 / / (3)
2.3 / Find the equation of the tangent to the curve at . / (3)
2.4 / The displacement , in metres, of a body after seconds is given by:
.
Determine the velocity of the body after 3 seconds. / (3)
[21]

QUESTION 3

3.1 / Find the integrals of the following:
3.1.1 / / (3)
3.1.2 / / (3)
3.2 / Evaluate:
/ (2)
3.3 / Given below is the graph of . Calculate the area between the .

/ (7)
[15]

QUESTION 4

4.1 / The sales manager at Config Computer Suppliers wants to determine whether there is a relationship between the number of sales calls made in a month and the number of computers sold that month. He/She picks out a random sample of 10 sales representatives and determines the number of sales calls each representative made last month and the number of computers sold. The sample information is shown in the table below.
Sales Representative / Number of Sales calls / Number of computers sold
Sipho Sithole / 20 / 30
Pat Shongwe / 40 / 60
Steven Mashinini / 20 / 40
Annabeth Cyanne / 30 / 60
Ashley Hilfiger / 10 / 30
Horatio Mthembu / 10 / 40
Alex Mzobe / 30 / 40
Patrick Mbatha / 20 / 50
Tahir White / 20 / 40
MM Brown / 30 / 70
4.1.1 / Construct a scatter plot for the above data with the number of sales calls on the horizontal axis and the number of computers sold on the vertical axis. / (5)
4.1.2 / Find the sample regression equation by the method of least squares. / (6)
4.1.3 / Predict the number of computers that would be sold had a representative made 25 sales calls. / (3)
4.2 / The marks of 8 learners in a test for which the maximum mark is 10, were:
6 ; 4 ; 5 ; 9 ; 4 ; 9 ; 4 ; 7
Calculate the standard deviation of this data. / (7)
4.3 / There are 4 green balls and 6 red balls in a bag. You take out one without looking. What is the probability of picking out a green ball? / (3)
4.4 / Rachel, Ross and Monica are playing a game of Monopoly. They in turn throw two dice.
4.4.1 / Rachel needs a double to get out of jail. Determine the probability that she would indeed throw a double. / (3)
4.4.2 / Ross needs a total score of 11 in order to buy Smith Street. Determine the probability of him landing on Smith Street. / (3)
4.5 / A fair coin is tossed three times. What is the probability of obtaining three heads? / (2)
4.6 / A fair coin is tossed and a fair die is rolled.
4.6.1 / Show this event on a tree diagram. / (4)
4.6.2 / Determine the probability of obtaining a tail and a 2. / (2)
4.6.3 / Determine the probability of obtaining a head and an odd number. / (3)
[41]
TOTAL: / 100

Formulae Sheet

1. /
2. /
3. /
4. / or
5. / or
6. / or
7. / If then or If then
8. / If then or If then
9. / If then or If then
10. /
11. /
12. / where is a constant value.
13. /
14. /
15. /
16. /
17. /
18. /
19. /
20. /
21. /
22. /
23. / variance = =
24. / standard deviation = =
25. / y = a + bx
26. /
27. / - -
a = y – bx
28. /
29. /