MATHEMATICS

PAPER 3

GRADE 12

SEPTEMBER 2012

TIME: 2 HOURS

MARKS: 100

RONDEBOSCH BOYS’ HIGH SCHOOL

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Examiner: P Ghignone

Moderator: R Harmuth

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This question paper consists of 12 pages, a formula sheet and

4 diagram sheets.

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INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.This question paper consists of 10 questions. Answer ALL the questions.

2.Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining the answers.

3.An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.

4.If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.

5.Diagrams are NOT necessarily drawn to scale.

6.Diagram sheets have been provided for you to use. Please hand them in with your script.

7.Number the answers correctly according to the numbering system used in this question paper.

8.It is in your own interest to write legibly and to present the work neatly.

Question 1

Given the sequence

1.1Write down the next two terms of the sequence. (2)

1.2Write down the recursive formula for the sequence. (3)

[5]

Question 2

The South African Traffic Service is doing a clamp down on speeding. During a recent speeding trap they collected the following data:

Speeding / Not Speeding / TOTAL
Male / 398 / 217 / 615
Female / 205 / 180 / 385
TOTAL / 603 / 397 / 1000

2.1Determine the probability that a driver selected at random is…

2.1.1 speeding.(2)

2.1.2 a female driver and NOT speeding.(2)

2.1.3 a male driver and speeding.(2)

2.2Are the events of being a male and speeding independent? Show ALL relevant working to support your answer. (4)

2.3The national road accident fund published the following statement:

“Fatal accidents along the N1 highway between Cape Town and Beaufort West have risen from 2365 in 2010 to 2944 in 2011 – an increase of almost 25%.”

Explain why the latter part of this statement could be misleading. (2)

[12]

Question 3

Jason’s dad has agreed to consider hiring a Hummer Limousine for Jason’s matric dance. It all depends on Jason’s Maths marks.

The probability of Jason getting an “A” is 0.7.

If Jason gets an “A” then the probability of his dad renting thelimousine is 0,9. If he does NOT get an “A”, then the probability ofhim renting the limousine is 0.4.

3.1Draw a tree diagram to show the possible outcomes for the hiring of the limousine. (4)

3.2What is the probability that Jason will get an “A” AND his dad will hire the limousine? (2)

3.3What is the probability that Jason will NOT get the limousine?(4)

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Question 4

Jason’s dad decides to hire the Hummer Limousineand it arrives to pick up Jason, his date and three other couples for the matric dance (a total of 4 couples).

The seating arrangement inside the hummer is below:

How many different ways can they be seated if:

4.1 Any person wants to sit in any chair?(2)

4.2Jason and his date want to sit closest to the door?(2)

4.3All the girls want to sit together? (I.e. without a boy or the table between them.) (3)

[7]

Question 5

The Marketing budgets and Sales Income (in millions of rands) of several companies were investigated and the following data was collected:

Company / 1 / 2 / 3 / 4 / 5 / 6
Marketing / 3 / 4,5 / 1 / 5 / 7 / 2,4
Sales Income / 32 / 56 / 18 / 48 / 60 / 25

5.1Use the grid provided on DIAGRAM SHEET 1 to draw a scatter plot for the data. (3)

5.2Determine the equation of the least squares regression line.(3)

5.3Determine the correlation coefficient of the data.(2)

5.4The CEO looks at the correlation coefficient and describes the relationship between the Marketing budget and the Sales Income as astrong, positive relationship. Explain with reference to the correlation coefficient. (2)

5.5Given the relationship above, what Sales Income would you predict for a company that has a marketing budget of R 3 500 000? (3)

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Question 6

Magnificent Milk manufactures bottles of milk. They are machine-filled to a volume of 1L (1000ml). It is observed that the machine fills the bottles according to a normal distribution with a standard deviation of 9ml.

6.1If the company produces 1500 bottles of milk a day, how many bottles, on average, will fall within one standard deviation of the mean? (2)

6.2The company regulations state that all milk bottles with a volume that is less than two standard deviations below the mean must be donated to a neighboring charity. What is this minimum volume?

(2)

6.3Of the 1500 bottles of milk produced per day, how many are donated to charity? (2)

6.4The bottling machine is upgraded and the standard deviation of the volume is improved to 7ml. How will this impact on the number of bottles donated to charity? Motivate your answer. (2)

[8]

Question 7

7.1In the diagram below, O is the centre of the circle. PT is a tangent to the circle at Q. R and S are points on the circumference of the circle. QR, RS and QS are joined.

Prove the theorem that states

(5)

7.2In the sketch below, is a cyclic quadrilateral. The diagonals AC and BD intersect at so that and both produced, meet at . The tangent meets produced at .

and

Calculate, with reasons, the values of:

7.2.1(2)

7.2.2(2)

7.2.3(4)

7.2.4(2)

[15]

Question 8

In the diagram, is a tangent to the circle at and

8.1If , write down three other angles equal to with reasons.

(6)

8.2If why is also equal to (1)

8.3Prove that (3)

8.4Prove that is a cyclic quadrilateral.(5)

[15]

Question 9

and are two secants of the circle, centre and radius

and . The ratio.

9.1Prove that (4)

9.2Show, with ALL steps and reasons, that (4)

[8]

Question 10

has and and intersect at Calculate with reasons the ratio .

[7]

INFORMATION SHEET: MATHEMATICS

/ M

In ΔABC:

RBHS Paper 3 September 2012

Gr 12 DIAGRAM SHEETS PG (RH)

Name ______

Q1 / Q2 / Q3 / Q4 / Q5 / Q6 / Q7 / Q8 / Q9 / Q10 / TOTAL
5 / 12 / 10 / 7 / 13 / 8 / 15 / 15 / 8 / 7 / 100

Diagram Sheet 1

Question 5

Company / 1 / 2 / 3 / 4 / 5 / 6
Marketing / 3 / 4,5 / 1 / 5 / 7 / 2,4
Sales Income / 32 / 56 / 18 / 48 / 60 / 25


Diagram Sheet 2

Question 7.1

Question 7.2

Name: ______

Diagram Sheet 3

Question 8


Diagram Sheet 4

Question 9

Question 10

1