Grade 12 Mathematics Paper 3 (LO1, LO3 & LO4 - Optional) Record Exam 2008 Page 1 of 8

Record Exam 2008

Grade 12Mathematics Paper 3 (LO1, LO3 & LO4 - Optional)

Date:Time: 1½ hTotal: 75

INSTRUCTIONS:

Read the following instructions carefully before answering the questions:

This question paper consists of 8 pages. An information sheet has been provided. Please ensure that you use it but DO NOT write on it. Please check that your paper is complete.

Read the questions carefully.

Answer ALL questions.

All Questions must be answered on question paper.

You may use an approved non-programmable and non-graphical calculator, unless a specific question prohibits the use of a calculator.

Round off answers to TWO decimal digits where necessary.

Read through the whole paper before starting.

All the necessary working details must be clearly shown.

Number your answers exactly as the questions are numbered.

Diagrams are not necessarily drawn to scale.

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

You may NOT use Tippex.

You may not borrow ANYTHING during the examination

QUESTION 1

1.1 Consider the sequence defined as follows: and for ,

1.1.1Write down the first FOUR terms of the sequence.(3)

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1.1.2What type of sequence is this?(1)

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1.1.3Write the formula for in its simplest, non-recursive form.(2)

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1.2Consider the sequence:

1.2.1What is the next term in the sequence?(1)

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1.2.2Write a recursive formula for this sequence.(3)

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[10]

QUESTION 2

2.1The table shows the results of experiments giving the average number of mosquito bites per 15 minutes versus the wind speed.

Wind speed (km/h): x / 0,5 / 2 / 4 / 6 / 8 / 14
Bites/15 min / 50 / 36 / 25 / 22 / 12 / 5

2.1.1Draw a scatter-plot of the data.(4)

2.1.2Calculate and then describe the type and strength of the correlation between the two sets of data. (3)

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2.1.3Draw the straight line of best fit and determine its equation.(3)

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2.2The following regression functions and relevant values for were obtained using technology:

Option 1: , with

Option 2:, with

Option 3:, with

The regression functions are shown below:

2.2.1What conclusion can be drawn from looking at the three options? (2)

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2.2.2Which option best describes the relationship between the wind speed and the number of mosquito bites per 15 minutes? (2)

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2.2.3Use Option 1 to predict the number of mosquito bites per 15 minutes if the wind speed on a specific day is 15 km/h. Interpret the answer. (2)

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[16]

QUESTION 3

3.1The tables below show the ages and the number of people killed on the roads in a certain province in one year.

Table A

Age group / 1-10 / 11-20 / 21-30 / 31-40 / 41-50 / 51-60 / 61-70 / 71-80
Number of dead / 32 / 109 / 174 / 62 / 78 / 50 / 38 / 42

3.1.1Calculate the modal class and the mean of the data.(4)

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3.1.2What type of display is used below to represent the data in Table A? (1)

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3.1.3Write down one conclusion that can be made from the data.(1)

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3.1.4Write down whether the data represents a normal distribution or not.

If not, state the type of distribution. Explain your answer.(3)

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3.2The annual profit made by a company in 2005, 2006 and 2007 is displayed by the three bar graphs below:

3.2.1Check whether the graphs display the same data.(1)

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3.2.2Discuss the differences between the graphs.(3)

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3.2.3What pattern is shown by the annual profit.(2)

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3.2.4The managing director wants to use one ofthe graphs in her annual report. Which graph would you recommend? Explain your answer. (2)

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QUESTION 4:

4.1A, B, C and D are points on a circle with centre O. If and , calculate the size of the following angles, giving reasons.

4.1.1 (2)

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4.1.2 (2)

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4.1.3 (2)

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4.1.4 (5)

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4.2Find a in the following sketch:(3)

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4.3In the figure KL and MN are two parallel chords of circle O. The radius of the circle is 5 cm. The longer chord is 8 cm and the distance between the chords is 1 cm.

4.3.1What is the length of the shorter chord? Show all working! (6)

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4.3.2What would the distance between the chords be if they were in opposite semicircles? (1)

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4.4In the figure below, AB is a chord of a circle with centre O. AO is produced to C such that ACBC. ODAB.

4.4.1Prove that ABC /// AOD(3)

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4.4.2Show that (2)

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4.4.3Hence prove that (6)

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[32]

TOTAL: 75