Preliminary Examination GRADE 12 PRELIMINARY EXAMINATION AUGUST 2009 HILTON COLLEGE MATHEMATICS: PAPER III. Time: 2 hours Marks: 100

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1 Preliminary Examination 009 GRADE PRELIMINARY EXAMINATION AUGUST 009 HILTON COLLEGE MATHEMATICS: PAPER III Time: hours Marks: 00 PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY. This question paper consists of 5 pages which includes a page information sheet and a page diagram sheet. Please check that your question paper is complete.. Read the question carefully. 3. You may use an approved non-programmable and non-graphical calculator, unless stated otherwise. 4. Round off your answers to two decimal digits where necessary. 5. All the necessary working details must be clearly shown. 6. It is in your own interest to write legibly and to present your work neatly.

2 Preliminary Examination 009 SECTION A QUESTION. Write down a recursive formula for the following : 7 ; 3 ; -; -5; (). Given:.. Write down the first 5 terms of the sequence... Is this an arithmetic or geometric sequence?..3 Write down a recursive formula for the sequence. (4) [6]

3 Preliminary Examination QUESTION. The table below summarise data obtained about peoples favourite colour. Boys Girls Men Women Blue Green Red Yellow 3 4 No preference Cannot choose only one Write the following probabilities as a fraction in their simplest form. What is the probability that a person, chosen at random, is:.. a male whose favourite colour is green? ().. a child whose favourite colour is red or yellow? ()..3 an adult who did not name a particular colour? ()..4 a female who had no preference? ()..5 a person whose favourite colour is not yellow? (). If the letters of the word MATHEMATICAL are arranged randomly into a word, How many arrangements would there be:.. if there are no restrictions? (3).. that start with C and end with double T? (3).3 There are 7 identical red discs and 5 identical blue discs in the same bag. Two discs are chosen at random, without replacement. Use a tree diagram, or otherwise, to find the probability that you get one of each colour disc. (4) [0]

4 Preliminary Examination QUESTION 3 3. A fruit farmer keeps a record of the mass, correct to the nearest kilogram, of plums he picks from 60 trees growing in one of his orchards (Orchard A) MASS OF PLUMS PER TREE (p) FREQUENCY ( ) MIDPOINT ( ),5,5 3 7,5 30,5 8 0,5 5 6,5 3 67,5 90,5 TOTAL Write down the modal class. () 3.. Complete the table on the copy provided on the separate sheet at the end of the paper. (5) 3..3 Calculate the standard deviation. () 3. The farmer has a second orchard (Orchard B) of 60 plum trees that he has fertilized with an experimental fertiliser. The frequency polygon below shows the distribution of the mass of plums picked. y 50 Mass of fruit from 60 plum trees Orchard B x

5 Preliminary Examination On the same set of axes, draw a frequency polygon of the distribution of plums picked from the unfertilized orchard (Orchard A). The set of axes is provided at the end of the paper. (3) 3.. Would you advise the farmer to continue to use the experimental fertilizer? Give a reason for your answer. () QUESTION 4 [] A restaurant has dish and meat dishes on the menu. The owner investigated the relationship between the number of people visiting the restaurant and the number of meat dishes ordered. Number of people Number of meat dishes Draw a scatter plot of the data on the attached grid. (4) 4. Describe the type and strength of the correlation between the variables. () 4.3 Determine the equation of the regression line correct to two decimal places. (3) 4.4 Determine how many meat dishes will be required if 00 people are expected for dinner. (3) 4.5 If there are only meat dishes left, how many people can they serve? () 4.6 Determine the correlation coefficient for the data correct to 4 decimal places. () 4.7 Interpret the correlation coefficient. () [7]

6 Preliminary Examination NAME: TEACHER S NAME: SECTION B REASONS TO BE GIVEN UNLESS OTHERWISE STATED DO NOT RE-DRAW DIAGRAMS. USE THE DIAGRAMS ON THE QUESTION PAPER TO INDICATE ANY ADDITIONAL LINES, ANGLES AND CONSTRUCTIONS. QUESTION 5 5. In the diagram, M is the centre of the circle and the diameter CMPD is perpendicular to the chord AB. and. C 50 M A P B t D 5.. Prove that (3) 5.. Calculate, giving reasons. (3) 5..3 Calculate the radius of the circle. ()

7 Preliminary Examination In the diagram, is the centre of the circle and and are points on the circumference such that R O 00 P S Q. Find the sizes of:.. () 5.. () 5..3 ()

8 Preliminary Examination In the diagram, points and lie on a circle with centre. Chords and intersect each other at.. P O Q 00 N 3 S R 5.3. Calculate, with reasons, the size of. () 5.3. Calculate, with reasons, the size of. () Calculate, with reasons, the size of. () Prove that is a cyclic quadrilateral. () [8]

9 Preliminary Examination QUESTION 6 6. In the diagram, a tangent is drawn at on the circle through and meets produced at is produced to such that =35 and. P T 3 Q R 3 S 6.. Calculate, giving reasons, the size of. () 6.. Calculate, giving reasons, the size of. () 6..3 Prove that is a cyclic quadrilateral. () 6..4 Find the size of and hence deduce that is a tangent to the circle through and () 6..5 Calculate, giving reasons, the size of. ()

10 Preliminary Examination In and A P B 9 6 R Q C 6.. Determine the ratio. () 6.. Hence calculate the length of (3)

11 Preliminary Examination and are tangents to the circle. and. and are straight lines. Let A K L M 4 P 3 x 3 C B 6.3. Complete, giving reasons: () 6.3. Write down, with reasons, 5 other angles equal to. (5) Prove that is a cyclic quadrilateral. () Show that (3) Hence deduce that ()

12 Preliminary Examination Is a tangent to the circle passing through and Give reasons for your answer. () [7] NAME: Question 3.. MASS OF PLUMS PER TREE (p) FREQUENCY ( ) MIDPOINT ( ),5,5 3 7,5 30,5 8 0,5 5 6,5 3 67,5 90,5 TOTAL 60 Question 3..

13 Preliminary Examination y 50 Mass of fruit from 60 plum trees Orchard B x Question 4.

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