ST MARY’S DSG, KLOOF

GRADE: 12AUGUST 2008
MATHEMATICS: PAPER III
TIME: 2 HOURSTOTAL: 70 MARKS

INSTRUCTIONS:

1.This question paper consists of 8 pages.

2.A formula sheet has been provided.

3.Answer all questions on the question paper in the space provided.

4.Read all the questions carefully.

5.An approved non-programmable and non-graphical calculator may be used, unless otherwise specified.

6.Round off your answer to 2 decimal digits unless otherwise specified.

7.All necessary working details must be clearly shown.

8.Present your work neatly and legibly.

Question 1
A sequence is defined by the recursive formula
; for all
1.1 / Give the first 4 terms of the sequence. / (2)
1.2 / Give the formula for the general term of the sequence. / (2)
1.3 / Calculate: / (2)
[6]

Question 2

2.1 / In how many different ways can a golfer play a nine hole golf course if there is no restriction on the order in which the holes must be played? / (3)
2.2 / Various choices are being offered if you purchase the new Safari Ranger. It is available in white, silver, blue or red. Upholstery can be leather or one of two other fabrics and the controls can be manual or automatic.
2.2.1 / How many different Safari Rangers are there to choose from? / (3)
2.2.2 / There is a model available immediately. Assuming that all variations are equally likely, what is the probability that this model is an automatic with leather upholstery and that is not white? / (3)
2.3 / Binary numbers consist of only 2 digits, 0 and 1. Eg: 10011
2.3.1 / How many five digit binary numbers can be represented, if the first digit has to be a 1? / (4)
2.3.2 / What difference would if make if the first digit was a 0 or a 1? / (3)
[16]

Question 3

The lengths, x, in mm of 50 hummingbirds have been measured and the results are recorded in the table below.
Length
(x mm) / / / / / / /
Frequency / 4 / 6 / 9 / 12 / 10 / 6 / 3
3.1 / Find the estimated mean length of the hummingbirds. / (3)
3.2 / Find the standard deviation of the length of the hummingbirds. / (1)
3.3 / What percentage of the hummingbirds fall outside one standard deviation of the mean length? / (3)
[7]

Question 4

50 learners take an English and Maths Exam. The distribution of their marks obtain is in the table below:
Mark / 21-30 / 31-40 / 41-50 / 51-60 / 61-70 / 71-80 / 81-90 / 90-100
No. of Learners / Eng / 0 / 1 / 4 / 20 / 14 / 8 / 2 / 1
Math / 2 / 3 / 6 / 10 / 12 / 10 / 4 / 3
The following graph shows the cumulative frequency for English marks.
Cumulative Frequency / Marks
4.1 / Show the cumulative frequency for the Maths marks on the graph. / (2)
4.2 / Complete the table below:
English / Mathematics
Median / 60
Inter-quartile range / 14
/ (3)
4.3 / Use the information in the table to comment on the differences between the two distributions of marks. / (2)
4.4 / Of the 50 learners, 30 pass the Maths exams at first attempt. From past performance it is known that, if a learner fails at the first attempt, the probability of passing the second attempt is 0,7. Calculate the probability that a learner, chosen at random, will pass the maths exam at either first or second attempt? / (2)
[9]

Question 5

Look at the three scatter graphs below:

Diagram 1Diagram 2Diagram 3




Write down the number of the diagram that is most likely to represent:
5.1 / The heights of a group of boys on the x –axis and the sizes of shirts worn by them on the y axis.
5.2 / The mean temperature during the day on the x axis and the amount of gas used to heat a house on the y axis.
5.3 / The shoe sizes of a group of adults on the x axis and their ages on the y axis.
[3]

Question 6

A sample of 8 US companies showed the following Sales and Profit levels (in millions) for the year ending April 1994.
Sales Turnover ($) / 22 / 36 / 26 / 14 / 25 / 34 / 6 / 18
Profit ($) / 1,8 / 4,9 / 0,8 / 0,9 / 3,2 / 3,7 / 0,5 / 2,1
6.1 / Draw a scatter diagram of this information using the axes provided.
/ (3)
6.2 / Calculate the equation of a line of best fit. / (2)
6.3 / Use the above equation to estimate Profit levels for two companies with annual turnovers respectively of $28 million and $42 million. / (2)
6.4 / State briefly which of the estimate in 6.3 is likely to be more accurate. Justify your choice. / (2)
[9]
Question 7
7.1 / In circle O, AB = BC, OP = 10, OB = 6. Find the length of AC


/ (3)
7.2 / In the figure below, P, Q, R and S are points on a circle with centre M. If and
Calculate the size of (giving reasons) / (5)
[8]

Question 8

In the diagram below, diameter AB is produced to C. CE is a tangent to the circle at E. AE is produced to D and DC AC.
Prove:
8.1 / BEDC is a cyclic quadrilateral
8.2 /
8.3 / CE = CD
8.4 /
[12]

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