ST STITHIANS BOYSCOLLEGE

GRADE 12

MATHEMATICS CORE PAPER 3

(LO 3 AND LO 4)

JULY 2008

Time: 2 hours 100 marks

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

1.This question paper consists of 8 pages,a two page detachable diagram sheet and a formula sheet. Please check that your paper is complete.

2.Read the questions carefully.

3.Answer all the questions.

4.Number your answers exactly as the questions are numbered.

5.You may use an approved non-programmable and non-graphical calculator, unless otherwise stated.

6.Round off your answers to two decimal digits where necessary.

7.All the necessary working details must be clearly shown.

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

QUESTION 1

The recursive formula for of a particular sequence is

where .

i)Find the sequence. (2)

ii)Find the explicit form of the sequence in the form (5)

[7 marks]

______

QUESTION 2

All answers using factorials ( n! ) must be evaluated: eg: 3! = 6

a)A restaurant offers a choice of 4 starters, 3 main courses and 5 desserts.

How many different combinations are possible, if a diner chooses one from

each option?(2)

b)If the letters of the word MATHEMATICAL are arranged randomly into

a ‘word’, how many arrangements will there be

i)if there are no restrictions? (3)

ii)that start with a C and end with a double T? (3)

c) A card is picked from a pack of cards, replaced and then a second card is

picked and replaced. Find the probability that both the cards are picture

cards?(Jack, Queen, King) (3)

d)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)

e)Michael and Peter decide to enter the Comrades Marathon.

The probabilities that they will complete the marathon are 0,9 and 0,65

respectively. What is the probability that only one of the two will complete

the marathon?( assuming that the performance of each is independent of

theperformance of the other). (5)

[20 marks]

QUESTION 3

Weight (kg) / Frequency f
1.0  w < 1.5 / 4
1.5  w < 2.0 / 7
2.0  w < 2.5 / 12
2.5  w < 3.0 / 14
3.0  w < 3.5 / 10
3.5  w < 4.0 / 9
4.0  w < 4.5 / 4
4.5  w / 0
Total = 60

This frequency table gives the weights of the first 60 babies born at a new clinic in Cape Town.

a) Construct a cumulative frequency tablefor the data, using TABLE 1 on the attached diagram sheet. (2)

b) Draw a cumulative frequency curve (ogive) for this data. Use DIAGRAM 1 on the diagram sheet. (2)

c) Estimate, from your graph, the median and quartiles for the weights of the babies. (3)

d) Calculate the estimated mean weight of the babies. (3)

e)Determine the standard deviation. (2)

[12 marks]

______

QUESTION 4

70 learners in Grade 12 were asked about the amount of pocket money they receive each week.

Amount of pocket money / 80 / 120 / 160 / 200 / 240 / 280 / 300 / 400 / 800 / 1200
Number of Learners / 10 / 3 / 2 / 18 / 5 / 10 / 13 / 4 / 3 / 2

At the PTA meeting it was stated by a parent that

“ The survey shows that the Grade 12 learners get about R240 pocket money.”

In the school newsletter an article stated:

“ The survey shows that most learners get R200 pocket money.

State, with a reason, which measure of central tendency (mean, median or mode)

i)the PTA is referring to? (2)

ii)the school letter is referring to? (2)

[4 marks]

QUESTION 5

Grade 12 learners were investigating whether there is a relationship between height and foot length in their class. They randomly selected 11 learners from whom to collect data.

Length of left foot
x (in cm) / 27,4 / 26,3 / 25 / 25,4 / 27,6 / 22,5 / 27 / 27,5 / 24,6 / 28 / 26,4
Height
y (in cm) / 175 / 172 / 167 / 169 / 173 / 162 / 168 / 170 / 158 / 172 / 180

a)Using DIAGRAM 2, on the diagram sheet, draw a scatter plot of the data

set. (3)

b)Calculate the equation of the regression line of best fit. (4)

c)Calculate the correlation coefficient for the data. (3)

d)What conclusions, based on your answer in c) above, can you draw about the relationship between the foot size and the height of the 11 Grade 12 learners in the data set? (2)

e)Show whether the point with coordinates lies on the line of best fit. (4)

[16 marks]

QUESTION 6

FOR THE GEOMETRY SECTION, REASONS SHOULD BE GIVEN UNLESS STATED THAT IT IS NOT REQUIRED.

a)In the figure alongside , has V the midpoint of PM.

and

Determine the following (without reasons)

i)(1)

ii)(2)

iii)(2)

b)PQRT is a rectangle.

1)Findthe size of each of the following angles in terms of y:

i)(2)

ii)(2)

2)Prove that

i)(3)

ii)(3)

[15 marks]

QUESTION 7

a)O is the centre of the circle.

units, units and units.

Find the value of x.(4)

b)O is the centre of the circle and . If calculate the sizes of each of the following angles (no reasons need be given):

i)

ii)

iii)

iv)

(4)

c)PQ is a diameter. and MT is a tangent.

Find the magnitude of:

i)(4)

ii)(2)

d)ABCD is a cyclic quadrilateral with AD produced to E such that .

C and E are joined and DB is the angle bisector of .

Let

i)Prove that (3)

ii)Prove that (2)

iii)Find in terms of x.(2)

[21 marks]

QUESTION 8

In the figure P,A,R, C, Q and B are points on the circumference of the circle.

i)Complete: ( ………………………………..)(1)

ii)Prove that (4)

[5 marks]

DIAGRAM 2

ST STITHIANS BOYSCOLLEGE

GRADE 12

MATHEMATICS CORE PAPER 3

(LO 3 AND LO 4)

JULY 2008

DIAGRAM SHEET

NAME: ______

TABLE 1:

Weight (kg) / Frequency f
1.0  w < 1.5 / 4
1.5  w < 2.0 / 7
2.0  w < 2.5 / 12
2.5  w < 3.0 / 14
3.0  w < 3.5 / 10
3.5  w < 4.0 / 9
4.0  w < 4.5 / 4
4.5  w / 0
Total = 60

DIAGRAM 1:

1