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KEARSNEY COLLEGE TRIAL EXAMINATION

6 SEPTEMBER 2019

MATHEMATICS: PAPER 1

Time: 3 hours 150 marks

EXAMINATION NUMBER 1 9 1 0 6 8 0 2

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY.

1. This question paper consists of 19 pages and an Information Sheet. Please check that

your paper is complete.

2. Read the questions carefully.

3. Answer ALL the questions on the question paper and hand it in at the end of the

examination. Remember to write your examination number on the paper.

4. Diagrams are not necessarily drawn to scale.

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

otherwise.

6. Round off your answers to one decimal digit where necessary, unless stated otherwise.

7. All necessary working details must be clearly shown.

8. Ensure that your calculator is in DEGREE mode.

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

NO WORKING WILL RESULT IN PENALISATION OF MARKS

Mathematics: Paper 1 Page 1 of 19

SECTION A (40 Marks)

EXAMINATION NUMBER 1 9 1 0 6 8 2

QUESTION 1

Solve for , correct to two decimal places where necessary.

(a) = 0 (4)

(b) (3)

(c) (3)

[10]Kearsney College Copyright © 2019 Trial Examination


QUESTION 2

Solve for and : and

[5]QUESTION 3

An arithmetic sequence is given as:

(a) Determine the value of and hence give the first three terms of the sequence. (4)

(b) Determine the term of the sequence. (2)

Kearsney College Copyright © 2019 Trial Examination


[6]QUESTION 4

Given:

(a) Simplify P. (3)

(b) Hence solve for x if P = 8. (2)

[5]

QUESTION 5

Given , determine from first principles.



[4]

QUESTION 6

Find the value of in the following:

[4]



QUESTION 7

Circle the correct answer.Show all working details clearly.

(a) The equation of the axis of symmetry of is: (2)

A: B: C: D:

(b) The domain of is represented by the inequality .

Which of the following describes the range of ? (4)

A: B: C: D:

[6]



SECTION B (35 Marks)


QUESTION 8

Consider the functions and

(a) Write down the equations of the asymptotes of . (2)

(b) Give the turning point of if . (4)

(c) Give the equation of , which is a representation of reflected about the line (2)

[8]



QUESTION 9

(a) Determine (3)

(b) Given: , calculate (4)

[7]



QUESTION 10

Given:

Determine the equation of the tangent to which is perpendicular to the line

[6]



QUESTION 11

Consider the function

Solve for if

[5]QUESTION 12

has the following properties:

and

Use the above information

to sketch on the axes below.



[4]

QUESTION 13

For which value(s) of does the sequence converge?

[5]



SECTION C (35 Marks)


______________________________________________________________________________

QUESTION 14

Joy loves dancing and is planning on developing a dancing school.

(a) Joy starts investing at the end of every month into an account that offers an interest rate of p.a. compounded monthly. Show that the investment grows to a greater value than over a period of 10 years.

(4)

(b) (4)


Ten years go by and eventually Joy finds the perfect property for her dance school. The cost of the property is R 1 205 000. She pays a deposit of R 135 000. Calculate the monthly payment needed to pay off the loan over a period of 20 years, if the rate of borrowing money is 9% p.a. compounded monthly, and the first payment is made at the end of the first month.


(c) Joy takes out the loan in (b) above, and starts paying it off every month. The business starts to go well and Joy starts to think about paying off her loan quicker.

(1) Calculate the balance outstanding on her loan at the end of 8 years. (4)

(2) If the balance outstanding on Joy’s loan at the end of 8 years is R 845 940,64, and she decides to increase her payments to R 25 000 per month, calculate how many more months it will take to pay off her loan. (4)

[16]



QUESTION 15

The graph shows the function

and . The two functions intersect at

.

(a) Determine the value of (2)

(b) If the point lies on , determine the new coordinates when is reflectedin the line (1)

(c) Write down the inverse function in the form (2)

(d) Determine the range of (2)

(e) Use your graphs to determine the values of for which ? (4)



[11]QUESTION 16

Given the sequence:

Determine the position of the first term of this sequence that will be greater than 5000.

[4]

QUESTION 17

The probability that I go for a run this evening is 0,3 and the probability that I will have pasta tonight is 0,6.

Calculate the probability that I will go for a run or eat pasta if these events are independent.



[4]SECTION D (40 Marks)


______________________________________________________________________________

QUESTION 18

(a) A group of 3 South Africans, 2 Australians and 2 Englishmen are staying at the same hotelwhile on holiday. Each person has his/her own room and the rooms are next to each other along a straight corridor.If the rooms are allocated at random, determine:

(1) how many different room allocations there are. (1)

(2) the probability that the 3 South Africans will be in adjacent rooms. (4)

(b) Determine the probability that a point selected at random within the large semi-circle is also within one of the equal sized small semi-circles.

(5)



[10]

QUESTION 19

Sketches of

and are drawn.

The asymptotes intersect at P

and is a point on and .

(a) Give the co-ordinates of P. (2)

(b) Describe the transformation from to if = . (2)

(c) Determine the values of for which (4)



[8]

QUESTION 20

The function is represented in the given sketch.

It has an intercept of , a intercept of and

it passes through point .

(a) Show that the equation of the

function is . (4)

(b) Show that A is the point of inflection of the function. (4)

(c) For what values of would the function have three real roots? (3)



[11]QUESTION 21

Consider the quadratic equation

If , and are positive real numbers and form a geometric sequence, discuss the nature of the roots of the equation, justifying your answer.

[5]



QUESTION 22

PQ is the diameter of the semi-circle PRQ and

Calculate the dimensions of the triangle when it has a maximum area.

Leave your answer in surd form where necessary.

[6]


qp

R

QP

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