JUNE 2014 EXAMINATIONS: MATRIC MATHEMATICS: PAPER IPage 1 of 12
JUNE MATRIC 2014
MATHEMATICS: PAPER I
Time: 3 hours 150 marks
Reading Time: 10 Minutes Examiner: R. Bourquin
Moderators: M Brown and R Karam
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1.This question paper consists of 12 pages, an Answer Sheet(1 page) and an Information Sheet. Please check that your paper is complete.
2.Question 4(b) must be completed on your Answer Sheet. Please make sure your answer sheet is placed in your answer book and is handed in.
Please make sure that your name is on your answer sheet.
3.All other questions must be answered in your answer book.
4.Read the questions carefully.
5.You may use an approved non-programmable and non-graphical calculator, unless otherwise stated.
6.All the necessary working details must be clearly shown.
7.Round off your answers to onedecimal digit where necessary, unless otherwise stated.
8.It is in your own interest to write legibly and to present your work neatly.
9.No diagrams are drawn to scale.
SECTION A
QUESTION 1
Solve for :
(a)(2)
(b)(4)
(c) (4)
(d)(3)
[13]
QUESTION 2
(a)Given:
(1)Write down the first three terms of the series.(1)
(2)Calculate the sum of the series.(4)
(b)Determine the first three terms of the geometric sequence of which the
6th termis and the 9th term is .(7)
[12]
QUESTION 3
(a)Botle’s Porsche Cayenne depreciates at a reducing balance rate of 10% p.a.
Determine how many years and months it will take for her Porsche to halve
in value.(4)
(b)
The graph above illustrates the growth of a lump sum of money that
Thato invested in Ámandla Bank.
Determine the annual interest rate she received as a percentage using
the graph above.(4)
(c)Bianca buys a house for R2 000000.
She puts down a deposit of R300000.
She makes the remainder of the payment by means of a loan from the bank at
a fixed interest rate of 9% p.a. compounded monthly.
She agrees to pay back the loan by means of equal monthly payments over
15 years starting one month after she loaned the money.
(1)Determine the equal monthly payments.(5)
(2)Assuming Bianca’s monthly repayments are R17 242,53 calculate the
outstanding balance of her loan after 7 years (immediately after she
makes her 84th repayment).(5)
(3)Calculate the total amount of interest Bianca would have paid to the
bank once she has fully paid back her loan at the end of 15 years.(3)
[21]
QUESTION 4
(a)
Refer to the figure above.
; and lie on
Determine:
(1)the equation of the axis of symmetry of .(1)
(2)the equation of in the form .(4)
(3)the domain and range of .(4)
(b)ANSWER THIS QUESTION ON YOUR ANSWER SHEET
Refer to the figure above of
On your answer sheet:
(1)draw a labelled sketch of on the axes provided.(3)
(2)determine the equation of (2)
(3)write down the equation of the line of reflection of and .(1)
(4) is reflected about the – axis and then the axis to form graph .
Determine the equation of (2)
[17]
QUESTION 5
(a)Determine from first principles if (5)
(b)Find given:
(1) ; (2)
(2) .(4)
(c)Determine the equation of the tangent to at .(4)
[15]
78 marks
SECTION B
QUESTION 6
(a)Given: and
Determine:
(1) the value(s) of for which A is undefined.(1)
(2) the value(s) of for which B is real.(3)
(3) the smallest natural number that can be when B is irrational.(1)
(4) the smallest integer that can be when B is non-real.(1)
(b)If is a rational number then
If is an irrational number then
Find the value of (2)
[8]
QUESTION 7
(a)The table below shows values satisfying the relationship:
n / 1 / 2 / 3 / 4 / 5 / 6/ 5 / 11 / A / 35 / 53 / 75
(1) Determine the value of A.(2)
(2) Determine the value of and .(4)
(b)The sum of the first terms of a sequence is given by:
=
Find:
(1) the sum of the first 3 terms.(1)
(2) the third term.(3)
(3) an expression for the term of the sequence.(4)
(c)Find the largest 4 digit number in the sequence: 1; 4; 7; 10; 13……g(3)
[17]
QUESTION 8
(a)
The graph of is illustrated above.
is shifted units to the right and units up to form graph .
and
Determine:
(1)The equation of .(2)
(2)The equation of the axis of symmetry of that has a negative gradient,
in terms of and (3)
(b)
Refer to the diagram above. This diagram is not drawn to scale.
Moteo, an enthusiastic basketball player is practising her shooting.
Each throw follows the path of a parabola.
She throws from a pointA which is above the floor.
On one of her throws, the ball reaches its maximum height of
when it has covered a horizontal distance of .
Unfortunately, on this throw, the ball does not go into the basket, but hits
the front of the rim of the basket which is above the floor.
CD and AE are perpendicular to the ground.
Determine:
(1), the horizontal distance between Moteo’s hand and the front
of the rim of the basket.(6)
(2), the actual distance between Moteo’s hand and the front
of the rim.(2)
[13]
QUESTION 9
(a)Rebecca has either pasta or pizza for lunch. If she has pasta one day, the
probability she has pasta the next day is 0,2. If she has pizza one day, the
probability she has pizza the next day is 0,4.
Rebecca has pizza on Wednesday 11th June.
(1)Draw a tree diagram to represent the above situation.(2)
(2)Hence, or otherwise, determine, to two decimal digits, the probability
that she has pastaon Friday 13th June. (3)
(b)Let and be two events in a sample space such that
and .
(1)If and are mutually exclusive,find .(3)
(2)If and are independent, but are not mutually exclusive,
find (4)
[12]
QUESTION 10
(a)Given:
Determine:
(1)(2)
(2)(4)
(3)(2)
(b)
Refer to the graph of illustrated above.
State whether the following are positive, negative or zero:
(1)(2)
(3) (4)
(5) (6)
(7) (8) (4)
(c)Given:
Find the coordinate(s) of the point(s) on the graph of at which the
tangent(s) are perpendicular to the line .
Give answer(s) to one decimal digit if necessary.(5)
[17]
QUESTION 11
The two roots of the equation differ by 5.
Calculate the value(s) of p.
[5]
72marks
Total: 150 marks
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