St Stithians Collegemaths.stithian.com/2013 New Prelim Papers/St Davids/St... · Web viewST DAVID’S MARIST INANDA PRELIMINARY EXAMINATION SEPT 2013 ST. DAVID’S MARIST INANDA MATHEMATICS

ST. DAVID’S MARIST INANDA

MATHEMATICS PAPER II

GRADE 12

SEPTEMBER 2013

EXAMINER: MRS L NAGY MARKS: 150

MODERATOR: MR M JEENAH TIME: 3 HOURS

Please put a tick next to your teacher’s name:

Mr Jeenah Ms Rider Mrs Nagy Mrs Kennedy

NAME:__________________________________________________________

INSTRUCTIONS:

This paper consists of 24 pages and a Formula sheet on page 24. ROUGH WORK can be done on page 23. Please check that your paper is complete.

Please answer all questions on the Question Paper. You may use an approved non-programmable, non-graphics calculator unless otherwise

stated. Answers must be rounded off to two decimal places, unless otherwise stated. It is in your interest to show all your working details. Work neatly. Do NOT answer in pencil. Diagrams are not drawn to scale.

SECTION A Q1

(19)

Q2

(8)

Q3

(18)

Q4

(17)

Q5

(13) (75)

SECTION B Q6

(9)

Q7

(15)

Q8

(10)

Q9

(14)

Q10

(18)

Q11

(9)

(75)

[150]

ST DAVID’S MARIST INANDA PRELIMINARY EXAMINATION SEPT 2013

Page 2 of 25

SECTION A

QUESTION 1

a) The box and whisker plot below represent the price of oil in 2010 (in USD) and has the following values:

(1) Use the given values to calculate the (i) lower quartile. (1)

(ii) maximum value. (1)

(2) If there are 12 terms in the data set above and there are 4 terms in A and 3 terms in D, how many terms are there in(i) B? (1)

(ii) C? (1)

(3) Do you agree with the following statement about the box and whisker plot above: The data is symmetrically distributed about the median. (2)


Page 3 of 25

(4) The table below gives the average rand/dollar exchange rate and the average monthly oil price for the year 2010.

Jan.

Feb.

Mar.

Apr.

May

Jun. Jul. Aug

.Sep

. Oct. Nov.

Dec.

Exchange rate in R/USD

7,5 7,7 7,2 7,4 7,7 7,7 7,6 7,3 7,1 7,0 6,9 6,8

Oil price in USD 69,9 68,0 72,9 70,3 66,3 67,1 67,

9 68,3 71,3 73,6 76 81

(i) Draw a scatter plot below to represent the exchange rate in (R/USD) and the oil price (in USD). (3)

(ii) Describe the relationship between the exchange rate (in R/USD) and the oil price (in USD). (2)

(iii) Determine the mean oil price. (2)


Page 4 of 25

(iv) Determine the standard deviation of the oil price. (2)

(v) Generally there is concern from the public when the oil price is higher than two standard deviations from the mean. In which month(s) would there have been concerns from the public? (2)

b) A group of students wrote a Geography test and the following data was obtained:

Standard Deviation Mean6 74

The teacher decided to decrease the marks by subtracting 4 marks from each person’s mark. For the new set of marks, write down

(1) the mean. (1)

(2) the standard deviation. (1)

[19]QUESTION 2

a) The points are given. Determine the value ofp if A, B and C are collinear. (3)


Page 5 of 25

b) Refer to the figure. Given The straight line f has the equation ax + by + c = 0. Determine the values of a, b and c.

x

y

αN

9 M

(5)

[8]


Page 6 of 25

QUESTION 3

a) is the centre of a circle and is a point on the circle.(1) Calculate the length of the diameter of the circle. (4)

(2) The equation of the tangent to the circle at A. (4)

b) If , determine the new centre and radius of the circle if it is first translated 4 units to the left and 3 units up, then enlarged about the origin by a factor . (4)


Page 7 of 25

c) In the diagram, centre C of the circle lies on the straight line 3x + 4y + 7 = 0. The straight line cuts the circle at D and E(-1; -1). The circle touches the y-axis at P(0 ; 2).

Determine:

(1) the circumference of the circle. (4)

(2) the coordinates of D. (2)

[18]


Page 8 of 25

QUESTION 4

Given , if on the set of axes below:

a) (1) Determine the general solution of (4)

(2) Write down the coordinates of A. (2)

b) Draw on the same set of axes , if . (3)

c) For which value(s) of x is

(1) (2)


Page 9 of 25

(2) (1)

(3) (3)

d) If write down the minimum value of h. (2)

[17]

QUESTION 5

a) Evaluate:

(6)


Page 10 of 25

b) If determine the following in terms of d:

(1) (2)

(2) (2)

(3) (3)

[13]


Page 11 of 25

SECTION B

QUESTION 6

are 4 distinct points and .

Calculate the value(s) of k, if :a) PQ // OR (6)

b) (Leave your answer in surd form.) (3)

[9]


Page 12 of 25


Page 13 of 25

QUESTION 7

In the diagram, a circle with centre C and with equation is given. PR is a tangent to the circle at P.

R(k ; 6)

O

y

x

P

C

a) Determine the coordinates of centre C and the length of the radius. (5)


Page 14 of 25

b) The length of a tangent from point R( k ; 6) to point P is 10 units. If k > 0, show that k = 13. (6)

c) If , determine the value of y. (4)

[15]


Page 15 of 25

QUESTION 8

a)

The triangular section PQR, of a flood warning sign is enlarged by factor k, through

the origin to form . If the area of triangle PQR is 18 and the area of

triangle is 50 and , determine the coordinates of (4)


RQ

x

yP( - 27 ; 15)

Page 16 of 25

b) The program selector of a washing machine can be rotated in

either direction. It stands on and you want to

select the program Cottons and Linens at point . What is the smallest angle through which the selector must be turned? (6)

[10]ST DAVID’S MARIST INANDA PRELIMINARY EXAMINATION SEPT 2013

SPIN

OFF

B( 7; 1)

A( -5; 5)

Page 17 of 25

QUESTION 9

a) In the diagram alongside R is a point in a Cartesian plane.

O

θ

x

y

R - p ; p - 3( )

(1) Express in terms of p. (4)

(2) Determine in terms of p if are supplementary. (2)


Page 18 of 25

(3) Hence, if p = 6, prove that

(4)

b) Determine, without using a calculator, the numerical value of the following (leaving the answer in surd form):

(4)

[14]ST DAVID’S MARIST INANDA PRELIMINARY EXAMINATION SEPT 2013

Page 19 of 25

QUESTION 10

a) Given the identity

(1) Prove the identity. (6)


Page 20 of 25

(2) For which values of B in the interval is the identity undefined? (4)

(3) HENCE, calculate the value of . Show ALL your work and do NOT use a calculator. (2)

b) Determine the general solution of . (6)

[18]


Page 21 of 25

QUESTION 11

The diagram alongside represents the right cylindrical oil storage tank seen above. T is the centre of the circular base. NA and KN are tangents to the base at A and K. T, A, N and K lie on the same horizontal plane. SK represents the vertical height of the cylindrical part of the oil storage tank.

a) Show that . (4)


β

α

d

h

r

S

K

N

A

T

http://www.bing.com/images/search?q=images+of+fuel+storage+tanks&id=3200ED6EFF98F29A1EB75EED838F877557C00ADC&FORM=IQFRBA#view=detail&id=4B14C24118D07EE8424D0DD58AB03C0B9AB4FE2A&selectedIndex=556

Page 22 of 25

b) If calculate the volume of the cylindrical section of the oil storage tank. (rounded off to the nearest cubic metre.)

(5)

[9][TOTAL MARKS: 150]


Page 23 of 25

ROUGH WORK


Page 24 of 25

ROUGH WORK


Page 25 of 25


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St Stithians Collegemaths.stithian.com/2013 New Prelim Papers/St Davids/St... · Web viewST DAVID’S MARIST INANDA PRELIMINARY EXAMINATION SEPT 2013 ST. DAVID’S MARIST INANDA MATHEMATICS