MATHEMATICS EXAMINATION – PAPER I

1stSEPTEMBER2011

GRADE 12

TIME: 3 HOURS TOTAL MARKS: 150

EXAMINER: L. le ROUX MODERATORS: M. SOLOMONS

A. LEVIN

NAME:______

CLASS:______

Instructions

Work neatly and accurately.

SHOW WORKING OUT WHERE NECESSARY!

Calculators may be used unless otherwise stated.

Round off your answers to ONE decimal place where applicable unless stated otherwise.

LEARNING OUTCOME

/

QUESTION

/ MAXIMUM MARKS / MARKS OBTAINED
LO 1 and LO 2 / 1 / 25
LO 1 / 2 / 15
3 / 11
4 / 4
LO 2 / 5 / 12
6 / 17
LO 1 / 7 / 20
LO 2 / 8 / 29
LO 1 / 9 / 17
QUESTION 1

1.1 Given:

Solve for x if:

1.1.1 (1)

1.1.2 (1)

1.1.3 (2)

1.2Solve for x:

1.2.1 (round off your answer to two decimal places) (2)

1.2.2 (show all your working) (4)

1.2.3 (4)

1.2.4 (5)

1.2.5 (3)

1.2.6 (3)

[25]

QUESTION 2

Alon was delighted to learn that he had won the “Customer of the month” award at his local bank. A computer would adjust his account on a daily basis by adding an amount according to the following sequence

R180 ; R160 ; R140 ; R120 …

2.1If Alon had R300 in his account on the day the first amount was added, calculate the amount in his account after the 9th prize payment. (4)

2.2Alon was keen to know after how many days he would receive a total of R840 from the “Customer of the month” award. He is puzzled when he obtains two possible values for n.

Check his calculations and suggest whether there is a reason for rejecting 1 value. (6)

2.3Alon’s puzzlement turns to shock when he calculated the amount in his account on the 50th day. How much will he have in his account and explain what happened. (5)

[15]

QUESTION 3

The seats in the theatre where Ari B makes his debut on “Broadway” is numbered using the

arrangement seen below.

3.1 How many seats are there in the 20th row? (2)

3.2Find the seat number of the 4th seat from the left in the 30th row? (5)

3.3How many rows (according to this pattern) are needed if the theatre has a capacity of 1786 seats? (4)

[11]

QUESTION 4

A circle is completely divided into n sectors in such a way that the angles of the sectors form an arithmetic sequence.

Calculate the value of n if the smallest angle is and the largest is . [4]

QUESTION 5

In the diagram, the graphs of the following functions have been sketched:

and

The two graphs intersect at and the turning point of the parabola lies at the point of intersection of the asymptotes of the hyperbola. The line is the axis of symmetry of the

parabola.

5.1Determine the equation of f in the form . (3)

5.2Determine the equation of g in the form . (3)

5.3State the range for the graph of f. (2)

5.4If the graph of f is shifted 1 unit left and 2 units downward, write down the equation of the new graph formed. (2)

5.5Write down the values of x for which . (2)

[12]

QUESTION 6

Sketched below are the graphs of and

6.1Write down the equation of the inverse of the graph of in the form

(2)

6.2On a set of axes, draw the graph of the inverse of showing intercepts. (2)

6.3Write down the domain of the graph of (1)

6.4Explain why the inverse of the graph of is not a function. (1)

6.5Consider the graph of

6.5.1Write down a possible restriction for the domain of so that the

inverse of the graph of g will now be a function. (1)

6.5.2Hence draw the graph of the inverse function in 6.5.1 (2)

6.6Describe the transformation of the graph of f, that would enable you to sketch the

graphs of:

6.6.1 (2)

6.6.2 (2)

6.7Sketch the graph of on a set of axes showing clearly any x- and y- intercepts

and asymptotes. (4)

[17]

QUESTION 7

7.1A motor car costing R200 000 depreciated at a rate of 8%

per annum on the reducingbalance method. Calculate how

long it took for the car to depreciate to a value of R90 000

under these conditions. (4)

7.2Adam starts a five year savings plan. At the beginning of the month he deposits R2000 into the account and makes a further deposit of R2000 at the end of that month. He then continues to make month end payments of R2000 into the account for the five year period (starting from his first deposit). The interest rate is 6% per annum compounded quarterly.

7.2.1Calculate the future value of his investment at the end of the five yearperiod. (6)

7.2.2Owing to financial difficulty, Adam misses the last two payments of R2000 each. What will the value of his investment be at the end of the five year period? (4)

7.3Jordan takes out a twenty year loan of R100000. She repays the loan by means of equal

monthly payments starting three months after the granting of the loan. The interest rate

is 18% per annum compounded monthly.

7.3.1Calculate the amount owing two months after the loan was taken out by Jordan. (2)

7.3.2Calculate the monthly repayments. (4)

[20]

QUESTION 8

8.1Given . Determine using first principles. (5)

8.2Given . Determine using first principles. (6)

8.3Determine the derivatives of the following functions, leaving answers with positive exponents:

8.3.1 (4)

8.3.2 (4)

8.3.3. (3)

8.4 Find the equation of the tangent to which is parallel to the line

(7)

[29]

QUESTION 9

The KDVP mixed doubles tennis team, consisting of boys and girls must be selected as follows:

-the team must have at least 2 members.

-the number of girls may not be more than 3 times the number of boys.

-the maximum number of members per team may not exceed 8.

Let x be the number of boys and ythe number of girls.

9.1 Formulate all the constraints for the team described above. (4)

9.2 If it is further given that, graph the constraints on the paper provided and clearly indicate the feasible region. (6)

9.3During the tournament every boy may take 5 supporters and every girl 7. Write this as an

objective function. (2)

9.4 Use your graph to determine how many people of each gender must be included to maximise the number of supporters. (3)

9.5 What is the maximum number of supporters? (2)

[17]

Name:______

QUESTION 9.2

1