QUESTION 1

(a)Solve for :

(1)(4)

(2)(3)

(3)(4)

(4)by completing the square(4)

(b)If , then solve for if (4)

(c)Given:

(1)Solve for .(4)

(2)Hence, or otherwise, determine the sum of all the integers satisfying the expression

.(2)

(d)Given:

(1)Simplify the expression fully.(4)

(2)Hence, solve for if (3)

(e)Determine, in terms of , the coordinates of the points of intersection of the graphs of

and , where .(5)

(f)Given:

For which value(s) of n will the roots be equal?(4)

[41]

QUESTION 2

(a)Given:

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

(2)Determine the and intercepts of the graph of .(4)

(3)Sketch the graph of on the Cartesian plane on the ANSWER SHEET.

Show all asymptotes and intercepts with the axes.(3)

(4)Write down the domain and range of .(2)

(b)Given:

(1)Determine the intercepts with the axes.(3)

(2)Sketch the graph of on the Cartesian plane on the ANSWER SHEET.

Label clearly all asymptotes and intercepts with the axes.(3)

(3)If , describe the transformation that has been applied to to result

in .(2)

[19]

QUESTION 3

A bank offers interest on investments at a rate of 15% per annum compounded monthly.

(a)Calculate the effective interest rate equivalent to this.(3)

(b)Determine how much a person must invest now (as a lump sum) so that they have R20000 in

fouryears’ time.(3)

(c)Suppose Angie follows the following savings plan (in the bank with 15% p.a. compounded

monthly):

1 September 2016:Deposit R3500

1 February 2018:Deposit R8100

1 January 2019:Withdraw R4200

1 July 2019:Deposit R8500

Determine if Angie will have more than R200000 in her account by 1st January 2020.

(Show all your working.)(5)

(d)Angie has a new trailer worth R8500. The depreciation rate on this item is 10% p.a. on the

reducing balance method. Calculate the value of her trailer after 4 years.(3)

(e)Draw a rough sketch graph showing the reducing balance of Angie’s trailer over the 4 year
period.(2)

[16]

QUESTION 4

(a)You are given the first 3 terms of a number pattern:1; 2; 4; ………….

Jonathan says that the next term is 7 but Amber says the next term is 8.

Explain how each learner determined the next term.(4)

(b)You are given the following quadratic number pattern:

Determine the value of .(7)

[11]

QUESTION 5

(a)For two events, A and B, in the Sample space S, it is given that:

P(A) = 0,55P(B) = 0,6P(A and B) = 0,25

(1)Draw a Venn Diagram to represent the information.(4)

Determine:

(2)(1)

(3)(2)

(b)The Titanic sank in 1912 without enough life boats for the passengers and crew.

The contingency table below provides data on the passengers who were on board during the

disaster.

Male / Female / Total
Survived / 344
Did not survive / 1 364 / 1 490
Total / 1 731 / 470

(1)Complete the contingency table on the ANSWER SHEET.(4)

Determine:

(2)The probability that a passenger survived the disaster.(2)

(3)The probability that a passenger that is female did not survive the disaster.(2)

(4)Whether the events M = {a passenger was male} and N = {a passenger did not survive}

are dependent or independent.(4)

[19]

QUESTION 6

The graph of is sketched, where

For each of the following, choose the statement ((i), (ii) or (iii))

that applies.

(a)(1)

(b)(1)

(c)(1)

(i)Roots are non-real

(ii)Roots are real and unequal

(iii)Roots are real and equal

[3]

QUESTION 7

(a)The diagram below shows a picture of a bow and arrow.

The picture is represented on the set of axes below.

Points A(3; 0), B(7; 0) and E(6; 6) are given. CD is perpendicular to AB.

(1)Determine the equation of the parabola in the form .(4)

(2)Determine the equation of AD if the gradient of AD is –2.(3)

(3)Hence, determine the length of CD.(4)

(b)The arrow will follow a parabolic path, with a maximum point of release.

It is given that the equation of the path is .

Determine the horizontal distance travelled by the arrow by the time it hits the ground.(3)

[14]

QUESTION 8

Refer to the figure showing the graphs of and with the intercepts indicated.

Use the graphs to answer the following questions:

(a)Determine the values of for which .(2)

(b)Determine the values of for which for (2)

(c)Determine the average gradient of on the interval (3)

[7]

QUESTION 9

Pete is driving his remote controlled car at the local track.

Once he sets the throttle, he starts to take note of how

far the car is from the starting line (in cm) at a particular

time (in seconds) and records his measurements.

His results are presented in the table below:

Assume the pattern continues.

(a)If the throttle setting and all other conditions remain the same, write down the values of A
and B in the table above.(2)

(b)Determine a general formula for the distance () from the start line after seconds.(4)

(c)Hence, how far was the car from the starting line after 10 seconds?(2)

(d)What is the average speed of the car for ?(2)

(e)Determine the minimum distance from the start line achieved by the car and the time at which it occurs. (4)

[14]

QUESTION 10

There are orange balls and 2 yellow balls in a bag. Craig randomly selects one ball from the bag,

records his choice and returns the ball to the bag. He then randomly selects a second ball from the bag,

records his choiceand returns it to the bag. It is known that the probability that Craig will select two

balls of the same colour is 52%.

Calculate how many orange balls are in the bag.(6)

[6]

TOTAL: 150