GANSBAAI ACADEMIA

MATHEMATICS
Grade 12 / /

TEST

Augustus 2014

Total: 60
Time: 1 hour 15 min
EXSAMINATOR
MODERATOR / L. Havenga
A. van Wyk / L. Mostert

INSTRUCTIONS

1.This question paper consists of 4 questions. Answer ALL questions.

2.Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers.

3.An approved scientific calculator (non-programmable and non-graphical) may be used,
unless stated otherwise.

4.If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.

5.Number your answers correctly according to the numbering system used in this question paper.

6.Diagrams are not necessarily drawn to scale.

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

QUESTION 121

ABCD is a quadrilateral with vertices A(1; 6), B(3; 0), C(6; 1) and D(7; t) on a Cartesian plane.
AD II BC.

1.1Calculate the gradient of BC.(2)

1.2Determine the equation of AD in the form y=…(3)

1.3Show that t=8.(2)

1.4Calculate the lengths of AD, BC and AB.(4)

1.5Show that AB is perpendicular to BC.(3)

1.6Calculate the area of the quadrilateral ABCD. (Simplify your answer).(4)

1.7Determine , the inclination of BC.(3)

[21]

QUESTION 2

In the figure, B(-1; 1) the centre of the circle. CA is ‘a tangent to the circle at A. C is the point (-1; 26). and CA = 20 units.

Determine:

2.1the length of AB and hence the value of tan.(4)

2.2the equation of the circle.(3)

2.3the equation of the tangent CR.(4)

2.4the equation of the radius AB.(3)

2.5the coordinates of A.(4)

[18]

QUESTION 3

A recording company investigates the relationship between the number of times a CD is played by a national radio station and the national sales of the same CD in the following week. The data below was collected for a random sample of 10 CDs. The sales figures are rounded to the nearest 50.

Number of times CD is played / 47 / 34 / 40 / 34 / 33 / 50 / 28 / 53 / 25 / 46
Weekly sales of the CD / 3950 / 2500 / 3700 / 2800 / 2900 / 3750 / 2300 / 4400 / 2200 / 3400

3.1Identify the independent variable.(1)

3.2Draw a scatter plot of this data on the grid provided on DIAGRAM SHEET 1.(3)

3.3Determine the equation of the least squares regression line.(4)

3.4Calculate the correlation coefficient.(2)

3.5Predict, correct to the nearest 50, the weekly sales for a CD that was played 45 times by the
radio station in the previous week.(2)

3.6Comment on the strength of the relationship between the variables.(1)

[13]

QUESTION 4

A company packaged their cereal in a box that has the shape of a rectangular prism as shown below. The volume of the box is 600 cm3, with a breadth of 6 cm and a length of x cm.

4.1Express the height of the box, h, in terms of x.(2)

4.2Show that the total surface area of the box (in cm2)
is given by:

(2)

4.3Determine the value of xfor which the total surface

area is a minimum.(4)

[8]

TOTAL: 60

DIAGRAM SHEET 1

NAME AND SURNAME: ………………………………………………………………………

QUESTION 3.2

1