thutong.doe.gov.za Grade 12 Mathematics Exemplar Exam Sample Question Paper : Department of Basic Education

Organisation : Department of Basic Education
Exam : Mathematics Exemplar Examination
Document Type : Sample Question Paper
Category or Subject : Grade 12

Website : http://www.thutong.doe.gov.za/Home/Curriculum/tabid/257/Default.aspx
Download Sample Question Paper :
Paper – 1 : https://www.southafricain.com/uploads/1709-Maths-Paper1.pdf
Paper – 2 : https://www.southafricain.com/uploads/1709-Maths-Paper2.pdf

Grade 12 Mathematics Exemplar Examination Question Paper :

Time: 3 Hours Marks: 150

Instructions And Information :
Read the following instructions carefully before answering the questions.
1. This question paper consists of 12 questions. Answer ALL the questions.

Related : National Senior Certificate Exam NSC Sample Question Paper : www.southafricain.com/1696.html

2. Clearly show ALL calculations, diagrams, graphs, etcetera that you have used in determining your 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. Diagrams are NOT necessarily drawn to scale.
6. Number the answers correctly according to the numbering system used in this question paper.
7. It is in your own interest to write legibly and to present the work neatly.

Question 1 :
1.1 Solve for x rounded off to two decimal places where necessary
1.2 Consider the inequality: 2 4x < 9 Determine the solution to this inequality if
1.2.1 x<{real numbers}
1.2.2 x>{integers}
1.3 Solve for x and y 2 3x – y = 2 and 3y + 9x = 4

Question 2 :
A sequence of isosceles triangles is drawn. The first triangle has a base of 2cm and height of 2cm. The second triangle has a base that is 2cm longer than the base of the first triangle. The height of the second triangle is 1cm longer than the height of the first triangle. This pattern of enlargement will continue with each triangle that follows.

2.1 Determine the area of the 100th triangle.
2.2 Which triangle will have an area of 2 240cm ?

Question 3 :
3.1.1 Calculate the sum of the given series. (4)
3.1.2 Hence calculate the sum of the following series
3.3.1 For which values of x will the series converge?

3.4 Malibongwe bought a franchise business on the 28th February 2009. He took out a loan to pay for the franchise which cost R2 000 000. On the 1st March 2009, he made a profit of R4. On the 2nd March, the profit made was R6. On the 3rd March, he made a profit of R9 and on the 4th March, a profit of R13,50. The profits made per day were deposited into a bank account. After how many days will he be able to pay off the R2 000 000 loan, using the amount saved in the bank account?

Question 4 :
4.1.1 Write down the equations of the asymptotes. (2)
4.1.2 Sketch the graph of f indicating the coordinates of the y-intercept as well as the asymptotes. (6)
4.1.3 Write down the equation of the graph formed if the graph of f is shifted 3 units right and 2 units upwards.
4.2.1 Restrict the domain of f in one specific way so that the inverse of f will also be a function. (1)
4.2.2 Hence draw the graph of your new function f and its inverse function 1 f – on the same set of axes.

Question 5 :
Consider: f (x) = 2cos x
5.1 Draw a sketch graph of y = -2 f (x) for x?[-90°;360°] (2)
5.2 Write down the amplitude of y = -2 f (x) .
5.3 Write down the maximum value of the graph of g(x) = f (x) – 2

Question 6 :
Sketched below is the graph of 2 f (x) = a(x + p) + q .
6.1 Determine the equation of f in the form 2 f (x) = a(x + p) + q . (4)
6.2 Write down the range of f. (1)
6.3 If the graph of f is reflected about the x-axis to form the graph of g, write the equation of g in the form 2 g(x) = a(x + p) + q .

Question 7 :
7.1 Patricia deposited a certain amount of money into a bank account paying 8% per annum compounded half-yearly. After four years, the money has a value of R100 000.

7.1.1 Convert the nominal interest rate into the equivalent annual effective rate. (2)
7.1.2 Hence, or otherwise, calculate the amount of money originally deposited into the bank account by Patricia.

7.2 A motor car which cost R200 000 depreciates at a rate of 8% per annum on the reducing balance method. Calculate how long it will take for the car to depreciate to a value of R90 000 under these conditions.

Question 8 :
Mpho takes out a retirement annuity that will supplement his pension when he retires in thirty years’ time. He estimates that he will need R2 500 000 in this retirement fund at that stage. The interest rate he earns is 9% per annum compounded monthly.

8.1 Calculate his monthly payment into this fund if he starts paying immediately and makes his final payment in 30 years’ time. (5)

8.2 The retirement fund does not pay out the R2 500 000 million when Mpho retires. Instead he will be paid monthly amounts, for a period of twenty years, starting one month after his retirement. If the interest that he earns over this period is calculated at 7% per annum compounded monthly, determine the monthly payments he will receive.