1

St Stithians Boys’ College
Mathematics Core Examination
Grade 12
March 2010
Paper 1

2 Hours 100 marks

LO 1: Number and Number Patterns
LO 2: Functions

Instructions:

  1. All working is to be shown in order to achieve the marks allocated for a question.
  2. A non-programmable calculator may be used unless stated otherwise.
  3. All answers are to be given correct to TWO decimal digits where necessary.
  4. It is in your best interests to work neatly and legibly.
  5. This examination paper consists of 5 pages.
  6. Please ensure that you have been given a separate formula sheet.

Question 1: Solve for :

1.1 (4)

1.2 (3)

1.3 (5)

Question 2: Simplify without the use of a calculator:

2.1 (4)

2.2 (4)

Question 3: Solve for and :

and (5)

Question 4: Given

4.1 Show that is a factor of (2)

4.2 Factorise completely (3)

4.3 Solve for if (1)

Question 5:

5.1 Evaluate (5)

5.2 Tim and Bob were investigating the following sequence of numbers:

i. Tim claimed that the 4th term is 54. Bob disagreed and said that the
next term is 38. Explain why it is possible that both of them are
correct. (4)

ii. Determine in both cases. (7)

iii. Calculate how many terms of Tim’s pattern will give a sum of
531 440. (3)

5.3 A claim to fame of the Bloukrans River Bridge is that it offers
the highest commercial bungy-jumping site in the world. At full
stretch, the bungy rope is 160m long. After the initial drop of
160m, a person usually rises up by of the distance that they
previously fell, then falls down to the full stretch of the rope
again.
Show that the total vertical distance covered by a jumper
before they are hoisted back to the platform will never exceed . (6)

Question 6:

The diagram shows the graphs of the functions and . The point is the point of intersection of the graphs and .

6.1 Calculate the value(s) of and . (4)

6.2 Write down the equation of if (1)

6.3 Explain why the inverse of is not a function.(2)

Question 7:

7.1 Given , determine:

i. (3)

ii. the domain and range of (2)

7.2 Given , find a simplified expression for:

(6)

Question 8: This question is to be answered on the sheet which is the first page
of your answer booklet.

Given

8.1 Sketch the graph of on the axes provided. Indicate clearly the
equations of the asymptotes, the intercepts of with the axes and
one other point. (6)

8.2 Determine the equation of , the vertical translation 2 units upwards
of . (1)

8.3 Determine the equation of , the horizontal translation 2 units to the
right of . (1)

Question 9:

The diagram shows the graphs of and

Determine the values of and (3)

Question 10:

Calculate how much should be deposited monthly for 15 years, starting
immediately, into a sinking fund if the investor is to realise an amount of
R1,5 million at an interest rate of 11,25% p.a. compounded monthly. (4)

Question 11:

11.1 Mike sets aside R900 each month towards his pension. He started doing
this a month after he turned 35 and has been receiving a constant
interest rate of 8,75% compounded monthly. If he retires on his 65th
birthday, show that he will have saved R 1 564 299,52.(3)

11.2 When Mike turns 65 he will use the amount of R 1 564 299,52 from
his retirement annuity saved to withdraw monthly amounts (starting
one month after his 65th birthday) for the next ten years. How much
money will he receive each month? (Assume the interest rate remains
unchanged) (3)

Question 12:

Given

12.1 Write in terms of (2)

12.2 Hence determine the value of (3)