St Stithians College
HERZLIA SENIOR HIGH SCHOOL
“If you will it, it is no legend”
MARKS: 125
TIME: [pic] HOURS
This question paper consists of 7 pages.
2
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of 7 questions.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams and graphs that you have used in determining your answers.
4. Answers only will NOT necessarily be awarded full marks.
5. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.
6. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.
7. Diagrams are NOT necessarily drawn to scale.
8. Number your answers correctly according to the numbering system used in this question paper.
9. It is in your own interest to write legibly and to present your work neatly.
3
QUESTION 1
1.1 Solve for x in each of the following:
1.1.1 [pic] (2)
1.1.2 [pic] (Correct to TWO decimal places) (4)
1.1.3 [pic] (8)
1.1.4 [pic] (2)
1.1.5 [pic] (3)
1.1.6 [pic] (5)
1.2 Solve simultaneously for x and y:
[pic]
[pic] (6)
1.3 Solve for p:
[pic] (4)
1.4 Simplify, without the use of a calculator:
[pic] (4)
1.5 The solutions of a quadratic equation are given by [pic].
For which value(s) of m will this equation have:
1.5.1 Two equal solutions (2)
1.5.2 No real solutions (1)
[41]
PLEASE TURN OVER
4
QUESTION 2
S(–2;0) and T(6;0) are the x-intercepts of the graph of [pic]
and R is the y-intercept. The straight line through R and T represents the
graph of [pic].
[pic]
2.1 Determine the value of d. (2)
2.2 Determine the equation of f in the form [pic]. (5)
2.3 Calculate the coordinates of the turning point of f. (3)
2.4 For which values of k will [pic] have two distinct roots? (2)
2.5 For which values of x is [pic]? (3)
[15]
5
QUESTION 3
3.1 Given: [pic]
3.1.1 Give the equations of the asymptotes of [pic]. (2)
3.1.2 Find the x- and y-intercepts of [pic]. (3)
3.1.3 Sketch the graph of [pic] in your ANSWER BOOK, clearly
showing the asymptotes and the intercepts with the axes. (4)
3.1.4 One of the axes of symmetry of [pic] is a decreasing function.
Write down the equation of this function. (2)
3.2 The graph of a hyperbola with equation [pic] has the following
properties:
• Domain: [pic], [pic]
• Range: [pic], [pic]
• Passes through the point [pic]
Determine [pic]. (4)
[15]
QUESTION 4
Consider the function [pic].
4.1 Write down the range of [pic]. (2)
4.2 Find the y-intercept of [pic]. (2)
4.3 Find the x-intercept of [pic]. Show all your working. (3)
4.4 Hence sketch the graph of [pic] in your ANSWER BOOK. (3)
4.5 Find x if [pic]. (2)
4.6 Hence find x if [pic]. (2)
[14]
PLEASE TURN OVER
6
QUESTION 5
5.1 Two friends each received an amount of R6 000 to invest for a
period of 5 years. They invested the money as follows:
• Rebecca: 8,5% per annum simple interest. At the end of
5 years, she receives a bonus of exactly 10%
of the principal amount.
• Sarah: 8% per annum compounded quarterly.
Who will have the bigger investment after 5 years? Show all
your calculations. (7)
5.2 After 5 years of reducing balance depreciation, an asset is [pic]of its
original value. Calculate the depreciation interest rate, as a percentage. (5)
5.3 An investment of R576 000 earns 7,5% interest per annum,
compounded monthly. At the end of 3 years, the interest rate
changes to 9% per annum, compounded monthly.
5.3.1 Calculate the effective interest rate per annum, as a
percentage, during the first year. (3)
5.3.2 Calculate the value of the investment at the end of
7 years. (5)
[20]
7
QUESTION 6
A survey is conducted among 174 students. The results are shown below:
• 37 study Life Sciences
• 60 study Physical Sciences
• 111 study Mathematics
• 29 study Life Sciences and Mathematics
• 50 study Mathematics and Physical Sciences
• 13 study Physical Sciences and Life Sciences
• 45 do not study any of Life Sciences, Mathematics or Physical Sciences
• x students study Life Sciences, Mathematics and Physical Sciences
6.1 Draw a Venn diagram to represent the information above. (6)
6.2 Show that [pic]. (2)
6.3 If a student were selected at random, calculate the probability that
he studies the following:
6.3.1 Mathematics and Physical Sciences but not Life Sciences (2)
6.3.2 Only one of Mathematics or Physical Sciences or Life
Sciences (2)
[12]
QUESTION 7
In all South African schools, every learner must choose to do either
Mathematics or Mathematical Literacy.
At a certain South African school, it is known that 60% of the learners
are girls. The probability that a randomly chosen girl at the school does
Mathematical Literacy is 45%. The probability that a randomly chosen
boy at the school does Mathematical Literacy is 55%.
7.1 Draw a tree diagram to represent all outcomes of the above
information. (5)
7.2 Determine the probability that a learner selected at random
from this school does Mathematics. (3)
[8]
TOTAL : 125
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NOVEMBER
EXAMINATION
GRADE 11
MATHEMATICS PAPER 1
MONDAY 24TH NOVEMBER 2014
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