Matric Exam(SG)
QUESTION1
Simplify each of the following without
the use of a calculator:
1.1 SQR18 x SQR24 (2)
1.2 32 - 3-2 (2)
1.3 ( 1 1 ) x ab (2)
___ + ___ ________ (6)
a b b + a -
QUESTION2
Solve for x,correct to two decimal places where
necessary:
2.1 2x�-4x=0 (3)
2.2 x-2= 9 (5)
___
x-2
2.3 x(3x+13)=11 (5)
QUESTION3
3.1 Discuss the nature of the roots of 3x�-5x-7=0
without solving the equation. (4)
3.2 Find the value of k if
2x�+(k-6)x+8=0 has equal roots. (5)
3.3 Show that the equation
mx�+5x=5m has real and unequal roots
for all real values of m. (5)
QUESTION4
4.1 Use the factor theorem to show
clearly that (x+2) is a factor of (3)
x3-3x�-16x-12.
4.2 Hence solve for x:
x3-3x�-16x-12. (5)
QUESTION5
5.1 solve for x and y: (7)
x+y=3 and x�-3xy+y�=99
QUESTION6
6.1 Simplify without the use of a
calculator:
a3/4 x 5a x 4SQRa (2)
6.1.2 125x x 25-x+2 (4)
____________________
25
6.1.3 4a+22a (3)
6.2 Solve for y: (3)
6.2.1 7y-3=49 (4)
6.2.2 3y�.3y=9 (4)
QUESTION7
7.1 A person has R20 000 to invest for 3
years and is faced with two options.
Proposal A is to invest R20 000 at
7,5% per annum compounded half-yearly
while proposal B is to invest at 8% (7)
per annum compounded annually.
Which is a better investment?
(Show clearly how you arrived at
your answer.)
QUESTION8
8.1 Rationalise the denominator of 5 (2)
_____
SQR3
8.2 Hence find the value of 5 (4)
_____
SQR3
in terms of t that SQR12=t
QUESTION9
9.1.1 Draw a neat sketch graph of
y=x�-5x-6 showing clearly
the co-ordinates of x and y
intercepts and the turning point.
9.1.2 On the same system of axes also (8)
draw the graph of y=-3x-3
9.2 Explain fully how your graphs can
be used to solve the equation (4)
x�-2x-3=0 and hence write
down the solution.
QUESTION10
10 The point (m;3) lies on the graph of (3)
y=2x�-5.Without drawing the graph
calculate the value(s) of m.
QUESTION11
11 Evaluate by writing out in expanded
form:
5
E (2n+1) (2)
n=1
11.2 2x;3x+4;4x+8---is an arithmetic
sequence.
11.2.1 What is the commmon differnce? (2)
11.2.2 Find in terms of x,the value (3)
of the eighty-first term.
11.2.3 If the sum of the first ten terms (5)
is 245,find the value of x.
11.3 Find the sum of the first twenty (3)
five terms of the sequence
3;-6;12---
11.4.1 If d;e;f---is a geometric
sequence,show that e = +- SQR(df)
11.4.2 Hence,or otherwise,prove that (5)
SQR5-1;2;SQR5+1 is a geometric sequence.
QUESTION12
12.1 If f(x)=6x use FIRST PRICIPLES (5)
to sshow that f'(x)=6.
12.2 If f(x)=11x+55,determine f'(x). (2)
12.3.1 If g(x)=11x+5,and p is a constant,
find g'(x).
12.3.2 If g'(x)=22,find the value of p. (3)
QUESTION13
13.1 If y=2x�+5x
13.1.1 find the value of dy/dx;and (5)
13.1.2 determine the gradient of the (2)
curve y=2x�+5x at x=2.
13.2 Consider y=x3-3x�
13.2.1 Find dy/dx
13.2.2 Show clearly that the curve (5)
of y=x3-3x� has a local
maximum at x=0 and a local minimum
at x=2.
13.2.3 Draw a neat sketch graph of (6)
y=x3-3x� showing clearly
the co-ordinates of the turning
points and the x intercepts.
QUESTION14
14 A piece of rope of length 40 metres has
been laid out so as to form a rectangle of
width x metres.Using calculus methods,(10)
determine the value of x for which the
area is at a maximum and calculate this
area in m�.