modul 3 add maths

ADDITIONAL MATHEMATICS
FORM 4
MODULE 3
INDICES AND LOGARITHMS
COORDINATE GEOMETRY
MODUL KECEMERLANGAN AKADEMIK

5 INDICES AND LOGARITHMS
 PAPER 1
1 Simplify 3
32
27
93



x
xx
.
Answer : …………………………………
2 Express )5(1555 12212 
 xxx
to its simplest form.
Answer : …………………………………
3 Show that 7 x
+ 7 x + 1
– 21(7 x – 1
) is divisible by 5 for all positive integers of n.
Answer : …………………………………
4 Find the value of a if log a 8 = 3.
Answer : a = ..…………………………
5 Evaluate 55log5 .

Answer : …………………………………
6 Given ma 10log and nb 10log . Express
b
a
100
log
3
10 in terms of m and n.
Answer : …………………………………
7 Given log 7 2 = p and q5log7 . Express 7
log 2 8 in terms of p and q.
Answer : …………………………………
8 Simplify
27log
243log13log
8
1364 
.
Answer : …………………………………
9 Solve the equation xx
95 12

.

Answer : …………………………………
10 Solve the equation log 3 (2x + 1) = 2 + log3 (3x – 2).
Answer : …………………………………
 PAPER 2
11 The temperature of an object decreases from 80C to T C after t minutes.
Given T = 80(08)t
. Find
(a) the temperature of the object after 3 minutes,
(b) the time taken for the object to cool down from 80C to 25C.
12 (a) (i) Prove that 9log ab = 3 3
1
log log )
2
( a b .
(ii) Find the values of a and b given that 3log 4 ab and
2
1
log
log
4
4

b
a
.
(b) Evaluate
1
1
5 5
3(5 )
n n
n



.
13 The total amount of money deposited in a fixed deposit account in a finance company after a period
of n years is given by RM20 000(104)n
.Calculate the minimum number of years needed for the
amount of money to exceed RM45 000.
14 (a) Solve the equation 5log
644 x
 .

(b) Find the value of x given that log 5 log 135x x
 = 3.
(c) Given
2
5
loglog 42  ba . Express a in terms of b.
15 (a) Solve the equation  9 3 16log log (2 1) log 4x   .
(b) Given that 3log 5 a and 3log 7 b , find the value of p if
2
3
log3
ba
p

 .

6 COORDINATE GEOMETRY
 PAPER 1
1 Given the distance between two points A(1, 3) and B(7, m) is 10 units. Find the value of m.
Answer : m = ……………………………
2 Given points P(2, 12), Q(2, a) and R(4, 3) are collinear. Find the value of a.
Answer : a = …………………………………
3 Find the equation of a straight line that passes through B(3, 1) and parallel to 5x – 3y = 8.
Answer : …………………………………

4 Find the equation of the perpendicular bisector of points A(1, 6) and B(3,0).
Answer : …………………………………
5 Given A(p, 3), B(3, 7), C(5, q) and D(3, 4) are vertices of a parallelogram. Find
(a) the values of p and q,
(b) the area of ABCD.
Answer: (a) p = …………………………
q = …………………………
(b) …………………………….
6 The points A(h, 2h), B(m, n) and C(3m, 2n) are collinear. B divides AC internally in the ratio of
3 : 2. Express m in terms of n.
Answer : …………………………………

7 The equations of the straight lines AB and CD are as follows:
AB : y = hx + k
CD : 3
6






 hx
k
y
Given that the lines AB and CD are perpendicular to each other, express h in terms of k.
Answer : …………………………………
8 Given point A is the point of intersection between the straight lines 3
2
1
 xy and x + y = 9.
Find the coordinates of A.
Answer : …………………………………
9 Find the equation of the locus of a moving point P such that its distance from point R(3, 6) is
5 units.
Answer : …………………………………

10 Given points K(2, 0) and point L(2, 3). Point P moves such that PK : PL = 3 : 2.Find the equation of
the locus of P.
Answer : …………………………………
 PAPER 2
11 Given C(5, 2) and D(2, 1) are two fixed points. Point P moves such that the ratio of CP to PD is
2 : 1.
(a) Show that the equation of the locus of point P is 034222
 yxyx .
(b) Show that point E(1, 0) lies on the locus of point P.
(c) Find the equation of the straight line CE.
(d) Given the straight line CE intersects the locus of point P again at point F, find the coordinates
of point F.
12 Given points P(2, 3), Q(0, 3) and R(6, 1).
(a) Prove that angle PQR is a right angle.
(b) Find the area of triangle PQR.
(c) Find the equation of the straight line that is parallel to PR and passing through point Q.
13 The diagram above shows a quadrilateral KLMN with vertices M(3, 4) and N(2, 4).Given the
equation of KL is 5y = 9x – 20. Find
(a) the equation of ML,
(b) coordinates of L,
(c) the coordinates of K,
(d) the area of the quadrilateral KLMN.
x
M(3, 4)
N(2,4) K
L
0
y

14 In the above diagram, PQRS is a trapezium.QR is parallel to PS and QRS = PSR = 90.
(a) Find
(i) the equation of the straight line RS,
(ii) the coordinates of S.
(b) The line PQ produced meets the line SR produced at T.Find
(i) the coordinates of T,
(ii) the ratio of PQ : QT.
15 The above diagram shows a rectangle ABCD with vertices B(3, 3), A and C are points On the x-axis
and y-axis respectively. Given that the equation of the straight line AB is 2y = x + 3, find
(a) the coordinates of A,
(b) the equation of BC,
(c) the coordinates of C,
(d) the area of triangle ABC,
(e) the area of rectangle ABCD.
C
B(3,3)
A
D
0 x
y
Q(2, 7)
P(0, 1)
R(10, 11)
S
0 x
y

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