O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Exponential Equation, Logarithms Worksheet. Prepared by Musicisintheworld. Copyright © 2011. All Rights Reserved. No part of this publication may be reproduced without permission from the author, Musicisintheworld.

1. GCE O LEVEL A MATHS
SEC 3
Simultaneous Equation, Indices, Surds, Exponential Equation,
Logarithms
Worksheet
Simultaneous Equations
1. The line py = qx + 1 intersects the curve xy = 7px - 9qy at the point A(1,1) and
at the point B.
i) Find the value of p and of q.
ii) Find the coordinates of B.
2. Find the coordinates of the points of intersection of the straight line 2y
+ 3x = 9 and the curve x2 + 2y2 +5x = 68.
3. Given that (1, p) is a solution to the pair of simultaneous equations 12x2
– 5y2 = 7 and 2p2x – 5y =7. Find the
i) value of p,
ii) other solution to the pair of simultaneous equation.
Indices, Surds and Exponential Equations
1. Given that 22x+2 x 7x-1 = 8x x 72x, evaluate 14-x.
2. By means of the substitution y=2x, find the value of x such that 22x+2 –
3 = 13 x 2x-1.
122 x
3. Given that = 2m3n, find the value of m and n in terms of x.
3x x 42-x
4. Without using a calculator, find the value of k such that
1 24 49 3
− + x = k 3.
6 3 294 2
Additional Mathematics O Level Syllabus, Sec 3
Simultaneous Equation, Indices, Surds, Exponential Equation, Logarithms Worksheet
Copyright © 2011. All Rights Reserved. No part of this publication may be reproduced without permission from
the author, Musicisintheworld.
2

2. 5.
ax by
6. Given that 3− x x y +1 2 = ab , find the value of x and y.
6
b (a )
7. By using a suitable substitution, solve the equation 22 x + 2 x +3 = 1 + 2 x .
8.
Logarithms
1. By using the substitution y = ex, find the value of x such that ex – 10e-
x
= 3.
2. Solve the equation 2logx3 = 3 – log3x.
Additional Mathematics O Level Syllabus, Sec 3
Simultaneous Equation, Indices, Surds, Exponential Equation, Logarithms Worksheet
Copyright © 2011. All Rights Reserved. No part of this publication may be reproduced without permission from
the author, Musicisintheworld.
2