IGCSEGSCE Practice Exam Questions

1
IGCSE/GSCE Practice Exam Questions
Adrian Sparrow
www.ibmaths.com
2
Straight lines and simultaneous equations
5. Make up your own table to plot the straight
line 3xy7. Draw this straight line on the same
grid as your other line.
1. Draw axis from -10 to 10 for both x and y.
2. Complete the table below to show y-values for
the equation y2x-8.
6. Write down the gradient (m) and the
y-intercept (c) of the straight line 3xy7.
m-1/3 c7
7. Use you graph to solve the simultaneous
equations, 3xy7 and y2x-8.
x3 y-2
3. Plot your points on your grid and draw the
straight line y2x-8.
8. Use algebra to solve the simultaneous
equations, 3xy7 and y2x-8.
4. Write down the gradient (m) and the
y-intercept (c) of the straight line y2x-8.
m2 c-8
3
Simultaneous equations - using algebra
1. Get one of the letters to be the same
coefficient.
2. Add or subtract the equations to eliminate a
letter. Remember SSS - Same signs subtract
DSA - Different signs add
3. Solve one of the letters.
4. Substitute into the original equation to find
the second letter.
1. 3x-y14 4xy14
3. 4x3y13 6x4y18
x4 y-2
x1 y3
2. 2x-y-11 6x-y-23
4. 5x-2y39 2x3y8
x-3 y5
x7 y-2
4
Graphs and Calculus
1. a) Factorise x3x2-6x
d) Find the gradient when x4.
x(x3)(x-2)
dy/dx21
b) Solve x3x2-6x0
e) Find the turning point of the
curve and state whether it is a maximum
or minimum point.
x0
x-3
x2
c) Sketch yx3x2-6x
minimum point (-1.25,-28.125)
2. a) y2x25x-25. Write in the form
y(2xa)(xb)
f) Find the domain and range of the
graph yx25x-25.
y(2x-5)(x5)
Domain any real number
b) Hence sketch the graph of
y2x25x-25.
Rangeany number greater than -28.125
g) Find the equation of the tangent to
the curve at the point where x1.
c) Find dy/dx.
dy/dx4x5
y9x-27
5
Graphs 2
a) Draw axes from -3 to 5 on x-axis, and -2 to
12 on the y-axis. 1
f) Use algebra to solve the equation x2-3x23.
4
b) Complete the following table for the equation,
yx2-3x2. 3
g) Draw a tangent at the point where x3 on your
graph. 3
h) Find the gradient of the curve yx2-3x2 at
the point where x3. 2
i) On the same axes draw the straight line
y3-(1/2)x. 2
c) Draw the graph of yx2-3x2. 3
k) Use your graph to solve, x2-3x23-(1/2)x 3
d) Use your graph to solve the equation
x2-3x20. 2
e) Use your graph to solve the equation
x2-3x23. 2
6
Calculus
2. The displacement, s metres, of a particle
from a point O after time t seconds is given by
the equation, st3-13t235t10
1. a) Differentiate the curve, y8-3x-2x2.
dy/dx-3-4x
b) Find the gradient of the curve y8-3x-2x2 at
the point where x3.
a) Find the initial displacement.
10 m
gradient -15
b) Find an equation for the velocity.
c) Find the turning point of the curve,
y8-3x-2x2.
v3t2-26t35
c) Hence find the velocity after 3 seconds.
x-0.75 y9.125
-16 m/s
d) Is this turning point a maximum or a minimum?
d) Calculate the points at the particle is
stationairy.
maximum, the curve is n-shaped
t5/3 secs, 7 secs
e) Find the acceleration at the point where t5
seconds.
e) Write down the equation of the line of
symmetry of the curve y8-3x-2x2.
4 m/s2
x-.75
7
Proportion
2. a varies indirectly with the square root of b.
It is known that when b is always positive and
that when b81, a1.
Direct proportion ykx
Indirect proportion yk/x
1. t varies with the square of s, such that when
t36, s3.
a) Find an equation connecting a and b.
a) Find an equation connecting t and s.
t4s2
b) Find the value of a when b144.
b) Find the value of t when s10.
a0.0625
t400
c) Find the value of b when a2.25.
c) Find the value(s) of s when t144.
b2
s6,-6
8
Proportion - questions
1. y varies with the square of x, such that when
y8, x4.
c) Find the value of q when p0.05.
q10
a) Find an equation connecting x and y.
y0.5x2
3. a varies indirectly with the square of b. It
is known that when b6, a0.667. Find the value
of a when b12.
b) Find the value of y when x12.
y72
a0.167
c) Find the value(s) of x when y50.
4. The square root of w and z are directly
proportional such that when w16, z0.5. Find the
values of w when z1.75.
x10,-10
2. p varies indirectly with the cube of q, such
that when p0.4 when q5.
a) Find an equation connecting p and q.
w196
5. c and the cube root of d are indirectly
proportional. c2 when d-8. Find the value of d
when c1.
b) Find the value of p when q2.
d-64
p6.25
9
Surds
Simplify each of the following 1. 2. 3. 4
. 5.
Simplify each of the following 6. 7. 8. 9
. 10.