THE INDIAN PUBLIC SCHOOL , COIMBATORE
Name :
1
MATHEMATICS – Revision
Algebra, Functions & Graphs
Grade : IX -
Solve the simultaneous equations
1
2
x + y = 5,
x - 2y = 6 .
y=
Answer x =
2
The quantity y varies as the cube of (x + 2).
y = 32 when x = 0.
Find y when x = 1.
Answer y =
3
[4]
[3]
The wavelength, w, of a radio signal is inversely proportional to its frequency, f.
When f = 200, w = 1500.
(a) Find an equation connecting f and w.
Answer (a)
[2]
Answer (b) f =
[1]
(b) Find the value of f when w = 600.
4
Pattern 1
Pattern 2
Pattern 3
The first three patterns in a sequence are shown above.
(a) Complete the table.
Pattern number
1
Number of dots
5
2
3
4
[1]
(b) Find a formula for the number of dots, d, in the nth pattern.
Answer (b) d=
[1]
Answer (c)
[1]
(c) Find the number of dots in the 60th pattern.
(d) Find the number of the pattern that has 89 dots.
Answer (d)
5
[1]
The length, y, of a solid is inversely proportional to the square of its height, x.
(a) Write down a general equation for x and y.
Show that when x = 5 and y = 4.8 the equation becomes x 2 y = 120 .
[2]
(b) Find y when x = 2.
[1]
(c) Find x when y = 10.
[2]
(d) Find x when y = x.
[2]
6 . In triangle ABC, the line BD is perpendicular to AC.
AD = (x + 6)cm, DC = (x + 2) cm and the height BD = (x + 1) cm.
The area of triangle ABC is 40 cm2
(i) Show that x2 + 5x – 36 = 0
(ii) Solve the equation x2 + 5x – 36 = 0
(iii) Calculate the length of BC
7
8.
9
y
15
0
–3
3
x
– 10
f (x) = x 3 - 5x + 3 for - 3 G x G 3
(a) On the diagram, sketch the graph of y = f (x) .
[2]
(b) Find the coordinates of the local minimum point.
( ...................... , ...................... ) [2]
(c) g (x) = 2x - 1
(i) Solve f (x) = g (x) for - 3 G x G 3.
...................... , ...................... , ...................... [3]
(ii) Use your answers to part(i) to solve f (x) 2 g (x) .
....................................................................... [2]
10
f (x) = 3x - 2
g (x) = 5x - 1
h (x) =
1
, x !-1
x+1
(i) Find
(a) f(3),
................................................. [1]
(b) h(f(3)).
................................................. [1]
(ii) Find f(g(x)) in its simplest form.
................................................. [2]
(iii) Solve f (x) = g (x) .
x = ................................................ [2]
(iv) Find g -1 (x) .
g -1 (x) = ................................................ [2]
11
y
24
–4
0
2
x
Find the equation of this quadratic curve.
Answer(b) ................................................................ [3]
12
Simplify
1
^16x 8 y 2h2 .
Answer ................................................................. [2]
13
y
12
–6
0
4
x
–12
f (x) =
(1 - 2x)
(x + 3)
(a) On the diagram, sketch the graph of y = f (x) for values of x between x =- 6 and x = 4 .
[3]
(b) Write down the equations of the asymptotes of the graph of y = f (x) .
Answer(b) ......................................................................
..............................................................
[2]
Answer(c) .............................................................
[2]
(c) Find the range of values for y when x H 0 .
y
(d)
12
–6
0
4
x
–12
On this diagram, sketch the graph of y =
(e) Solve
(1 - 2x)
.
(x + 3)
[2]
(1 - 2x)
= 6.
(x + 3)
Answer(e) x = ............................ or x = ...................... [2]
14
Solve the following equations.
(a) log x + log 3 = log 12
Answer(a) x = ................................................................ [1]
(b) log x = 3
Answer(b) x = ................................................................ [1]
(c) 2log x – log 5 = log 20
Answer(c) x = ................................................................ [3]
15
(a) Simplify.
6x - 3y + 2x + y
Answer(a) .............................................................
(b) Find the value of
2a + b + 3c
when a = 3, b =- 2 and c = 4 .
Answer(b) .............................................................
(c)
[2]
[2]
L = 2x + 3y
Find the value of x when L = 18.6 and y = 2.8 .
Answer(c) x = .............................................................
[2]
Answer(d) x = ..............................................................
[2]
(d) Solve the equation.
5x - 3 = 7
(e) Complete the mapping diagram for
(f)
f : x " 2x - 1.
x
f(x)
0
....
1
1
2
....
3
....
[2]
Solve.
2x + 3 G 4 (x - 2)
Answer ................................................................ [3]
16
These are sketches of the graphs of six functions.
A
0
C
x
x
y
0
x
y
0
F
x
y
0
D
y
0
E
B
y
x
y
0
x
In the table below are four functions.
Write the correct letter in the table to match each function with its graph.
Function
Graph
f (x) = 2x - 3
f (x) = (x - 2) 2
f (x) = 4x - x 3
f (x) = 5 - 2x
[4]