QUESTION
BANK
CLASS-9
1.Number Systems
1.
State whether the
following statements are true or false. Justify your answer.
a)
Every irrational
number is a real number
b)
Every real number
is an irrational number.
2. Identify Ö27 as a rational number or irrational
number
3. Find
the decimal expansion of 13/4 and 1/7
4. Classify
the following numbers as rational number or Irrational number
3 - Ö4 and 5 - Ö2
5.
Divide 15Ö2
by3 Ö4
6.
Find six rational
number between 7 and 8
7.
Find three
different Irrational number between the rational number 2/5 and 3/7
8.
If 1/7 =0.
, find the value of 
and
9.
Rationalize the
denominators of the following
.
10. Find
the value of (125) – 1 and
(16)4
11. Show
how 9.2 can be represented on a Number line.
12. Visualize 4.265 on the number
line.
13. Express the following in the form
of p/q (1) 0.
and (2) 0.
14. Simplify 
+
15. What can be the maximum number of
digits in the repeating block of digits in the decimal expansion of 
? Perform the division to check your answer.
16. Express 0.9999 .. .…. in the form
of rational number . Are you surprised by your answer?
17. If a and b are rational numbers
and 
, find the values of a and b
18. Represent the following on number
line: 
.
19. If =1.732 then find the
value of 
+
+
-
2.POLYNOMIALS
Q.1.
Define the
following
a. Zero polynomial
b. Quadratic polynomial
Q.2.
Write the degree
of each of the following
a. 5-x2
b. 6
Q.3.
Find the zero of
the polynomial p (x)=7x-2
Q.4.
Give one example
for each of the following
a. a linear polynomial in variable x
b. a monomial of degree 10 in variable y
Q.5.
Find the value of
the polynomial l6-3x2+7x if x = -1 and x = 2
Q.6.
Using
remainder theorem check whether 3x3 + 2x2 –425 Is divisible by x-5
Q.7.
Factorize 12x2-7x+1
Q.8.
Evaluate the
following products without multiplying directly 95 x 96 and104 x 96
Q.9.
a) Find the
remainder when x3-ax2+6x-a is divided by (x-a)
b) Check whether 7+ 3x is a factor
of 3x3 + 7x
Q.10.
( a) Expand using suitable
identity(3a-7b+2c)2
(b) If (x +
y + z) = 0 show that x3 + y3 + z3 =3xyz
Q.11.
If x + y = 10 and xy = 21 then evaluate
(a) x3 + y3 b) x3 – y3 (x > y)
Q.12.
If x-2 is a factor of x3 – 3x2
+k then k = ?
Q.13.
Find the value of 103 x 107 using suitable
algebraic identity.
Q.14.
By using Factor theorem, show that x+2 is a
factor of the polynomial 3x3 - x2-20 x
-12. Hence factorise the given polynomial.
Q.15.
Without actually calculating the
cubes 483 -303 - 183
Q.16.
15 x2
+ y2 + z2 =250 and ab + bc+ ca= 3 then find the value of
a+b+c.
Q.17.
16. show that polynomial 3x3
+8 x2 -1 has no integral zeros.
3.CO-ORDINATE
GEOMETRY
1.
Determine the
quadrant in which the following co-ordinates lie (3, -7) & (-4, -2)
2.
If a point has
co-ordinates (0, -4) does it lie on the x-axis or y- axis?
3.
Does the point
(2, -1) lie above the x-axis or below the x-axis?
4.
Which of the
following points lie on the y-axis?
(1,1) (0,4) (-4, -7) (0, -7) (9,0)
(-8,0) (6, -6)
5.
What is the name
of horizontal and vertical lines drawn to determine the position
of any point in the Cartesian plane?
6.
Locate the points
in the Cartesian plane
(5,0) (0,5) (2,5) (5,2) (-3,5)
(-3,-5) (5,-3) and (6,1)
7.
Plot these pairs
of numbers as points in the Cartesian plane. Use the scale
1cm=1unit on the axes
|
x |
-3 |
0 |
-1 |
4 |
2 |
6 |
3 |
|
y |
7 |
1 |
-3 |
4 |
-3 |
-8 |
7 |
8. Plot the following points on the
graph paper and show that they are collinear
(-1,-1) (2,3) and (8,11)
9.Answer
the following with the help of the figure:
(i)
The coordinates of A
(ii)
The coordinates of B
(iii)The
point identified by the coordinates (2,-4)
(iv)
The abscissa of D
(v)
The ordinate of point E
(vi)
The coordinates of the point F
(vii)
The coordinates of the point G
(viii)
The coordinates of H
10.
A point lies on x-axis at a distance of 9 units from y-axis. What are its
coordinates? What will be its coordinates if it lies on y-axis at a distance of
9 units from x-axis.
11.
ABC is an equilateral triangle as shown in the figure. Find the coordinates of
its vertices.
12.
Name the quadrant or axis in or on which the following points lie
(-65,-14),
(32,-37), (-77,66), (29,39), (53,0), (0,45), (-78,0) and (0,-14)
13.
Plot the following points on the Cartesian plane
|
x |
3 |
5 |
0 |
-4 |
-2 |
0 |
-1 |
5 |
|
Y |
2 |
-1 |
-3 |
-5 |
6 |
4 |
0 |
0 |
4.LINEAR
EQUATION IN TWO VARIABLES
1.Find which of the following
equations have x=2,y=1 as a solution?
a)
2x + 5y =9
b)
5x + 3y =14
c)
x +y +4 = 0
2.
Which of the
following statements is true and why?
Y=3x + 5 has i) a unique solution
ii) Only two solution
iii) Infinitely many
solution
3.
Write four
solutions for each of the following equations
a) 2x + y=7
b) π x + y=9
4.Check which of the following are
solutions of the equation x – 2y = 4 and which are not a) (0,2) b) (2, 4) c) (1,1)
5.Find the value of k if x =2, y =1
is a solution of the equation 2x + 3y = k
6. Draw the graph of each of the
following linear equations in two variables
a) x +y =4 b) 2x +
y = 3
7.Find solutions of the form x =9 ,y
= 0 & x =0 y =6 for each of the following pairs
of equations. Do they have any two common solutions?
a)
3x + 2y = 6 and
5x –2y =10
b)
9x + 7y = 63 and
x-y =10
8.
Find the value of
‘a’ so that each of the following equations may have x =1 y =1 as a solution
a)
3x + ay =6 c) 9ax + 12ay =63
b)
x –y =a d) 5x +2ay =3a.
9.
Draw the graph on
the following linear equations.
a). x = 2
b). y = 3 c). x = -1 d). x = 0
e). y = 0 f). 2y + 5 = 0 g). 3x-2 = 0
10.
I). See the graph and state whether the point
B is a solution of y = 7x.
11.
Give the equation of two lines passing through
(2,14). How many more such lines are
there and why?
12 The tax fare in a city is as follows.
For the first kilometer, the fare is Rs.9 and for the subsequent distance it is
Rs.5 per kilometer. Taking the distance
concerned as x km and total fare Rs.7, write a linear equation for this information
and draw its graph.
13 The work done by a body on
application of a constant force is directly proportional to the distance
traveled by the body. Express this in
the form of an equation in two variables and draw the graph of the same by
taking the constant force is 5 units. Read from the graph the work done when
the distance traveled by the body is (i) 2 units (ii) 0 units.
14 Yamini and Padmini two students of IX
of a school together contributed Rs.100/- towards the PM’s Relief fund, to help
the earthquake’s victims. Write a linear
equation in which the data satisfies.
You may take their contributions as Rs.X and Rs.Y. Draw the graph of the same.
15 In countries like USA and Canada,
temperature is measured in Fahrenheit, whereas in countries like India it is
measured in Celsius. Here is a linear
equation that converts Fahrenheit to Celsius.
F = (9/5) C + 32
(i).
Draw the graph of the above linear equation using the Celsius for x axis
and Fahrenheit for the y axis
(ii).
If the temperature is 30 0 c what is the temperature in
Fahrenheit?
(iii). If the temperature is 95
0 F What is the temperature in
Celsius?
(iv). Is there a temperature which is
numerically the same in both Fahrenheit and Celsius? If yes, find it.
(v). If the temperature if 00 C,
what is the temperature in Fahrenheit and if the temperature is 00F,
what is the temperature in Celsius?
16 The acceleration produced in a body
is directly produced to the force applied on the body. Write an equation to
express this situation and plot the graph of the equation.
5.INTRODUCTION TO EUCLID’S
GEOMETRY
2 marks.
1.
If point D lies between two points A and B such that
AC=1/2AB. Explain by drawing the figure.
2.
In the figure
given, if AC=BD then prove that AB=CD
3.
If A,B, Care 3
points on a line & B lies between A and C then prove that AB=BC=AC.
4.
Why is axiom 5 in
the list of Euclid’s axioms considered a universal truth?
5.
How will you
rewrite Euclid’s fifth postulate so that it would be easier to understand?
6.
Does Euclid’s fifth
postulate imply the existence of parallel lines? Explain.
3 marks.
1.
Prove that an
equilateral triangle can be constructed on any given line segment.
2.
Consider the
following statement. There exists at
least one triangle in which the sum of the measures of the interior angles is
1800. Do you think that this
statement is (or is not) a consequence of Euclid’s postulate 5? Explain.
3.
Consider two
“postulates” given below.
(i)
Given any two
decimal points A and B, there exists a third point C which is in between A and
B.
(ii)
There exist at
least 3 points that are not on the same line.
Do the
postulates contain any undefined terms?
Are these postulates consistent?
Do they follow from Euclid’s postulates?
Explain.
4.
Prove that an
equilateral triangle can be constructed on any given line segment.
5.
Explain why you
think that Play-fair’s axiom is (or is not) equivalent to Euclid’s fifth
postulate.
4 Marks
1.
Write the Euclid’s 7 definitions.
2.
Write the Euclid’s 7 axioms.
3.
Write the Euclid’s 5 axioms.
4.
If a point C lies between two points A and B such that AC=BC, then prove that 
5.
In the figure, if AC=BD, then prove that AB=CD (Using an Euclid’s axiom)
6.
In the figure, AC=XD, C is the midpoint of AB and D is the midpoint of XY.
Using an Euclid’s axiom, show that AB=XY.
6 LINES AND ANGLES
(2 Marks)
1.
In the
figure given POQ is a line.
= 4x and 
= 2x. Find the value
of x.
2.In the figure given if x + y = w +
z prove that AOB is a straight line.
3.In the given figure find COD 
when 
AOC+BOD = 100
4.Find the value of x and y and show
that AB//CD.
5.Determine the value of x
6.
IN the figure 1 = 600 
= 1200. Is m//n?
7.
If AB//CD, 
= 500, 
= 1270. Find x and y.
8 Which pair of lines are parallel
and why?
(3 MARKS)
1.
In the figure ray
OC stands on the line AB, ray OL and ray OM are angle bisectors of 
and 
. Prove that 
= 900.
2.
In the figure
AB//DE,
350,
530. Find 
3.
Find the values
of x and y in
4.
In the figure
AB//CD x:y=3:2. Find x and y
5 In the figure transversal EF
intersects parallel lines AB and CD at points P and Q respectively such that 
750. Find CQPand CQF
6. In
the figure AB//DE. ABC = 750, CDE=1450.
Find BCD
D E
A B 145
75
C
(4 marks)
1.
Prove that two
lines that are respectively perpendicular to two parallel lines are parallel to
each other.
2.
In the figure if
AD//CD, CD//EF and y:z = 3:7. Find x.
3.
In the figure if
AB//CD, EF
CD.GED=1260.
Find 
4.
Prove that
through a given point we can draw only one perpendicular to a given line.
5.
If the sides of
an angle are respectively parallel to the sides of another angle, prove that
these angles are either equal or supplementary.
6.
O is a point in
the interior of parallel lines AB and CD.
O is joined to two points M and N on AB and CD. Prove that 
+
+OMB = 3600.
7.TRIANGLES
2 Marks
1.
One of the angles
of a triangle is 650. Find
the remaining two angles, if their differences are 250.
2.
If the lines AE,
BC intersect at D, such that ABC=800, BAC=430 and 
=590. Find
x.
3.
If PA=PD and
PB=PC , Show that 
PAB
PDC.
4.
ABC=ACB. AD is bisector of
BAC and AD meets BC at D.
Prove that D is mid point of BC.
5.
ABCD is a
quadrilateral such that AB=AD and AC is bisector of the angle A of the
quadrilateral. Show that ABC
and BC=DC.
6.
In aABC, prove that AB+BC+CA>2AB.
7.
In the figure of
AB//DC, P is the mid point of B, prove that P is also the mid point of AC.
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