PRACTICE PAPER

GRADE IX

SECTION-A

Section A consists of 20 questions of 1 mark each.

1 Which of the following is not irrational? 1

(a) (2 – √3)2 (b) (√2 + √3)2

(c) (√2 -√3)(√2 + √3) (d)2√7

2 The product of two different irrational numbers is always 1

(a) rational (b) irrational (c) both of above (d) none of above
3 Which one of the following option is true for the solutions of y = 11 + 5x? 1
a) Unique solution b) Only two solutions c) Infinitely many solutions d) None of these

4 Which point lies on x-axis? 1

a) (0, 7) b) (-3,-1) c) (5, 0) d) (-4,-5)

5 3√2 + 7√2 is equals to : 1

a) 2√10 b) 10√2 c) 2√3 + 7√2 d) none of these

6 Which of the following is not a criterian for congruence of triangle? 1

a) SAS b) ASA c) SSA d)SSS

7 If the coordinates of a point are (0, -4), then it lies in 1

a) X-axis b) Y-axis c) At origin d) Between x-axis and yaxis

8 Degree of linear polynomial is : 1

a) not define b) any number c) 1 d) 0

9 The number of lines which can be drawn through one unique point is : 1
a) two b) one c) three d) infinitely many

10 The factors of x2- 4 is : 1

a) (x+2)(x-2) b) x (x-2) c)(x+2)(x-3) d) x (x+3)
11 The point where two coordinate axes meet is known as : 1
a) Quadrant b) Origin c) Abscissa d) Ordinate

12 The number of dimensions, a point has : 1

a) 1 b) 2 c) 3 d) none

13 The measure of an angle which is 24° more than its compliment : 1

a) 66° b) 57° c) 156° d) 114°

14 Zero of the polynomial p(x) = 5x + 10 is : 1

a) 2 b) -2 c) 6 d) -12

15 If A, B, and C are three points on a line such that A lies in between B and C, then : 1
a) BC = 1/2 AC b) AC = BC/4 c) AC = BC d) AB + AC = BC

16 Which of the following rational numbers is equivalent to a decimal that terminates : 1

a) 2/6 b) 3/7 c) 1/8 d) 8/9

17 If lines PQ and RS intersect each other point at O. If ∠POR : ∠ROQ = 5 : 7, Find ∠POS. 1

a) 75o b) 85o c) 60o d) 105o

18 Write – 8x + 7y = 6 equation in the form ax + by + c = 0 and indicate the values of a, b and c in it 1

respectively.
a) – 8, 3, 6 b) - 8, 3, -6 c) -8, 7, -6 d) None of these
19 DIRECTION: In question number 19 and 20, a statement of assertion (A) is followed by a 1
statement of Reason (R).
Choose the correct option
Assertion: A Linear equation 2y = 7x + 8 has infinitely many solutions.
Reason: A linear equation in two variables has a unique solution.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion(A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion(A)

(c) Assertion (A) is true but reason (R) isfalse.

(d) Assertion (A) is false but reason (R) istrue
20 Assertion: In ∆XYZ, if YZ = XY and ∠Z=65o , Then
∠Y= 65o . 1

Reason: Angles opposite to equal sides of a triangle are equal.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct
explanationof assertion(A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct
explanation of assertion(A)

(c) Assertion (A) is true but reason(R) is false.

(d) Assertion (A) is false but reason(R) is true.

SECTION-B

Section B consists of 5 questions of 2 marks each.

21 Multiply (√7 + √11) (√5 - √11). 2

OR

Add (5√2+ 5√3) and 5(√2 – 5√3).

22 If a point C lies between two points A and B such that AC = BC, then prove that AC = 1AB. 2
2
Explain by drawing the figure.
23 Use suitable identity and find product (5x + 3) (7x - 5) 2

OR
Evaluate using identity 105 X 103
24 From the graph, find the coordinate of M. What is the perpendicular distance of M on x-axis? 2
25 In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex 2
∠COE

SECTION-C
Section C consists of 6 questions of 3 marks each
26. Represent .5 on number line. 3

27 From the figure, write the coordinates of A, B, C ,D ,E, F and H 3

OR
Plot the following points
(1,2), (-3,3), (0,4), (6,0), (-3,7)

28 Factorise : 2y3 +y2 –2y–1 3

29 ABC is an isosceles triangle with AB = AC. P and Q are points on AB and AC respectively such that AP = AQ. 3
Prove that CP = BQ.

30 In the given figure, ∆ABD and BCD are isosceles triangles on the same base BD. 3
Prove that ∠ABC = ∠ADC

31 a) Find two solutions of x - 3y = 6 3

b) Find the value of k if x = -2, y = 1, is a solution of the equation 2x + 3y = k.

SECTION-D

Section D consists of 4 questions of 5 marks each

32 Simplify by rationalising the denominator : 5

33 a) Expand the cube using identity : 5

3
(2a - 5b)
b) Without actually calculating the cubes, find the value of ( −10)3+ (8)3+(2)3
34 5
If x + 1 = 6, find the values of 2+ 1
2 and x .

35 In triangle ABC, if AB=BC and ∠B = 70, Find∠A 5

 SECTION-E

Section E consists of 3 questions of 4 marks each

36 One day, Principal of a particular school visited the classroom. Class teacher was teaching the 4
concept of Polynomial to students. He was very much impressed by her way of teaching. To check,
whether the students also understand the concept taught by her or not, he asked various questions to
students. Some of them are given below. Answer them.
p(x) = 2x² + 7x + 3

a) What is the degree of given polynomial? (1)

b) Find the value of p(-2).(1)

c) Find the factors of p(x). (2)
37 To Eco-club of a school decided to develop a garden of the school and planted two types of plants A 4
and B. Number of plant of A is twice that of plant B.

Based on the above information answer the following questions :

a) Write the correct representation of the above situation in linear equation. (1)
b) If number of plants of A is 40. Find the number of plants of B. (1)
c) Write the equation in the form of Ax + Bx + C =0 and write A, B and C. (2)

38 A quadrilateral shaped agricultural field APBQ is divided by a farmer in four parts. In two parts of his 4
field he wants to grow sugarcane and other two parts he wants to grow wheat. He want to grow wheat
on the field division which are exactly same in shape and size, the same he wants to do for growing
sugarcane.

AB is a line segment. P and Q are points on opposite sides of AB, such that each of them is
equidistant from the points A and B.
Based on the above information answer the following questions:
a) If he decides to grow wheat in △PAQ, then which other triangle is of exact shape and

size? (1)

b) Prove that △PAQ ≅△PBQ? (1)

c) Is ∠APC=∠BPC (2)