Class 9 Question Paper 2024-25 Maths (Mid Term)

MID-TERM EXAMINATION

Question Paper
2024-25
NCERT BASED SYLLABUS

FOR CBSE AND STATE BOARD
FOLLOWING NCERT

Mid Term Exam Question Paper 2024-25

MID-TERM EXAMINATION
SESSION: 2024-2025
SUBJECT: MATHEMATICS
CLASS – IX
Time Allowed: 3 Hrs 15 Mins Max. Marks: 80
General Instructions:
1. This question paper contains 38 questions.

2. This Question Paper is divided into 5 Sections A, B, C, D and E.

3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no.
19 and 20 are Assertion- Reason based questions of 1 mark each.

4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying
02 marks each.

5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03
marks each.

6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05
marks each

7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each
with sub parts of the values of 1, 1 and 2 marks each respectively.

8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2
Questions of Section C and 2 Questions of Section D has been provided. An internal choice
has been provided in all the 2 marks questions of Section E.

9. Draw neat and clean figures wherever required.

10. Take π =22/7 wherever required if not stated.

11. Use of calculators is not allowed.

12. This question paper consists of 5 printed pages.

Page 1 of 5

Section A (1X20=20)
−2
1 Which of the following is not a polynomial? (a) x (b) x²/2 (c) 𝑥 (d) x²+x+1 1
2 Which of the following is an irrational number? (a) 2 (b) -5/2 (c) π (d) 0 1
3 Which of the following equation represent X-axis? (a) x=0 (b) y = 0 (c) x=1 (d) y=1 1
4 Which of the following is a solution of the equation 2x+4y = 12? 1
(a) ( 1,1 ) (b) ( 2,2 ) (c) ( 1,2 ) (d) (2,1)
5 How many straight lines can be drawn through two points? (a) 1 (b) 2 (c) 0 (d) infinite 1
6 If two complementary angles are in the ratio 13 : 5, then the smaller angle is 1
(a) 65° (b) 25° (c) 5° (d) 50°
7 Choose the correct option 1
(a) There are exactly one rational number between two rational numbers
(b) There is no rational number between two rational numbers
(c) There is infinity many rational numbers between two rational numbers
(d) There are 3 rational numbers between two rational numbers
8 Which of the following is/are the zeros of the polynomial P(x) = (x-1)(x+2)? 1
(a) 2,1 (b) -1,-2 (c) 1,-2 (d) 3,4
9 At what point the line 2x+3y = 12 will touch the X-axis? 1
(a) (3,0) (b) (6,0) (c) (7,0) (d) (4,0)
10 How many lines can pass through one point? (a) 1 (b) 2 (c) No line (d) Infinite 1
11 Which type of angles are equal in measure? 1
(a) Supplementary angles (b) Complementary angles
(c) Vertical angles (d) Adjacent angles
12 The number 1.101001000100001... is 1
(a) a natural number(b) a whole number (c) a rational number(d) an irrational number
13 If x + y = 3, x² + y² = 5 then xy is (a) 1 (b) 3 (c) 2 (d) 5 1
14 Which point lies to the right of y-axis? (a) (0, 3) (b) (-2,-1) (c) (3, 5) (d) (-3,-2) 1
15 Through which of the following points, the graph of y=x pass through? 1
(a) (1,2) (b) (2,2) (c) (2,3) (d) (3,4)
16 How many dimension does a surface has? (a) 1 (b) 2 (c) 3 (d) 4 1
17 Which of the following pairs of angles are supplementary? 1
(a) 30° and 150° (b) 45° and 45°(c) 60° and 30° (d) 90° and 91°
18 What is the image of (2,3) on the origin? (a) (-2,3) (b) (2,-3) (c) (0,0) (d) (-2,-3) 1
DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is
followed by a statement of Reason (R).
Choose the correct option
(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) is false.
(d) Assertion (A) is false but reason (R) is true.
19 1 1
Assertion : Rational number lying between two rational numbers x and y is (x + y).
2
Reason: There is one rational number lying between any two rational numbers

Page 2 of 5

20 Assertion: The constant polynomial 0 is called zero polynomial. 1
Reason: √x+3 is a polynomial.
Section B (2X5=10)
21 Write three rational numbers between and 3 4 2
5 5
OR
Write any two irrational numbers between 2.5 and 2.7
22 Check whether (x+1) is a factor of x³-x²-(2+√2)x+√2 2
23 For the point (3,5) mention it's quadrant, images in x-axis , y-axis and the origin. 2
24 Write any two postulates of Euclid's geometry. 2
OR
Define line and surface.
25 In the given figure, find x. Further find <BOC , <COD and <AOD. 2

Section C (3X6=18)
26 Represent √2 in number line 3
OR
Write five rational numbers between 3 and 4
27 If x = 2+√3 , find the value of x+ 1 and x - 1 3
𝑥 𝑥
OR
2+√3 2−√3
Find the value of +
2−√3 2+√3
28 If a+b+c = 0 , then find the value of 𝑎2 + 𝑏2 + 𝑐 2 3
𝑏𝑐 𝑐𝑎 𝑎𝑏

29 Find the value of a, when x+1 is a factor of ax³+x²-2x+4a-9 3
30 Given y varies directly as x. If y=12 when x=4 then write a linear equation in x and y. 3
What is the value of y when x=5?
31 Write the coordinate of the indicated points. 3

Page 3 of 5

Section D (5X4=20)
32 Show that (x-2) is a factor of the polynomial f(x)=2x³-3x²-17x+30. Hence factorize f(x). 5
OR
State factor-theorem. Using factor theorem, factorise (𝑥 3 − 2𝑥 2 − 5𝑥 + 6).
33 Consider the following statements: 5
Statement 1 : (2,1) is a solution of 2x+3y = p
Statement 2 : (-2,-3) is a solution of 3x-4y= q
Find the value of p²+q²
34 In the figure, PQ and RS are two mirrors placed parallel to each other. An incident ray 5
AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes
the mirror RS at C and again reflects back along CD. Prove that AB || CD.

35 Factorise : (i) (𝑥 − 𝑦)3 + (𝑦 − 𝑧)3 + (𝑧 − 𝑥)3 5
3 3 2 2
(ii) 8a + b + 12a b + 6ab
OR
(i) Find 𝑎 + 𝑏 + 𝑐 2 when a+b+c = 20 and ab+bc+ca = 2
2 2

(ii) Expand : (a+2b+3c)2
Section E (3X4=12)
36 Case Study : A Mathematics Exhibition is being conducted in your school and one of 4
your friends is making a model of a factor tree. He has some difficulty and asks for
your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

a. What will be the value of x?
b. What will be the value of y?
c. What will be the value of z?
OR
Find the prime factorization of 13915.
Page 4 of 5

37 Case Study : Deepak bought 3 notebooks and 2 pens for Rs. 80. His friend Ram said 4
that the price of each notebook could be Rs. 25. Then three notebooks would cost
Rs.75, the two pens would cost Rs.5 and each pen could be Rs. 2.50. Another friend
Ajay felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the
price of each notebook would also be Rs.16
Lohith also bought the same types of notebooks and pens as Aditya. He paid 110 for 4
notebooks and 3 pens. Later, Deepak guesses the cost of one pen is Rs. 10 and Lohith
guess the cost of one notebook is Rs. 30.

(i) Form the pair of linear equations in two variables from this situation by taking the
cost of one notebook as Rs. x and the cost of one pen as Rs. y.
(ii) Find the cost of one pen
(iii) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.
OR
Find whose estimation is correct in the given statement.
38 Case Study: Maths teacher draws a straight line AB shown on the blackboard as per
the following figure.

1. Now he told Raju to draw another line CD as in the figure
2. The teacher told Ajay to mark ∠ AOD as 2z
3. Suraj was told to mark ∠ AOC as 4y
4. Clive Made and angle ∠ COE = 60°
5. Peter marked ∠ BOE and ∠ BOD as y and x respectively
Now answer the following questions:

1. What is the value of x?
2. What is the value of y?
3. What is the value of z?
OR
What should be the value of x + 2z?

Page 5 of 5

QUESTION PAPERS
GET PREVIOUS YEAR QUESTION PAPERS FOR ALL CLASSES FOR CBSE, ISCSE, ISC AND ALL ALL
STATE BOARDS HERE AT

Andhra Pradesh Board Question Papers
BOARD
WISE Assam Board Question Papers
Bihar Board Question Papers
Chhattisgarh Board Question Papers
Goa Board Question Papers
Gujarat Board Question Papers
Haryana Board Question Papers
Himachal Pradesh Board Question Papers
J&K State Board Question Papers
Jharkhand Board Question Papers
Karnataka Board Question Papers
Kerala Board Question Papers
Madhya Pradesh Board Question Papers
Maharashtra State Board Question Papers
Manipur Board Question Papers
Meghalaya Board Question Papers
Mizoram Board Question Papers
Nagaland Board Question Papers
Orissa Board Question Papers
Punjab Board Question Papers
Rajasthan Board Question Papers
Tamil Nadu Board Question Papers
Telangana State Board Question Papers
Tripura Board Question Papers
Uttarakhand Board Question Papers
Uttar Pradesh (UP) Board Question Papers
West Bengal (WB) Board Question Papers