Class 9 Mid Term Question Paper 2025-26 Maths

CBSE CLASS 9
Mid Term Question Paper
Session 2025-26

MATHS

Exam CBSE Class 9
Subject Maths
Session 2025-26
Document Type Mid Term Question Paper

Notes · Sample Papers · Previous Year Papers · Mock Tests

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MID TERM EXAMINATION 2025-26
DAV INSTITUTIONS, JHARKHAND ZONE - F
QUESTION PAPER
FIRST TERM EXAMINATION ( 2025-26)

CLASS – IX FULL MARKS - 80

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SUBJECT - MATHEMATICS SET-A TIME ALLOWED : 3 HRS

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General Instructions :

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Read the following instructions very carefully and strictly follow them:

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 This question paper contains 38 questions. All questions are compulsory.
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 This question paper is divided into five Sections A, B, C, D and E.
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 In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and questions number 19

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and 20 are Assertion-Reason based questions of 1 mark each.
 In Section B, Questions no. 21 to 25 are very short answer (VSA) type questions, carrying 2 marks
each.
 In Section C, Questions no. 26 to 31 are short answer (SA) type questions, carrying 3 marks each.
 In Section D, Questions no. 32 to 35 are long answer (LA) type questions carrying 5 marks each.
 In Section E, Questions no. 36 to 38 are case study based questions carrying 4 marks each.
 There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,
2 questions in Section C, 2 questions in Section D and 2 questions in Section E.
 Use of calculators is not allowed.

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SECTION A
This section comprises multiple choice questions (MCQs) of 1 mark each.

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1. The value of f(x) = 5x−4x2+3 when x = -1, is: 1

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a. 3 b. -12 c. -6 d. 6

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2. If 𝑃(𝑥) = 𝑥 − 2𝑥 + 3, then 𝑓(𝑥) + 𝑓(−𝑥) = ⋯ . . 1
a. 2x2-4x+6 b. 2x2-4x c. -4x+6 d. 2x 2+6
3. 1
If = 23, then is equal to
a. 15 b. √23 c. 5 d. 9
4. Axioms are assumed 1
a. Theorems c. Universal truths specific to geometry
a. Definitions d. Universal truths in all branches of mathematics

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5. It is known that if 𝑥 + 𝑦 = 10, then 𝑥 + 𝑦 + 𝑧 = 10 + 𝑧.The Euclid`s axiom that 1

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illustrates this statement is ….axiom

c. Aolinear equation in two variables 𝑥 and 𝑦 is of the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0, where m
a. 1st b. 2nd c. 3rd d. 4th

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6. 1

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las 7. Write the coordinates of the points which lie on x-axis and are at a distance ofa4 gunits the y-axis.
a. 𝑎 ≠ 0, 𝑏 ≠ 0 b. 𝑎 ≠ 0, 𝑏 = 0 c. 𝑎 = 0, 𝑏 ≠ 0 d. 𝑎 = 0, 𝑏 = 0

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a. (0,4) b. (1,0) c. (4,0) d. (−6,0)

8. The product of two rational numbers is 1
a. always irrational b. always rational
c. always an integer d. sometimes rational sometimes irrational
9. The decimal representation of the rational number is 1
a. Always terminating b. Either terminating or repeating

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c. Either terminating or non-repeating d. Neither terminating nor repeating

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10. √6 × √27 is equal to 1
a. 9√2 b. 3√3 c. 2√2 d. 9√3
11. The linear equation 3x-11y=10 has: 1
a. Unique solution b. Two solutions c. Infinitely many solutions d. No solutions
12. Abscissa of all the points on the x-axis is 1
a. 0 b. 1 c. 2 d. any number
13. The area of an isosceles triangle having a base 2 cm and the length of one of the equal sides 4 cm, 1
is
a. √15 cm2 b. √(15/2) cm2 c. 2√15 cm2 d. 4√15 cm2
14. In triangle ∆ABC if 𝐵𝐶 = 𝐴𝐵 and ∠ B=1000,,then ∠A=….. 1
a. 800 b. 400 c. 500 d. 100 0

15. In ∆ABC and ∆DEF, AB=FD and ∠A= ∠D, the two triangles will be congruent by SAS if 1
a. BC=EF b. AC=DE c. AC=EF d. BC=DE
16. If the supplementary angles are in the ratio 3:2 then the angles are…. 0 and ….0, 1
a. 70 and 108 b. 72 and 108 c. 70 and 110 d. 72 and 108
17. An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4:5. The 1
angles of the triangle are
a. 48°, 60°, 72° b. 50°, 60°, 70° c. 52°, 56°, 72° d. None of these
18. If the perimeter of equilateral ∆ is 60m,then the area is….m2 1
a. 10√3 b. 15√3 c. 20√3 d. 100√3
For questions 19 and 20, two statements are given - one labelled Assertion (A) and the other
labelled Reason (R). Select the correct answer to these questions from the code (a), (b), (c) and (d)
as given below:
i) Both A and B are true and R is the correct explanation of the assertion
ii) Both A and B are true and R is the not correct explanation of the assertion
iii) A is true but R is false
iv) A is false but R is true
19. Assertion (A): The decimal value of 437/999 is 0.437437…..which is rational. 1
Reason(R) : A non- terminating repeating decimal number is a rational number
a. (i) b. (ii) c. (iii) d. (iv)
20. Assertion (A): The point (-6,0) lies on Y-axis and point (0,-7) lies on X-axis. 1
Reason(R) : Every point on the X-axis has zero distance from X-axis and every point on
the Y-axis has zero distance from Y-axis.
a. (i) b. (ii) c. (iii) d. (iv)
SECTION B

21. 2
Find four rational numbers between and
OR.
Find two irrational number between √2 𝑎𝑛𝑑 √3.
22. Express 0. 63 in the form of p/q . 2

23. If the point (3,4) lies on the graph of the equation 3𝑦 = 𝑎𝑥 + 7, find the value of a. 2

24. Find the area of a triangle whose two sides are 8cm and 11cm and the perimeter is 32cm. 2

25. Prove that sides opposite to equal angles of an isosceles triangle are equal. 2

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Prove that the angles opposite to equal sides of a triangle are equal. ag
SECTION C
26. √ √ 3
If = 𝑎 + 𝑏√6 , find the value of 𝑎 𝑎𝑛𝑑 𝑏.
√ √
27. Give possible expression for the length and breadth of the rectangle having 35y 2+8y-16 as 3
its area.
28. Factorize : 125𝑥 + 𝑦 3

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om9x + 4y if 𝒙𝒚 = 𝟔 and 𝟑𝒙 + 𝟐𝒚 = 𝟏𝟐. . co
Factorize: (−2𝑥 + 3𝑦 + 2𝑧)

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2 2
29. Compute the value of 3

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OR
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If a, b, c are all nonzero and
𝑎 + 𝑏 + 𝑐 = 0, prove that + + =3
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30. Draw a a
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rectangle with vertices A(3,1),B(-5,1),C(-5,-3) and D(3,-3) and find its area. 3

31. A. Express the following linear equations in the form ax + by + c = 0 and indicate the 3
values of a,b and c in each case:
(i) −𝟐𝒙 + 𝟑𝒚 = 𝟔 (ii) 𝒚 − 𝟐 = 𝟎
B. Write three different solutions of the equation 𝑥 + 2𝑦 = 6

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SECTION D

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32. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that 5

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∠BAD = ∠ABE and ∠EPA = ∠DPB. Show that (i) ΔDAP ≅ ΔEBP (ii) AD = BE

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33. i. Prove that the bisectors of the angles of a linear pair are at right angles. 5
ii. POQ is a line ray OR is perpendicular to line PQ. OS is another ray lying between
rays OP and OR. Prove that ∠ROS = (∠QOS –∠ POS).

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34. 5

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Simplify :

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( ) ( ) ( )

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OR
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s e ii) If 𝑥 + 𝑦 + 𝑧 = 0. show that x3+y3+z3=3xyz
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a (7)3−(4)3− (3)3
35. The triangular side walls of a flyover have been used for advertisements .The sides of the 5
walls are 122m, 22m and 120m respectively. The advertisement yield an earning of
Rs.5000 per m2 per year. A company hired one of the wall for 3 months .How much rent
did it pay?
OR
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42
cm.
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SECTION E

36. Maths teacher draws a straight line AB shown on the black board.
Now, he told Raju to draw another line CD.
The teacher told Ajay to mark ∠𝐴𝑂𝐷 as 2𝑧.
Suraj was told to mark ∠𝐴𝑂𝐶 as 4𝑦.
Rita was told to mark ∠𝐶𝑂𝐸 = 60°.

Peter marked ∠𝐵𝑂𝐸 and ∠𝐵𝑂𝐷 as 𝑦 and 𝑥 respectively.
On the basis of above information answer the following questions.
i. What is the value of x?
ii. What is the value of y?
iii. What should be the value of 𝑥 + 2𝑧 ?
1
OR 2
What is the relation between 𝑦 and 𝑧 ? 2
37. A team is planning to construct a triangular field ABC of two equal sides are 65m and
third side is 50m. So prepare a map for it. But before starting construction they want to
clear following doubts:
i. What is the type of triangular field? 1
ii. If ∠ A=400 then (∠B+∠C). 1
iii. What is the area of triangular field? 2
OR
iv. What is the area of equilateral triangular field, if its sides are 20cm

38. Ram draws a gate of temple on the graph paper. He has following points
(−,0), (1,0), (1,1), (−1,1) 𝑎𝑛𝑑 (0,2)
i. In which quadrant (-1,1) lies? 1
ii. Write the ordinate of the point (1,0).
iii. Name the closed figure obtained. 1
OR 2
iv. Write the abscissa of the point (0,2).

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