Class 9 Half Yearly Question Paper 2025-26 Maths

CBSE CLASS 9
Half Yearly Question Paper
Session 2025-26

MATHS

Exam CBSE Class 9
Subject Maths
Session 2025-26
Document Type Half Yearly Question Paper

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Question Paper
HALF YEARLY EXAMINATION
SESSION 2025-2026 ag
Class: IX MAXIMUM MARKS: 80
SUBJECT: MATHEMATICS TIME: 3Hrs
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions and no. 06 of pages.
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2. This Question Paper is divided into 5 Sections A, B, C, D and E.

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3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no.

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19 and 20 are Assertion- Reason based questions of 1 mark each.
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4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02

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marks each.
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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

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choice has been provided in all the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.

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10. Use of calculators is not allowed.

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SECTION
1. On dividing 6√27 by 2√3 , we 1
(A) 3√9 (B) 9 (C) 6 (D) None of these
2. Which of the following is an irrational number? 1
A) √5 B) √121 C) D) 0.3.
3. The value of √2 1

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A) 2 B) 2 C) 2 D) 2

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4. The decimal expansion of the number √2 is
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A) a finite decimal

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B) 1.41421

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C) non-terminating recurring

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D) non-terminating non-recurring

a 5. How many zeroes are there in Zero polynomial? 1
A) 0 B) infinite C) One real number D) One rational
number.

6. If x2+kx+6 = (x+2) (x+3) for all k, find the value of k. 1

A)1 B) -2 C) 10 D) 5

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7. The degree of a non-zero constant polynomial is: 1

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(A) not de ined (B) 0 (C) 1 (D) 2

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8. If AB || CD, EF ⊥ CD and ∠GEF = 45° as per the figure given below
w. 1

The value of ∠AGE is::
A) 120° B) 140° C) 90° D) 135°

9. An exterior angle of a triangle is 105° and its two interior opposite angles
a are 1
equal. Each of these eqqual angles is _____.
A) 37 ½° B) 72 ½°
½ C) 75° D) 52 ½°
10. Which of these statemeents do not satisfy Euclid’s axiom? 1
A) Things which are eqqual to the same thing are equal to one anotheer
B) If equals are added to equals, the wholes are equal.
C) If equals are subtraccted from equals, the remainders are equal.
D) The whole is lesserr than the part.
11. Sohan is of the same age
ag as Mohan. Ram is also of the same age as Mohan. 1
State the Euclid’s axiom
om that illustrates the relative ages of John andd Ram
A) First Axiom B) Second Axiom
C) Third Axiom D) Fourth Axiom
12. In triangle ABC, if ABB=BC and ∠B = 70°, ∠A will be: 1
A) 70° B) 110° C) 55° D) 130°

13. If ABC and DBC are two
t isosceles triangles on the same base BC. Then: 1
A) ∠ABD = ∠ACD
B) ∠ABD >∠ACD
C) ∠ABD <∠ACD
D) None of the above

14. In triangles ABC and P PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. Thee two 1
triangles are
A) Isosceles and congrruent
B) Isosceles but not coongruent
C) Congruent but not isosceles
i
D) Neither congruent nor
n isosceles

15. If all sides of a trianglee are doubled, how does the area change? 1
A) Remains the same
B) Doubles
C) Quadruples
D) Increases by a factoor of 8
16. If the perimeter of an equilateral
e triangle is 180 cm. Then its area w
will be: 1
A) 900 cm2 B) 9000√3 cm2 C) 300√3 cm2 D) 600√3 cm m2

17. The sides of a triangle are in the ratio 12: 17: 25 and its perimeter iss 540 cm. 1
The area is:
A) 1000 sq.cm B)) 5000 sq.cm C) 9000 sq.cm D) 80000 sq.cm
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18. The area of an equilateeral triangle is 36√3 #$ . The length 1
the triangle is:
(A) 24 cm (B) 60 cm
c (C) 36 cm (D) 12 cm
DIRECTION: In the foollowing questions (19 and 20), a statement oof
assertion (A) is followeed by a statement of reason (R).
Mark the correct choicce as:
(a)Both assertion (A) and
a reason (R) are true and reason (R) is the ccorrect
explanation of assertioon (A). (
b) Both assertion (A) aand reason (R) are true but reason (R) is not thhe correct

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explanation of assertioon (A).

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

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(d)Assertion (A) is falsse but reason (R) is true.
19.
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Assertion: Rational nuumber lying between two rational numbers x and y is 1
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(x+y)/2.
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Reason: There is one rational
r number lying between any two rationnal
numbers.
20. Assertion: In the givenn figure, BO and CO are the bisectors of ∠B and ∠C 1
respectively. If ∠A = 550° then ∠BOC = 115°
Reason: The sum of alll the interior angles of a triangle is 1800

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SECTION B
21.
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Are the square roots off all positive integer’s irrational? If not give aan
example of the square root that is a rational number.
2

22. Find the value of ", if % & " is a factor of % ' & "% ( 2% ( " ( 1. 2
Or
Compute the value of 99x2 + 4y2 if xy = 6 and 3x + 2y = 12.
23. Y and MN intersect at O. If ∠POY = 90° and aa: b = 2:
In the Figure, lines XY 2
3, find c.

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24. In triangles ABC and DEF,
D ∠B = ∠E, ∠C = ∠F, and BC = EF. Are thhe two 2
triangles congruent? Iff yes, write the congruence criterion.
25. Find the area of an isossceles triangle whose equal sides measure 13 cm each 2
and the base measures 20 cm.
Or
The sides of a triangle are 122 m, 22 m and 120 m respectively. Finnd the area

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of the triangle.

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SECTION C
26. Represent√4.5geomettrically on number line. 3
Or
Prove that ) ( √* iss a irrational number where p and q is prime.

`27. Using the Factor Theorrem to determine whether g(x) is a factor of p(x)
p in the 3
following case
p(x) = 2x³+x²–2x–1, g(x)
g = x+1

28. If a point C lies betweeen two points A and B such that AC = BC, theen prove 3
that AC = 1/2 AB, expllain by drawing the figure.
29. Two lines +, and -. intersect each other at the point 2 such that ,-
, ∥ .+ 3
and ,- / .+. Show thhat O is the midpoint of both the line-segmennts AB
and CD.

30. In figure, POQ is a linee. Ray OR is perpendicular to line PQ. OS is another 3
ray lying between rayss OP and OR.
Prove that: 0 123 / 40 523&0 6237

Or

In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE
E, ∠GEF
and ∠FGE.

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31.
l as
PQ ⊥ PS, PQ || SR, ∠SQR = 28° and ∠QRT = 65° then
In the given figure, if P 3
s find the values of x andd y.
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SECTION D 3

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32. Show the following inn the form p/q, where p and q are integers andd q ≠ 0: 5

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0.404040…

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If 4% ( "7 is.a factor oof both the polynomials % ( )% ( * and % ( $% ( e m
33.
m" / .
9, prove ethat
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g % & 6% ( 11% & 6
= >

aFactorise: '

34. AB is a line segment aand P is its mid-point. D and E are points on thhe same 5
side of AB such that ∠BAD
∠ = ∠ABE and ∠EPA = ∠DPB. Show thaat
(i) ∆DAP ≅ ∆EBP
(ii) AD = BE

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a triangles on the same base BC
∆ABC and ∆DBC aree two isosceles B and
vertices A and D are on
o the same side of BC (see the figure). If A
AD is
extended to intersect BC at P, show that
(i) ∆ABD ≅ ∆ACD
(ii) ∆ABP ≅ ∆ACP
(iii) AP bisects ∠A as well as ∠D.
(iv) AP is the perpenddicular bisector of BC.

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35. The sides of a quadrilaateral, taken in order as 5, 12, 14, and 15 meteers, 5
respectively, and the anngle contained by the first two sides is a rightt angle.
Find its area.
SECTION E
36. Preeti and Nandhini staarted a new business under EMC business blaaster. The
investment made by booth partner is represented by a polynomial

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l)4%7 / 4% ( 12% ( 5. The factors of the polynomials are the indi dividual

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share of both.

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Based on the above infformation answer the following questions
i)If x=100 then find thee money invested.
ii)What is the degree of
o the invested polynomial? 1
iii)Find the shares inveested by Preeti and Nandini separately 1
Or
Find the value of p(10)) – p(0) 2
37. In a very crowded city,y, there are three main roads+,, -.&@D situaated
parallel to each other facing
f North-South direction. During office hoours,
heavy traffic occurs in all three streets. It is eventually creating a prroblem for
cyclist, street paddler, vendors
v to go from one corner of the city to aanother
corner. Keeping this inn mind, the city governance has made two shoort but
very useful paths @,& &@+ each connecting all three paths at differen ent points.
All the useful informattion are given in below diagram.

Based on the above infformation, answer the following questions
(i) Check whether +@ ⊥ -..
(ii) Find %. 1
(iii) (a) Find A & 4B ( 5%. 1
OR 2
(iii) (b) Find %: B: A.
38. Mayank bought a trianngle shape field and wants to grow potato andd wheat on
his field. He divided hiis field by joining opposite sides. On the largeest park
he grew wheat and on the rest part he grew potato. The dimensions of a park
are shown in the park.
On the basis of the aboove information, solve the following questionns:
i) Find the length of AC C in ∆ABC. 1
ii) Find the perimeter of total park. 1
iii) If the cost of plougghing park is ₹5 per cm2, then find the total coost of 2
ploughing the park.
Or
Find the area of ∆ABC C using Heron’s formula.

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