SAMPLE QUESTION PAPER 2023-24

CLASS – IX
MATHEMATICS
Max marks: 80 Time: 3 hours

GENERAL INSTRUCTION
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of the values of 1, 1
and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks and 2
Questions of 5 marks has been provided. An internal choice has been provided in the 2 marks questions of
Section E.
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated

SECTION-A
Q Section A consists of 20 questions of 1 mark each. M
1. An irrational number between 2 and 3 is 1
a) 2.33 b) 2.333…. c) 2. 191919….. d) 2.393993999……
2. State which of the following statements is true 1
(a) Every natural number is a whole number.
(b) Every integer is a whole number.
(c) Every rational number is a whole number.
(d) Every rational number is an integer.
3 Which one of the following algebraic expressions is a polynomial in one variable? 1
2 1
(a) x2 + 𝑥2
(b) √𝑥 + (c) x2 + 1 (d) None of these
√𝑥
4 The maximum number of zeroes a cubic polynomial can have, is 1
(a) 1 (b) 2 (c) 3 (d) 4
5. The linear equation 3x-11y =10 has 1
a) Unique solution b)Two solutions c) Infinitely many solutions d)No solutions
6 Through which of the following points, the graph of y = –x passes? 1
(a) (1, 1) (b) (0, 1) (c) (–1, 1) (d) none of these
7 Abscissa of a point is positive in 1
(a) I and II quadrants (b) I and IV quadrants (c) I quadrant only (d) II quadrant only
8. The perpendicular distance of the point P(3,4) from the x-axis is 1
(a) 3 (b) 4 (c) 5 (d) 7
9 Which of the following is solution of the equation x – 2y = 4 1
(a) (0, 2) (b) (2, 0) (c) (4, 0) (d) (1, 1)
10. Which of the following is a zero of the polynomial p(x) = 2x + 1. 1
4 −1
(a) 1 (b) (c) (d) 2
5 2
11. Euclid divided his famous treatise “The Elements” into : 1
(a) 13 chapters (b) 12 chapters (c) 11 chapters (d) 9 chapters
12 In figure the value of x is 1

(a) 120° (b) 130° (c) 110° (d) 100°

13. 1 1
If M is the midpoint of hypotenuse AC of right trangle ABC then BM = 2 ____
(a)AC (b)BC (c) AB (d) none of these
14. Which one of the following is not congruency criteria 1
(a)SAS (b)ASS (c)AAS (d)SSS
15 The quadrilateral formed by joining the midpoints of the sides of the quadrilateral PQRS taken in order, is 1
a rectangle if
(a) diagonals of PQRS are at right angles
(b) PQRS is rectangle
(c)PQRS is a parallelogram
(d) none of these
16. The length of a chord AB which is at a distance of 6cm from the center O of a circle having radius 10 cm 1
is
(a) 8cm (b). 4cm (c). 16cm (d). 12cm
17 Heron’s formula to find the area of an equilateral triangle of side ‘a' is given by: 1
(a) √𝑎2 𝑠 2 (b) √𝑠(𝑠 − 𝑎)(𝑠 − 𝑏) (c) [𝑠(𝑠 − 𝑎)2 ] (d)√𝑠(𝑠 − 𝑎)3
18 Given below are the seats won by different political parties in the polling outcome of a state assembly 1
elections:

Which political party won the maximum number of seats?

(a) A (b) B (c) C (d) D
ASSERTION-REASON BASED QUESTIONS
Direction: In question numbers 19 and 20, a statement of Reason (R) follows a statement of
Assertion (A). Choose the correct option.
19. Assertion: In Δ ABC, BC = AB and B = 800 ,Then , ∠A = 500 1
Reason: In a triangle, angles opposite to two equal sides are equal
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 but 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.
20 Assertion : The class marks of the class interval 120-150 is 140. 1
Reason: Class mark is mean of lower limit and upper limit of class limit.

(upper limit + lower limit)

Class mark = 2
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 but 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. Diagonal AC of a parallelogram ABCD bisects ∠ A . Show that 2
(i) It bisects ∠ C also,
(ii) ABCD is a rhombus

22 Compute the value of : 9x2 + 4y2 if xy = 6 and 3x + 2y = 12 2

23 Write the coordinates of each of the points Q, R, S and T from the given figure. 2

24 Write four solutions for each of the following equations: 2x + y = 7 2

OR
Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
25 Write any two postulates of EUCLID. 2
OR
In Fig, if AC = BD, then prove that AB = CD.

SECTION-C
Section C consists of 6 questions of 3 marks each.
26 Show that 1.272727……………can be put in form of p/q where p and q are integers and q≠0. 3
OR
4 3 5
Simplify : √81 - 8 √216 + 15 √32 +√225.
27 A triangular park ABC has sides 120m, 80m and 50m 3
(see Fig. 10.4). A gardener Dhania has to put a fence
all around it and also plant grass inside. How much
area does she need to plant? Find the cost of fencing it
with barbed wire at the rate of ₹20 per metre leaving a
space 3m wide for a gate on one side.

28 Factorise : 25a2 – 35a + 12 3

OR
Factorize: 27𝑥 3 + 216𝑦 3 + 54𝑥 2 𝑦 + 108𝑥𝑦 2
29 Find p (0), p (1) and p (2) for the polynomial 𝑝(𝑡) = 2+ 𝑡 + 2 t2 – t3 3

30 It is given that ∠XYZ =640,and XY is produced to point P.Draw a 3

figure from the given information. If ray YQ bisects ∠ ZYP , find
∠XYQ,and reflex of ∠QYP.
OR
In Fig. , ray OS stands on a line POQ. Ray OR and ray OT are angle
bisectors of ∠ POS and ∠ SOQ, respectively. If ∠ POS = x, find ∠
ROT.

31 Show that the bisectors of angles of a parallelogram form a rectangle. 3

 SECTION-D

Section D consists of 4 questions of 5 marks each

32 Prove:Two triangles are congruent if two angles and the included 5

side of one triangle are equal to two angles and the included side of
other triangle.
OR
In right triangle ABC, right angled at C, M is the mid-point of
hypotenuse AB. C is joined to M and produced to a point D such
that DM = CM. Point D is joined to point B . Show that: (i) ∆ AMC
≅ ∆ BMD (ii) ∠ DBC is a right angle. (iii) ∆ DBC ≅ ∆ ACB (iv)
1
CM =2 AB

33 Three girls Reshma, Salma and Mandeep are playing a game by standing on a circle of radius 5m drawn 5
in a park. Reshma throws a ball to Salma ,Salma to Mandeep ,Mandeep to Reshma .If the distance
between Reshma and Salma and between Salma and Mandeeep is 6m each ,what is the distance between
Reshma and Mandeeep?
OR
Two chords AB and CD of length 5cm and 11cm respectively of a circle are
parallel to each other and are on opposite sides its center. If the distance
between AB and CD is 6cm, find the radius of the circle.

34 (i) Locate √3 on the number line. 5

3+√2
(ii) Find the value of a and b if 3−√2
= 𝑎 + 𝑏√2

35 A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled 5
cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones
is to be painted and the cost of painting is ₹12 per m2 , what will be the cost of painting all these cones?
(Use π = 3.14 and take √1.04 = 1.02)
SECTION-E
Section E has 3 Case Based integrated units of assessment (4 marks each)
36 Case Study – 1 4
Prime Minister's National Relief Fund (also called PMNRF in short) is the fund raised to provide support
for people affected by natural and man-made disasters. Natural disasters that are covered under this
include flood, cyclone, earthquake etc. Man-made disasters that are included are major accidents, acid
attacks, riots, etc.Two friends Sita and Gita, together contributed Rs. 200 towards Prime Minister's Relief
Fund. Answer the following :

(i) Which out of the following is not the linear equation in two variables ? 1
(a) 2x= 3 (b) x2 + x = 1 (c) 4 = 5x – 4y (d) x – √2y = 3
(ii) How to represent the above situation in linear equations in two variables ? 2
OR
If Sita contributed ₹76, then how much was contributed by Gita ?

(iii) If both contributed equally, then how much is contributed by each? 1

37 Case Study – 2 4
Once four friends Anuj, Manish, Deepak and Shubham went for a
picnic at a hill station. Due to peak season, they did not get a proper
hotel in the city. The weather was fine so they decided to make a
conical tent at a park. They were carrying 200 m² cloth with them. As
shown in the figure they made the tent with height 8 m and diameter
12 m. The remaining cloth was used for the floor.(𝜋 = 3.14)
(i) What was the area of the floor? 1

(ii) How much Cloth was used for the floor? 2

OR
What was the volume of the
tent
(iii) What is the slant height of the tent? 1

38 Case Study – 3 4
HISTOGRAM: This is a form of
representation like the bargraph,but it is
used for continuous class intervals.We
draw rectangles (or rectangular bars) of
width equal to the class size and lengths
according to the frequencies of the
corresponding class intervals. A
Mathematics teacher asks students to
collect the marks of Mathematics in Half
yearly exam. She instructed to all the
students to prepare frequency disctribution
table using the data collected. Ram
collected the following marks out of
100,obtained by 50 students

(i) Which class interval has highest number of students. 1

(ii) How many students failed if passing marks are 40 marks. 1

(iii) Draw a HISTOGRAM corresponding to this frequency distribution table. 2
OR
Draw a frequency polygon for above frequency distribution table.
 ANSWERS
SECTION A
Q A
1 d
2 a
3 c
4 c
5 c
6 c
7 b
8 b
9 c
10 c
11 a
12 b
13 a
14 b
15 c
16 c
17 d
18 a
19 a
20 d

SECTION B
22. 72
23. Q(-3,0) R(-2,-3) S(2,1) T(4,-2)
24. OR k=7
126 14
26. 99
= 11 OR 0

27. Perimeter of park = 250 m

Area of park = 375√15𝑚2

Cost = ₹4940
28. (25a-12)(a-1) OR (3𝑥 + 6𝑦)3
29. p(0)=0, p(1)=4 and p(2)=4
30.∠𝑋𝑌𝑄 = 122°, ∠𝑄𝑌𝑃 = 58° 𝑂𝑅 90°
33. Distance= 9.6m OR Radius of circle = 5.6 cm
34. OR a = 1 and b = 6/7
35. Cost = ₹384.84
36. (i) b (ii) x+y =200 OR ₹124 (iii)₹100 each
37. (i) area of the floor 113.04m2
(ii) Cloth used = 422.4m2 OR Volume=513.3 m2
(iii) slant height= 12.2m
38. (i) 10-20 (ii) 25