Goa Board Class 9 Sample Paper 2025 Maths (Semester I)

2025

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MODEL QUESTION PAPER (2024-2025)
SEMESTER I
SUBJECT: MATHEMATICS
Time: 3 hrs GRADE 9 Max. Marks: 80
__________________________________________________________________

INSTRUCTIONS:
i) This question paper consists of 55 questions. All questions are compulsory.
ii) This question paper is divided into four Sections.-A , B , C and D.
iii) In Section A, Question Nos. 1 to 40 are multiple choice questions (MCQs)
carrying 1 mark each which are to be answered on an OMR sheet. The OMR
sheet shall be collected after 90 mins.
iv) In Section B, Question Nos. 41 to 47 are short answer type I (SA-I) questions
carrying 2 marks each.
v) In Section C, Question Nos. 48 to 53 are short answer type II (SA-II)
questions carrying 3 marks each.
vi) In Section D, Question Nos. 54 and 55 are long answer (LA) questions
carrying 4 marks each.
vii) There is no overall choice. However, an internal choice has been provided in
three questions of 2 marks each in Section B and two questions of 3 marks
each in Section C.
viii) In questions on constructions, the drawing should be clear and exactly as
per given measurements. The construction lines and arcs should also be
maintained.
ix) Graph page will be provided on request.
x) Use of calculator is not permitted.

Section A ( 1 mark each)
Choose the correct alternative from those given below each statement:

1. The number , where ‘a’ and ‘b’ are integers , is not a rational number if ‘b’ is :

A. -1

B. 0

C. 1

D. 10

2. Which of the following is an irrational number ? :

A. √ + √

B. √ -- √

C. √ x √

D. √ √

3. The rational number which has a terminating decimal expansion is :

A.

B.

C.

D.

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

A. 0

B. 1

C. 2

D. 3

5. The zero of the polynomial x is :
A.

B.

C. 0

D.

6. The equation of the x-axis is given by :

A. x =0

B. y = 0

C. x = 1

D. y = 1

7. A graph of a linear equation in two variables is a:

A. circle

B. semicircle

C. curve

D. straight line

8. If (3 , 2) lies on the graph of 5x+ky=11 , then the value of ‘k’ is :

A.

B.

C. 2

D. 7

9. The relation between sin ,cosθ and tan θ is:

A. Sin θ +cos θ=tan θ

B. Sin θ -cos θ=tan θ

C. Sin θ cos θ=tan θ

D. Sin θ = tan θ

10. The value of tan2300 is :

A.
√

B.

C. √

D. 3

11. In ΔABC, if A = 4x°, B = 24° and C = 36°, then the value of ‘x’ is :

A. 30

B. 60

C. 75

D. 120
12. The complement of an angle of measure (58 + a)° is :

A. (32 +a)°

B. (122 – a)°

C. (32 -a)°

D. (122 +a)°
13. If RTM is an exterior angle of ΔRST, R = 70° and S = 25°, then the measure of
RTM is :

A. 45°

B. 85°

C. 95°

D. 110°

14. In the figure, if P is the mid-point of AB and CAP = DBP, then the congruence
rule by which ΔAPC ΔBPD is :

A. SAS

B. ASA

C. AAS

D. RHS
15. If the largest side of a triangle is 12 cm, then the other two sides can be:

A. 7.6 cm, 3.4 cm

B. 6.4 cm, 2.8 cm

C. 4.2 cm, 7.8 cm

D. 4.8 cm, 8.2 cm
16. If both diagonals of a parallelogram are equal, then it is a:

A. Trapezium

B. Kite

C. Rectangle

D. Rhombus
17. The value of the polynomial p(y) = 2y³ +y² - 5 at y = -1 is:

A. -8

B. -6

C. -4

D. -2

18. A solution of the equation 2x – y = 5 is:

A. ( 2, 1 )

B. ( 4, -3 )

C. ( 1, -3 )

D. ( 3, 2 )
19. The equation of a line parallel to the X-axis and 4 units above the origin is:

A. x = -4

B. y = -4

C. x = 4

D. y = 4
20. The value of sin 26° cos 64° is:

A. 0

B. 1

C. 38

D. 90
21) The zero of the polynomial 3x + 7 is:
A.

B.

C.

D.

22) The simplified form of is:

A. -9

B.

C.

D. 9
23) If +51 is divided by x+1, then the remainder is:

A. 0

B. 1

C. 49

D. 50

24)The simplified form of is:
√ √
A.
√

B. √

C. 3 2√

D. 3+2√

25) If + = 1 where a, b then the value of is :

A.

B.

C.

D.

26) If x is a factor of x2 +3ax – 2a , then the value of a is:

A.

B.

C.

D. 2

27) If (x is a factor of ax4+bx3+cx2+dx+e then :

A. a + c+ e = b + d

B. a + b + e = c + d

C. a+ b + c = d + e

D. b + c + d = a + e
28) If x = 2 and y = is a solution of the equation 2x + 3y = k then the value of k is:

A. 1

B. 5

C. 6

D. 7
29) The present age of A is 3 years more than thrice the present age of B. If the
present ages of A and B are ‘x ‘ and ‘y’ years respectively ,then the algebraic equation
representing the given situation is:

A. x + 3 = 3y

B. x 3y

C. x + 3y + 3 = 0

D. x 3 + 3y = 0

30) In the given figure, line segments CD and AB intersect at O. If ACO=80⁰, BDO=70⁰
and COA=40⁰, then the value of x + y is:

A. 190⁰

B. 210⁰

C. 230⁰

D. 270⁰

31. In the given figure, MNO = 2 NOM, NQ is the bisector of MNO and MN=PO.
Therefore, MNQ is congruent to:

A. QPO

B. POQ

C. OQP

D. NQP

32. The value of + is:

A. 3

B. 1

C. 0

D. 1

33. If Sin 2A = Cos (A Where 2A is an acute angle, then the value of A:

A. 0⁰

B.

C.

D.

34. ABC is a right triangle, right angled at B. If AB = 10cm and C= , then the length
side BC is:

A. 5 cm

B. 10√ cm

C. 20 cm

D. 20√ cm
35. If one angle of a triangle is equal to the sum of the other two angles then, the
triangle is

A. an acute triangle

B. an obtuse triangle

C. a right angled triangle

D. an equilateral triangle

36. In the given figure, AB divides DAC such that the measure of CAB is thrice the
measure of DAB. If AB = DB and EAC = ,
then the value of is:

A.

B.

C.

D.

37. In the given figure , XY PQ
If AEF = and BXQ = , then
the value of is:
A.

B.

C.

D.

38. If the angles of a quadrilateral taken in order are in the ratio 3:7:6:4, then the
quadrilateral is a:

A. rhombus

B. parallelogram

C. trapezium

D. kite

39. In the given figure, points A, B and C are the mid-points of sides PQ, QR and PR
of PQR respectively. If the perimeter of PQR is 4 cm, then the perimeter
of ABC is:

A. 1 cm

B. 2 cm

C. 3 cm

D. 4 cm

40. REST is a rhombus . If = (3 2) and S= (50 ) , then the
measure of is R

A.

B.

C.

D.

Section B ( 2 marks each)
41. Represent √ on number line.
42. Factorise the following quadratic polynomial by splitting the middle term.

4x2 11x + 6

OR

5x2 + 12x – 9

43. Factorise using a suitable identity: 27a3 - 64b3 .

44. Expand using a suitable identity: ( 3x + 5y + 8z)2

OR

Evaluate using a suitable identity: ( 103 )3

45. In ΔABC , B = 900 , AB = 5 cm and BC = 12 cm. A
Find the length of AC and the value of Cos C.

OR
B C
Evaluate the following trigonometric expression using known trigonometric
values of specific angles:

5 Tan2 300 + 3 Sin2 450
A C
46. Given : In the adjoining figure ,
lines AB and CD intersect at ‘O’
Prove that: AOC = BOD
O

D B

P
47. Given : ΔPQR is an Isosceles triangle such that PQ = PR .
Ray PS is the bisector of QPR

Prove that : Q= R

Q R
S

Section C ( 3 marks each )

48. Draw the graph of the following linear equation in two variables.

2x + y = 9
x
Y
( plot at least three points)

Q
49. In the given figure, PQSR is a quadrilateral

In which Q = R and PS bisects QPR
P S
Prove that : ΔPQS ΔPRS.

50. Given: □ABCD is a parallelogram.BD is the diagonal R
Prove that: AB CD and AD=BC
A B

D C
OR
Given that: In □PQRS , diagonals PR and QS intersect at O.
PO=OR and QO=SO P Q
Prove that: □PQRS is a parallelogram.

O

S R
51. Given: ABCD is a quadrilateral in which
P, Q, R and S are the mid-points of the D R
sides AB, BC, CD and DA. C
AC is the diagonal.
If SR= 5.2cm and QR=6.4cm,then S
Find the length of AC, PQ and PS
Q

A
P B

52. Construct Δ ABC such that BC = 7.5 cm , B = 750 and AB + AC = 13 cm.
OR
Construct Δ PQR such that QR = 6.5 cm , Q = 600 and PR -- PQ = 3. 5 cm.

53. Factorise the polynomial : a3 + 13a2 + 32a + 20

Section D ( 4 marks each)

54. Given : Δ ABC and Δ DBC are two isosceles triangles on the same base BC
and the vertices A and D are on the same side of BC. A
AD is extended to intersect BC at E.

Prove that : Δ ABE Δ ACE .
D

B E C

55. Construct Δ PQR such that , Q = 450 , R = 600 and PQ + QR + PR = 11 cm.
Measure and state the length of PQ, QR and PS.

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