Goa Board Class 9 Sample Paper Maths

Sample Paper
&
Question Paper Pattern
2022
2023

GOA BOARD

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
PORTION AND MARKS DISTRIBUTION FOR STD IX (2022-2023)
SUBJECT: MATHEMATICS
First Quarterly Test
Ch.no. Name of the chapter Marks
1 Number System 6
5 Introduction to Euclid’s Geometry 2
6 Lines and Angles 7
11 Constructions 5
Total 20
First Term Exam
Ch.no. Name of the chapter Marks
2 Polynomials 10
3 Co-ordinate Geometry 3
7 Triangles 7
8 Quadrilaterals 5
1 Number System 5
5 Introduction to Euclid’s Geometry 2
6 Lines and Angles 5
11 Constructions 3
Total 40

Assignment : Financial Education (10marks)
The vision of Financial Education is to train our students to be financially
responsible adults .It could enable them, at their level of need, to understand
the role of money in their life, the need and use of savings, the advantages of
using the formal financial sector and various options to convert their savings into
investments, protection through insurance and a realistic recognition of the
attributes of these options.
After creating awareness and educating students on access to financial services,

Assignment based on guidelines given or any other innovative idea/activity
could follow.

Second Quarterly Test
Ch.no. Name of the chapter Marks
4 Linear Equations in two Variables 6
9 Areas of Parallelograms and Triangles 4
12 Heron’s Formula 6
15 Probability 4
Total 20

Second Term Exam
Ch.no. Name of the chapter Marks
10 Circles 6
13 Surface Areas and Volumes 10
14 Statistics 9
4 Linear Equations in two Variables 6
9 Areas of Parallelograms and Triangles 3
12 Heron’s Formula 3
15 Probability 3
Total 40

Project(10marks): Can be based on any one of the following chapters
Ch.no. Name of the chapter
12 Heron’s formula
13 Surface Areas and Volumes
14 Statistics
15 Probability
Y.R.A(20marks) -To include marks for
class response(5+5)marks, notebooks(5+5)marks for both the terms.

Assignment : Financial Education (10marks)
Guidelines taken from Circular No.44 dated 27/09/2016

Additional suggestions:
Prepare a portfolio on types of accounts/ loans offered by a Bank, filling up
forms for opening a savings bank account/fixed deposit/ recurring deposit,
filling up a withdrawal slip/deposit slip/cheque , calculation of interest on
savings bank account /fixed deposits/ recurring deposits/Housing loans,
preparing a Budget etc.

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
Model paper
First Term Examination (2022-23) Max. Marks: 40
1
STD : IX SUBJECT: Mathematics Time : 1 Hr.
2

Q 1 A) Select and write the most correct alternative from those given below: (1)
The zero of the polynomial 7x- 2 is
−7 −2 2 7
(a) (b) (c) (d)
2 7 7 2

B) Find the value of k if (x+2) is a factor of x3- 2x2 + 3x + 2k (2)
1
C)1) Factorise ANY ONE of the following by splitting the middle term: (1 )
2
i) 3x2 + 2x – 8
ii) 5x2 - 14x + 8
1
2) Evaluate ANY ONE of the following using a suitable identity: (1 )
2
i) (101)3
ii) 108 X 92
D) 1) Expand ANY ONE of the following using a suitable identity: (2)
3
i) (2x-5)
ii) (2x-y+3z)2
2) Factorise ANY ONE of the following using a suitable identity: (2)
3 3
i) 27x -343y
ii) 8x3+y3+z3-6xyz
Q 2 A) Select and write the most correct alternative from those given below: (1)
If ∆AMN ≅ ∆XYZ , ∠M = ∠Y = 90⁰, AM=3cm and YZ =4cm,then the length of AN is
(a) 3cm. (b) 4cm. (c) 5cm. (d) 7cm.
B) In the adjoining figure, ∠B < ∠ A D
and ∠C < ∠𝐷 B (2)
Prove that: AD< 𝐵𝐶
O
A
C

C)Plot the following points in a Cartesian plane: (3)
P(-3,-2) ; Q(6,0) ; R(5,-3) ; S(0,-4) ;T(-4,8);A(5,4)

D) Attempt the following:
1)State with reason whether it is possible to draw ∆DEF with the lengths of
it’s sides as DE=5.2cm, EF=2.4cm and DF=2.8cm. (1)
A
2)In the adjoining figure, BE and CF are two equal altitudes on (3)
Side AC and side AB of ∆ABC respectively.
Prove that: ∆ABC is Isosceles F E

B C
Q 3 A) Select and write the correct alternative from those given below: (1)
Two lines PQ and RS intersect each other at O such that ∠POR=65⁰.Therefore the
measure of ∠POS is
(a) 25⁰ (b) 65⁰ (c) 115⁰ (d) 295⁰
B) In the adjoining figure, points A and B are on line segment XY such that XB=YA. (2)
Prove that: XA = YB X
A B Y
V V V
C) Construct ∆PQR in which ∠Q=45⁰, ∠R=60⁰ and PQ+QR+PR=13.7cm. (3)
D)Attempt the following:
1) In the adjoining figure, XYZ is a triangle. Line PQ is drawn passing through vertex X and (2)
parallel to side YZ. Q
P X
Prove that: ∠YXZ+∠XYZ+∠XZY =180⁰

Y Z
2) In the given figure, AB‖𝐶𝐷, PQ Ʇ CD and ∠PRQ=36⁰ (2)
find
1)∠RQC A B
R P
2)∠PQR
36⁰

C Q D

Q 4 A) Select and write the correct appropriate alternative from those given below: (1)
If the diagonals of a quadrilateral are equal and bisect each other at right angles
then it is a
(a) parallelogram (b) rectangle (c) rhombus (d) square
𝑝
B) Express 1.27 in the form of where p and q are integers
𝑞
and q ≠0 (2)
C)Attempt the following:
1
1) Write the decimal form of 4 (1)
4
4
2) Rationalise the denominator of (2)
(1+√3)
D) Attempt the following:
1) In the adjoining figure, □PQRS is a parallelogram.PM and RN are perpendiculars from
vertices P and R on diagonal QS at M and N respectively (2)
Show that: ∆PMS ≅ ∆RNQ S R
M
N
P Q
2)PQRS is a quadrilateral in which A,B,C and D are the midpoints of sides PQ,QR,RS and PS
respectively S
Prove that: □ABCD is a parallelogram. C (2)
D R

P B
A
Q
----------------------------------X-------------------------------------------------X-----------------------------------------

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
Model Paper
Second Term Examination : ( 2022 – 23 )
Std: IX Subject: Mathematics Max. Mks: 40 Time: 1½ hrs
-----------------------------------------------------------------------------------------------------------------------------
Q.1.A) Select and write the correct alternative from those given below : (1)
The class interval with class mark 25 and class size 10 is :
(a) 15 – 25 (b) 15 – 30 (c) 20 – 25 (d) 20 – 30
B) Attempt the following. (2)
1) The heights (in cm) of 10 students of a class are as follows:
155, 160, 145, 149, 151, 147, 153, 144, 148, 145
Find the median height of this data.
2) A die is thrown once. Find the probability of getting a prime number on its top face.
C) The table below shows the marks obtained by a certain number of students in a (3)
math test. Complete the table and find the mean mark obtained.

Marks ( xi ) No. of students ( fi ) fi . xi
5 07 ……..
10 11 ……..
15 13 ……..
20 09 ……..
25 07 ……..
30 03 ……..
Σ fi = …….. Σ fi . xi = ……..

D) Draw a histogram and hence a frequency polygon for the following frequency (4)
distribution.

Daily earnings 700 – 750 750 – 800 800 – 850 850 – 900 900 – 950
(in Rs) : (C.I)
No. of workers 6 9 3 7 5
(fi)

Q.2.A) Select and write the correct alternative from those given below : (1)
The total surface area of a solid hemisphere of radius ‘ r ’ is :
(a) 2πr² (b) 3πr² (c) 4πr² (d) 5πr²
B) Attempt the following. (2)
1) Find the curved surface area of a right circular cone of slant height 10 cm and

base radius 7 cm. ( Take π = 22/7 )
2) The radius of a sphere is 3 cm. Find its volume. ( Do not substitute for π)

1

C) A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. (3)
If the bowl is filled to a height of 4 cm, then find the quantity of soup in litres that
the hospital has to prepare daily to serve 100 patients. ( Take π = 22/7 )
D) Attempt the following.
1) The length, breadth and height of a room is 5m, 4m and 3m respectively. (2)
Find the cost of white washing its four walls at the rate of ₹ 25 per m².
2) The diameter of a right circular cone is 7 cm. If its volume is 154 cm³, find (2)
the height of the cone. ( Take π = 22/7 )

Q.3.A) Select and write the correct alternative from those given below. (1)
The equation x = 7, in two variables, can be written as :
a) x + 0y = 7 (b) 0x + y = 7 (c) 7x + 0y = 7 (d) x + y = 7
B) Attempt the following. (2)
1) Find the value of ' k ’ if x = 2 and y = –1 is a solution of the equation 5x + ky =13 .
2) 3 kg rice and 2 kg sugar together cost ₹ 190. Represent this statement in the form of
a linear equation if the cost of 1 kg rice and 1 kg sugar is ₹ x and ₹ y respectively.

C) Draw the graph of the linear equation y = 3x – 5 (3)
Rewrite and complete the following table.
( Plot at least 3 points for this line on a graph paper )
y = 3x – 5
x
y
(x,y)

D) Attempt the following.
1. Three coins are tossed simultaneously 100 times. The following outcomes (2)
are recorded.
Outcome 3 tails 2 tails 1 tail No tail
Frequency 23 27 26 24

Find the probability of getting:
i) more than one tail.
ii) all heads

2. □ABCD is a parallelogram, AE ⊥ BC and AF ⊥ CD as shown in the figure. (2)
If BC = 12 cm, CD = 8 cm and AE = 4 cm, then
find:
i) area of parallelogram ABCD
ii) length of AF

2

Q.4.A) Select and write the correct alternative from those given below : (1)
A triangle and a parallelogram are on the same base and between the same parallels.
If the area of the parallelogram is 64 cm² then the area of the triangle is:
a) 128 cm² b) 64 cm² c) 32 cm² d) 8 cm²

B) With reference to the adjoining figure and given conditions write the proof of (2)
the theorem given below:
Given: AB and CD are congruent chords of a Circle
with centre O.

Prove that: ∠ AOB = ∠ COD

C) A rhombus shaped field has green grass for 18 cows to graze. (3)
If the perimeter of the rhombus is 120 m and its longer
diagonal is 48 m, then find the area of the grass field each
cow will get to graze.

D) Attempt the following.
1) □ABCD is a cyclic quadrilateral with BC as diameter (2)
and AD = CD . If ∠ ACB = 40°, then find the measure of:
i) ∠ ABC
ii) ∠ ACD

2) In the given figure ∆PQR is inscribed in a circle with centre O. (2)

If ∠ OPQ = 35°, then find :
i) ∠ PRQ
ii) m( arc PRQ )

-------------------------------------------------------(÷ × + – )-------------------------------------------------------

3