Goa Board Class 10 Sample Paper 2024 Maths

Sample Paper
&
Question Paper Pattern
2023
2024

GOA BOARD

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
ALTO -BETIM GOA 403521
FIRST INTERNAL TEST (2023-2024)
Subject: MATHEMATICS(E)- LEVEL 1 (REGULAR MATHEMATICS)
Time: 1Hour CLASS: X Max. Marks: 20
**************************************************************************
The weightage or the distribution of marks over different dimensions of the
question paper shall be as follows:
1. Weightage to the Learning Objectives
Sr. No. Learning Marks Percentage of Marks
Objectives
1. Knowledge 3 15%
2. Understanding 9 45%
3. Application 5 25%
4 Skill 3 15%
TOTAL 20 100%
2. Weightage to the different areas of Content
Ch.no. Name of the chapter Marks
2 Polynomials 5
3 Pair of Linear Equations in Two Variables 9
6 Triangles 6
Total 20

3. Weightage to different form/type of Questions
Sr. Type of Questions Marks for Number Total
No. each of Marks
question questions
1 Very Short Answer Type (VSA) 1 4 4

2 Short Answer Type (SA-I) 2 2 4
3 Short Answer Type (SA-II) 3 4 12
Total 10 20

4. Weightage to Difficulty Level of Questions
Sr. No. Estimated difficulty level of questions Percentage
1 Easy 20%
2 Average 60%
3 Difficult 20%
Total 100%

5. Number of Questions: There will be 10 questions

PATTERN OF SSC FIRST INTERNAL TEST QUESTION PAPER (2023-2024)
Subject: MATHEMATICS (E) LEVEL - 1 (Regular Mathematics)
Time: 1hr Class X Max. Marks: 20

Q. Topic Thrust areas Type of Weightage
No. Question
1 Polynomials Any Concept from Polynomials VSA(MCQ) 1 mk
2 Triangles Any Concept from Triangles VSA(MCQ) 1 mk
3 Polynomials • Given a graph of a (linear/quadratic) polynomial to VSA 1 mk
identify the zero(s)/
• To write a quadratic polynomial given sum and
product of two zeroes/
• To write a quadratic polynomial given two zeroes/
• To find sum / product of zeroes of a quadratic
polynomial
4 Pair of Linear • Find the value of k for which the given pair of VSA 1 mk
Equations in linear equations will have a unique solution or
Two Variables no solution or infinitely many solutions /
• Find whether the given pair of linear equations
are consistent or inconsistent/
• If ax +by=m and bx +ay=n then find the value of
x+ y or x-y
5 Pair of Linear Write a pair of Linear equations in two variables for SA I 2 mks
Equations in the given word problem.
Two Variables
6 Triangles Numerical Application on any one of the 4 SA I 2 mks
theorems on Triangles
7 Polynomials • Divide p(x) by g(x) and find q(x) and r(x) and SA II 3 mks
write in the form
p(x) = g(x) × q(x) + r(x)/
• To find g(x) when p(x) ,q(x) and r(x) are given/
• Given two zeroes find remaining two zeroes
8 # Pair of Linear a) Find the solution of the pair of linear equations SA II 3 mks
Equations in by Elimination method
Two Variables OR
b) Find the solution of the pair of linear equations
by Substitution / Cross multiplication method
9 Triangles • To prove a rider on Triangles/ SA II 3 mks
• Proof of any one theorem. (B.P.T./ Pythagoras
Theorem/ converse of Pythagoras theorem)

10 Pair of Linear Find solution of a pair of linear equations in two SA II 3 mks
Equations in variables by graphical method.
Two Variables
# Internal choice to be provided

FIRST INTERNAL TEST (2023-2024)
Subject: MATHEMATICS(E)- LEVEL 2 (Basic Mathematics)
Time: 1Hour CLASS: X Max. Marks: 20
**************************************************************************

The weightage or the distribution of marks over different dimensions of the
question paper shall be as follows:
1. Weightage to the Learning Objectives
Sr. No. Learning Objectives Marks Percentage of Marks
1. Knowledge 3 15%
2. Understanding 11 55%
3. Application 3 15%
4 Skill 3 15%
TOTAL 20 100%
2. Weightage to the different areas of Content
Ch.no. Name of the chapter Marks
2 Polynomials 5
3 Pair of Linear Equations in Two variables 9
6 Triangles 6
Total 20

3. Weightage to different form/type of Questions
Sr. Type of Questions Marks Number Total
No. for each of Marks
question questions
1 Very Short Answer Type (VSA) 1 4 4
2 Short Answer Type (SA-I) 2 2 4
3 Short Answer Type (SA-II) 3 4 12
Total 10 20

4. Weightage to Difficulty Level of Questions
Sr. No. Estimated difficulty level of questions Percentage
1 Easy 20%
2 Average 60%
3 Difficult 20%
Total 100%
5. Number of Questions: There will be 10 questions

PATTERN OF FIRST INTERNAL TEST QUESTION PAPER (2023-2024)
Subject: MATHEMATICS (E) LEVEL - 2 (Basic Mathematics)
Time: 1hr Class X Max. Marks: 20

Q. Topic Thrust areas Type of Weightage
No. Question
1 Polynomials Any concept from Polynomials VSA(MCQ) 1 mk
2 Triangles Any concept from Triangles VSA(MCQ) 1 mk
3 Polynomials • Given a graph of a (linear/quadratic) VSA 1 mk
polynomial to identify the zero(s)/
• To write a quadratic polynomial given sum
and product of two zeroes/
• To write a quadratic polynomial given two
zeroes/
• To find sum / product of zeroes of a
quadratic polynomial
4 Pair of Linear • Find the value of k, if x=a and y=b is a VSA 1 mk
Equations in solution of the given Linear equation in
Two Variables two variables
• If ax +by=m and bx +ay=n then find the
value of x+ y or x-y
5 Pair of Linear Attempt the following: SA I 2 mks
Equations in i)Find the value of k for which the pair of
Two Variables Linear equations in two variables will have
a unique solution or no solution or infinitely
many solutions.
ii)Find whether the pair of Linear equations
in two variables are consistent or
inconsistent
6 Triangles Numerical Application on any one of the 4 SA I 2 mks
theorems on Triangles
7 Polynomials Divide a cubic polynomial p(x) SA II 3 mks
by a linear polynomial g(x) and write the
result in the form
p(x) = q(x) × g(x) + r(x)
8 # Pair of Linear a) Find the solution of the pair of linear SA II 3 mks
Equations in equations by Elimination method
Two Variables OR
b) Find the solution of the pair of linear
equations by Substitution method
9 Triangles Proof of any one theorem. SA II 3 mks
• B.P.T./
• Pythagoras Theorem/

• converse of Pythagoras theorem
10 Pair of Linear Finding solution of a pair of linear equations SA II 3 mks
Equations in in two variables by graphical method.
Two Variables
# Internal choice to be
provided

SECOND INTERNAL TEST (2023-2024)
Subject: MATHEMATICS(E)- LEVEL 1 (REGULAR MATHEMATICS)
Time: 1Hour CLASS: X Max. Marks: 20
**************************************************************************

The weightage or the distribution of marks over different dimensions of the
question paper shall be as follows:
1. Weightage to the Learning Objectives
Sr. No. Learning Objectives Marks Percentage of Marks
1. Knowledge 3 15%
2. Understanding 8 40%
3. Application 6 30%
4 Skill 3 15%
TOTAL 20 100%
2. Weightage to the different areas of Content
Ch.no. Name of the chapter Marks
4 Quadratic Equations 7
8 Introduction to Trigonometry 4
9 Some Applications of Trigonometry 3
10 Circles 3
11 Constructions 3
Total 20

3. Weightage to different form/type of Questions
Sr. Type of Questions Marks Number Total
No. for each of Marks
question questions
1 Very Short Answer Type (VSA) 01 4 4
2 Short Answer Type (SA-I) 02 2 4
3 Short Answer Type (SA-II) 03 4 12
Total 10 20

4. Weightage to Difficulty Level of Questions
Sr. Estimated difficulty level of questions Percentage
No.
1 Easy 20%
2 Average 60%
3 Difficult 20%
Total 100%

5. Number of Questions: There will be 10 questions

PATTERN OF SECOND INTERNAL TEST QUESTION PAPER (2023-2024)
Subject: MATHEMATICS (E) LEVEL - 1 (Regular Mathematics)
Time: 1hr Class X Max Marks: 20

Q. Topic Thrust areas Type of Weightage
No. Question
1 Introduction to Any concept from Introduction to Trigonometry VSA(MCQ) 1mk
Trigonometry
2 Quadratic Equations Any concept from Quadratic Equations VSA(MCQ) 1 mk
3 Introduction to Trigonometric ratios of Complementary angles VSA 1mk
Trigonometry
4 Circles Numerical Application VSA 1mk
5 Circles • Proof of Theorem 10.2/ SA-I 2mks
• Numerical Applications
6 #Introduction to a) Given a trigonometric ratio to find the value SA-I 2 mks
Trigonometry of other trigonometric ratio using k method
OR
b) Evaluate trigonometric expression using
known trigonometric values of specific angles
7 #Quadratic a) Find roots of the quadratic equation by SA-II 3mks
Equations factorisation method
OR
b) Find roots of the quadratic equation by
quadratic formula / completing square
method
8 Applications of Word Problem with figure showing SA-II 3mks
Trigonometry • two angles of elevation /
• two angles of depression /
• one angle of elevation and one angle of
depression.
9 Constructions • Construct Similar triangles as per given scale SA-II 3mks
factor/
• To construct tangents to a circle from an
external point(Ex 11.2)
10 Quadratic Equations • Word problem SA-II 3mks
# Internal choice to be provided

SECOND INTERNAL TEST (2023-2024)
Subject: MATHEMATICS(E)- LEVEL 2 (BASIC MATHEMATICS)
Time: 1Hour CLASS: X Max. Marks: 20
**************************************************************************
The weightage or the distribution of marks over different dimensions of the
question paper shall be as follows:
1. Weightage to the Learning Objectives
Sr. No. Learning Marks Percentage of Marks
Objectives
1. Knowledge 3 15%
2. Understanding 10 50%
3. Application 4 20%
4 Skill 3 15%
TOTAL 20 100%

2. Weightage to the different areas of Content
Ch.no. Name of the chapter Marks
4 Quadratic Equations 7
8 Introduction to Trigonometry 4
9 Some Applications of Trigonometry 3
10 Circles 3
11 Constructions 3
Total 20

3. Weightage to different form/type of Questions
Sr. Type of Questions Marks Number Total
No. for each of Marks
question questions
1 Very Short Answer Type (VSA) 01 4 4
2 Short Answer Type (SA-I) 02 2 4
3 Short Answer Type (SA-II) 03 4 12

Total 10 20

4. Weightage to Difficulty Level of Questions

Sr. No. Estimated difficulty level of questions Percentage

1 Easy 20%
2 Average 60%
3 Difficult 20%
Total 100%

5. Number of Questions: There will be 10 questions

PATTERN OF SECOND INTERNAL TEST QUESTION PAPER(2023-2024)
Subject: MATHEMATICS (E) LEVEL - 2(Basic Mathematics )
Time: 1hr Class X Max. Marks: 20

Q. Topic Thrust areas Type of Weightage
No. Question
1 Introduction to Concept from Introduction to Trigonometry VSA(MCQ) 1mk
Trigonometry
2 Quadratic Equations Concept from Quadratic Equations VSA(MCQ) 1 mk
3 Introduction to Trigonometric ratios of Complementary VSA 1mk
Trigonometry angles
4 Circles Numerical Application VSA 1mk
5 Circles • Proof of Theorem 10.2/ SA-I 2mks
• Numerical Applications
6 # Introduction to a)Given a trigonometric ratio to find the SA-I 2 mks
Trigonometry value of other trigonometric ratio using k
method
OR
b)Evaluate trigonometric expression using
known trigonometric values of specific
angles
7 Quadratic Equations Find roots of the quadratic equation by SA-II 3mks
Factorisation method
8 Applications of Problem with figure showing SA-II 3mks
Trigonometry • an angle of elevation/
• an angle of depression.
9 Constructions • Construct Similar triangles as per given SA-II 3mks
scale factor/
• To construct tangents to a circle from an
external point
10 Quadratic Equations Find roots of a quadratic equation by using SA II 3mks
quadratic formula
# Internal choice to be provided

Third Internal Test (20marks)
(LEVEL 1-Regular Mathematics) and (LEVEL 2-Basic Mathematics)
INNOVATIVE TEST on any two /three chapters given below or
Presentation/Project/Assignment based on anyone of the following chapters

Ch.no. Name of the chapter
6 Triangles
7 Co-ordinate Geometry
9 Some Applications of Trigonometry
13 Surface areas and Volumes
14 Statistics

PORTION FOR STD X - MATHEMATICS (LEVEL2)(Basic Mathematics )
Name of the Chapter Portion
1)Real Numbers whole topic is included for evaluation
2)Polynomials a) Concept of a Polynomial, degree
& types
b) Zero of a Linear Polynomial
,Quadratic Polynomial- geometric
meaning of the zeroes of a Polynomial,
relationship between zeros and
coefficients
c)Finding a Quadratic Polynomial given
sum and product of zeroes /zeroes
d)To find the Quotient and remainder
when a Cubic Polynomial is divided by
a Linear polynomial and to express in
the form:
Dividend =divisor x Quotient
+Remainder
3)Pair of Linear equations in Two a) General form of a pair of linear
variables equations in two variables
b) Conditions for a pair of Linear
equations in two variables to have-a
unique solution, no solution, infinitely
many solutions -finding the value of
the unknown
c)Find the solution of a pair of linear
equations in two variables by
(I) Elimination method
(II)Substitution method (one equation
should have coefficient of x and y as
one) (III)Graphical method (one
equation should have coefficient of x
and y as one and the other equation
should have coefficient of any one x or

y as one)

4)Quadratic Equations a) Concept of a Quadratic equation-
standard form
b) Finding the Roots of a Quadratic
equation by
(I)Factorisation method
(II)Quadratic formula
C)Nature of Roots based on
discriminant
5)Arithmetic Progressions a) Concept of an AP-first term,
common difference
b) Questions based on nth term, sum
of n terms of an AP
a) Concept of Similarity of Triangles-
6)Triangles Tests for similarity of Triangles
b) Concept of theorem on Areas of
Similar Triangles (Proof not for
evaluation)
c)B.P.T., Pythagoras theorem and
Converse of Pythagoras theorem
(Proofs for evaluation)
d)Numerical applications of the above
4 theorems
7)Coordinate Geometry Concepts /Applications of
(I) Distance Formula
(II)Section Formula
(III)Area of Triangle Formula
8)Introduction to Trigonometry a) Concept of Trigonometry
b) Trigonometric ratios and their
relationships, k method
c) Proving with the figure
I) Sin2θ+Cos2θ=1
II) 1+Tan2θ= Sec2θ
III) 1+Cot2θ= Cosec2θ

d)Expressions involving Trigonometric
ratios of some specific angles:
0⁰, 30⁰,45⁰,60⁰,90⁰
e) Trigonometric ratios of
complementary angles

9)Some Applications of Trigonometry a) Heights and Distances: Angle of
Elevation and Angle of Depression
b) Problems on heights and
Distances. Problems should have only
one right triangle with either angle of
elevation or depression.
10)Circles a) Concept of Tangent,
Thm.10.1(proof not for Evaluation)
Thm.10.2(with Proof)
b)Numerical applications
11)Constructions a) Construction of Tangents to a
Circle from a point outside the circle
b) Construction of Similar Triangles
as per given scale factor.
Note : Angles can also be drawn using
a protractor
12)Areas Related to Circles a) Perimeter and Area of a Circle
b) Areas of Segment, Sector,
Quadrant of a Circle and Semicircle
c) Applications to find areas of shaded
region involving two plane figures
13)Surface Areas and Volumes Whole topic is included for evaluation
14)Statistics a) Concept of Mean, Median, Mode
b) To find Mean of grouped data by
Direct method
c)To find Mode of grouped data.
15)Probability a) Concept of Theoretical Probability
b) Probability of a Sure event and an
Impossible event, 0≤P(E)≤1, P (not E)
c) Problems based on coins,
Dice (only 1), playing cards, numbered
cards, items in a box.

PORTION FOR STD X - MATHEMATICS (LEVEL 1)(Regular Mathematics)
a) Everything is included from ch. 1 to ch.15.
b) In the topic of Triangles, Rider and numerical applications based on the theorems will be
tested.
c)In the topic of Constructions , a pair of compasses and ruler to be used to draw specific
angles
-------------x----------------------------------x-----------------------------x-----------

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
ALTO-BETIM GOA 403521
DESIGN OF SSC FINAL EXAM QUESTION PAPER (2023-2024)
Subject : MATHEMATICS (E) - LEVEL 1 (Regular Mathematics)

Time : 2½ hrs Class : X Max. Marks :80

***********************************************************************************************

The weightage or the distribution of marks over different dimensions of the
question paper shall be as follows:
1. Weightage to the Learning Objectives
Sr. No. Learning Objectives Marks Percentage of Marks
1. Knowledge 10 12.5%
2. Understanding 39 48.75%
3. Application 21 26.25%
4. Skill 10 12.5%
Total 80 100%

2.Weightage to the different areas of Content
Chapter Topic Marks
No.
1. Real Numbers 05
2. Polynomials 05
3. Pair of Linear Equations in Two Variables 10
4. Quadratic Equations 07
5 Arithmetic Progressions 04
6. Triangles 06
7. Coordinate Geometry 04
8. Introduction to Trigonometry 07
9. Some Applications of Trigonometry 03
10. Circles 04
11. Constructions 06
12. Areas Related to Circles 05
13. Surface Areas and Volumes 05
14. Statistics 07
15. Probability 02

Total 80

3. Weightage to different form/type of Questions

Sr. No. Form of Questions Marks for Number of Total
each question questions Marks
1. Very Short Answer Type (VSA) 1 20 20
2. Short Answer Type I (SA-I) 2 9 18
3. Short Answer Type II (SA-II) 3 10 30
4. Long Answer Type (LA) 4 3 12
Total 42 80

4. The expected time for different type of questions would be as follows:
Sr.No. Form of Questions Approx. Number Approx. time
time for of for each form
each questions of questions in
question in (n) mins (t) x (n)
mins (t)
1. Very Short Answer Type (VSA) 2 20 40
2. Short Answer Type I (SA-I) 3 9 27
3. Short Answer Type II (SA-II) 5.9 10 59
4. Long Answer Type (LA) 8 3 24
Total 42 150

5. Weightage to Difficulty level of questions:
Sr. No. Estimated difficulty level of questions Percentage
1. Easy 20%
2. Average 60%
3. Difficult 20%
Total 100%

6. Number of Questions:
There will be 42 questions

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
ALTO-BETIM GOA 403521
BLUE PRINT OF SSC FINAL EXAM QUESTION PAPER (2023-2024)
Subject : MATHEMATICS (E) - LEVEL 1 (Regular Mathematics)
Time : 2½ hrs Class : X Max. Marks :80

NOTE: Figures outside the bracket indicate the question number and figures within the bracket indicate
marks .
*Indicates any one will be tested from that chapter
NOTE: Questions on Skill
i)If Solution by Graphical method is tested then Mean will be tested.
ii)If Ogive is tested then Word Problem on Pair of Linear Equations will be tested.

This is a model Blue print. Paper setter may make changes in the objectives
chapter wise.

PATTERN OF SSC FINAL EXAM QUESTION PAPER (2023-2024)
Subject : MATHEMATICS (E) - LEVEL 1 (Regular Mathematics)

Time : 2½ hrs Class : X Max. Marks :80

General Instructions:
Read the following instructions very carefully and strictly follow them.

i) This question paper consists of 42 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 16 are multiple choice questions (MCQs) and
Question Nos. 17 to 20 are very short answer type questions (VSA) of 1 mark
each.
iv) In Section B , Question Nos. 21 to 29 are short answer type I (SA-I )
questions carrying 2 marks each.
v) In Section C, Question Nos. 30 to 39 are short answer type II (SA-II)
questions carrying 3marks each.
vi) In Section D , Question Nos. 40 to 42 are long answer (LA ) questions
carrying 4marks each.
vii) There is no overall choice . However an internal choice has been provided in
two questions of 2marks each in Section B and two questions of 3marks
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 is provided on the answer booklet.
x) Use of calculators and mathematical tables is not permitted.

Q Topic Thrust areas Type of Weightage
No Question
Section A
1 Real Numbers Any concept from Real numbers VSA(MCQ) 1mk
2 Polynomials Any concept from Polynomials VSA(MCQ) 1mk
3 Polynomials Any concept from Polynomials VSA(MCQ) 1mk
4 Pair of Linear Any concept from Pair of Linear VSA(MCQ) 1mk
Equations in Equations in Two Variables
Two Variables
5 Pair of Linear Any concept from Pair of Linear VSA(MCQ) 1mk
Equations in Equations in Two Variables
Two Variables
6 Arithmetic Any concept from Arithmetic VSA(MCQ) 1mk
Progressions Progressions

7 Triangles Any concept from Triangles VSA(MCQ) 1mk
8 Introduction to Any concept from Introduction to VSA(MCQ) 1mk
Trigonometry Trigonometry
9 Introduction to Any concept from Introduction to VSA(MCQ) 1mk
Trigonometry Trigonometry
10 Introduction to Any concept from Introduction to VSA(MCQ) 1mk
Trigonometry Trigonometry

11 Circles Any concept from Circles VSA(MCQ) 1mk
12 Areas Related Any concept from Areas Related to VSA(MCQ) 1mk
to Circles Circles
13 Surface Areas Any question on Surface Areas VSA(MCQ) 1mk
and Volumes
14 Surface Areas Any question on Surface areas VSA(MCQ) 1mk
and Volumes
15 Statistics Any concept from Statistics VSA(MCQ) 1mk

16 Probability Any concept from Probability VSA(MCQ) 1mk

17 Pair of Linear •
Find the value of k for which the VSA 1mk
Equations in given pair of linear equations will
Two Variables have a unique solution or no
solution or infinitely many
solutions /
• Find whether the given pair of
linear equations are consistent or
inconsistent/
• Write a pair of Linear equations in
two variables for the given word
problem.
18 Circles Numerical problem VSA 1mk
19 Areas related • Find l(arc)/ VSA 1mk
to Circles • ar(sector)
(figure may be provided)
(Do not substitute for 𝜋 )
20 Probability Find the probability of the given event VSA 1mk
Section B
21 Real Numbers • Prove 𝑎 ± √𝑏 is irrational/
• Find HCF of two numbers using SA-I 2 mks
Euclid’s division lemma/
• Without performing long division
method, to find whether the given
rational number is terminating or
nonterminating and to write its
decimal expansion.
22 Real Numbers Word Problem SA-I 2 mks
(Application of HCF/LCM)
23 Triangles Numerical application on any one of SA-I 2 mks
the 4 theorems on Triangles
24 Coordinate Problem based on the concept of SA-I 2 mks
Geometry • Distance formula/
• Section formula
25 #Coordinate Using the Area of a triangle SA-I 2 mks
Geometry formula in Co-ordinate Geometry

to find
• a)area of a triangle
OR
• b) co-ordinate k of any one vertex
OR
• c) area of a special parallelogram
(Any two to be asked)

26 #Introduction a) Given a trigonometric ratio, to find SA-I 2 mks
to the value of the other trigonometric
Trigonometry ratio using k method
OR
b) Evaluate trigonometric expression
using known trigonometric values of
specific angles
27 Introduction to To prove a trigonometric identity SA-I 2 mks
Trigonometry
28 Circles Numerical problem SA-I 2mks
29 Statistics • Find the mode / SA-I 2 mks
• median of grouped data
Section C
30 Polynomials • Divide p(x) by g(x) and find q(x) and SA-II 3 mks
r(x) and write in the form
p(x) = g(x) × q(x) + r(x)/
• To find g(x) when p(x) ,q(x) and r(x)
are given/
• given two zeroes find remaining two
zeroes
31 #Pair of Linear a) Find the solution of the pair of SA-II 3mks
Equations in linear equations by Elimination
Two Variables method
OR
b) Find the solution of the pair of
linear equations by Substitution /
Cross multiplication method
32 #Quadratic a)Find roots of the quadratic equation SA-II 3mks
Equations by factorisation method
OR
b) Find roots of the quadratic
equation by quadratic formula /
completing square method
33 Arithmetic Question/Word problem -Sn, an, d, a SA-II 3mks
Progressions
34 Triangles To prove a rider on Triangles SA-II 3mks

35 Some Word problem with figure showing SA-II 3mks
Applications of • two angles of elevation/
Trigonometry • two angles of depression /
• one angle of elevation and one
angle of depression.

36 Constructions Construct tangents to a circle from SA-II 3mks
an external point.
37 Constructions Construct similar triangles as per SA-II 3mks

given scale factor
38 Areas related Find the area of a shaded region SA-II 3mks
to circles
39 Surface Areas Word problem on concept of volume SA-II 3mks
and Volumes

Section D
40 Pair of Linear • Word problem / LA 4mks
Equations in • Find solution of a pair of linear
Two Variables equations in two variables by
graphical method.
41 Quadratic Word problem LA 4mks
Equations
42 Statistics Find mean LA 4mks
• by assumed mean method /
• step deviation method /
• Cumulative frequency curve
(given 6 class intervals)

# Internal choice to be provided
***************************************************************************************************

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
ALTO – BETIM GOA 403521
DESIGN OF SSC FINAL EXAM QUESTION PAPER (2023 – 2024)
Subject: MATHEMATICS(E)-LEVEL 2 (BASIC MATHEMATICS)
Time: 2½ Hours CLASS : X Max. Marks: 80
***************************************************************************
The Weightage or the distribution of marks over different dimensions of the question paper
shall be as follows:
1. Weightage to the Learning Objectives

Sr. No. Learning Objectives Marks Percentage of Marks
1 Knowledge 12 15 %
2 Understanding 42 52.5 %
3 Application 16 20 %
4 Skill 10 12.5 %
Total 80 100 %

2. Weightage to the different areas of Content

Chapter No. Topic Marks
1 Real Numbers 05
2 Polynomials 05
3 Pair of Linear Equations in Two Variables 10
4 Quadratic Equations 07
5 Arithmetic Progressions 04
6 Triangles 06
7 Coordinate Geometry 04
8 Introduction to Trigonometry 07
9 Some Applications of Trigonometry 03
10 Circles 04
11 Constructions 06
12 Areas Related to Circles 05
13 Surface Areas and Volumes 05
14 Statistics 07
15 Probability 02
Total 80

3. Weightage to different form/type of Questions

Sr. No. Types of Questions Marks for Number of Total

each question questions Marks
1 Very Short Answer Type (VSA) 1 20 20
2 Short Answer Type I (SA-I) 2 8 16
3 Short Answer Type II (SA-II) 3 12 36
4 Long Answer Type (LA) 4 2 08
Total 42 80

4. The expected time for different type of questions would be as follows:

Sr. Form of Questions Approx time Number Approx. time
No for each of for each form
question in questions of questions in
mins (t) (n) mins (t) × (n)
1. Very Short answer Type (VSA) 2 20 40
2. Short Answer Type I (SA-I) 3 8 24
3. Short Answer Type II (SA-II) 6 12 72
4. Long Answer Type (LA) 7 2 14
Total 42 150

5. Weightage to Difficulty Level of Questions
Sr. No. Estimated Difficulty level of Questions Percentage
1 Easy 20 %
2 Average 60 %
3 Difficult 20 %
Total 100 %

6. Number of Questions:
There will be 42 questions
************************************************************************************

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
ALTO-BETIM GOA 403521
BLUE PRINT OF SSC FINAL EXAM QUESTION PAPER (2023-2024)
Subject : MATHEMATICS (E) - LEVEL 2 (Basic Mathematics)
Time : 2½ hrs Class : X Max. Marks :80
Sr Objectives Knowledge Understanding Application Skill
No Forms of Questions VSA SA I SA II LA VSA SA I SA II LA VSA SA I SA II LA VSA SA I SA II LA
Content/marks 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Total
1 Real Numbers 1(1) 21(2)
22(2) 3(5)
2 Polynomials 2(1) 29(3)
17(1) 3(5)
3 Pair of Linear Equations 3(1) 4(1) 30(3) 42(4)
in Two Variables 18(1) 5(10)
4 Quadratic Equations 5(1) 31(3)
32(3) 3(7)
5 Arithmetic Progressions 6(1) 33(3) 2(4)
6 Triangles 36(3) 7(1) 26(2) 3(6)
7 Coordinate Geometry 27(2) 28(2) 2(4)
8 Introduction to 8(1) 24(2)
Trigonometry 9(1) 25(2)
10(1) 5(7)
9 Some applications of 37(3)
Trigonometry 1(3)
10 Circles 11(1) 38(3) 2(4)
11 Constructions 34(3)
35(3) 2(6)
12 Areas related to Circles 12(1) 39(3)
19(1) 3(5)
13 Surface Areas and 13(1) 14(1) 40(3)
Volumes 3(5)
14 Statistics 15(1) 23(2) 41(4) 3(7)
15 Probability 16(1)
20(1) 2(2)
10(10) 1(2) 7(7) 5(10) 7(21) 1(4) 3(3) 2(4) 3(9) 2(6) 1(4)
Total 11(12) 20(42) 8(16) 3(10) 42(80)

NOTE: Figures outside the bracket indicate the question number and figures within the bracket indicate marks.

This is a model Blue print. Paper setter may make changes in the objectives
chapter wise.

PATTERN OF SSC FINAL EXAM QUESTION PAPER (2023 – 2024)
Subject : MATHEMATICS (E) - LEVEL 2 (Basic Mathematics)
Time: 2½ Hrs Class : X Max. Marks: 80
General Instructions:
Read the following instructions very carefully and strictly follow them.
(i) This question paper consists of 42 questions. All questions are compulsory.
(ii) This question paper is divided into four Sections – A, B, C and D
(iii) In Section A, Questions Nos. 1 to 16 are multiple choice questions (MCQs) and questions
Nos. 17 to 20 are very short answer type questions (VSA) of 1 mark each.
(iv) In Section B, Questions Nos. 21 to 28 are short answer type I (SA- I) questions
carrying 2 marks each.
(v) In Section C, Questions Nos. 29 to 40 are short answer type II (SA- II) questions
carrying 3 marks each
(vi) In Section D, Questions Nos. 41 and 42 are long answer (LA) questions carrying
4 marks each.
(vii) There is no overall choice. However, an internal choice has been provided in two
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 the given
measurements. The construction lines and arcs should also be maintained.
(ix) Graph page is provided on the answer booklet.
(x) Use of calculators and mathematical tables is not permitted.

Q. Topic Thrust areas Type of Weightage
No. Question
Section A
1 Real Numbers Any concept from Real Numbers VSA 1 mk
(MCQ)
2 Polynomials Any concept from Polynomials VSA 1 mk
(MCQ)
3 Pair of Linear Equations Any concept from Pair of Linear VSA 1 mk

in Two Variables Equations in Two Variables (MCQ)
4 Pair of Linear Equations Any concept from Pair of Linear VSA 1 mk
in Two variables Equations in Two Variables (MCQ)
5 Quadratic Equations Any concept from Quadratic Equations VSA 1 mk
(MCQ)
6 Arithmetic Progressions Any concept from Arithmetic VSA 1 mk
Progression (MCQ)

7 Triangles Any concept from Triangles VSA 1 mk
(MCQ)
8 Introduction to Any concept from Introduction to VSA 1 mk
Trigonometry Trigonometry (MCQ)
9 Introduction to Any concept from Introduction to VSA 1 mk
Trigonometry Trigonometry (MCQ)
10 Introduction to Any concept from Introduction to VSA 1 mk
Trigonometry Trigonometry (MCQ)
11 Circles Any concept from Circles VSA 1 mk
(MCQ)
12 Areas Related to Circles Any concept from Area Related to VSA 1 mk
Circles (MCQ)
13 Surface areas and Any question on Surface Areas VSA 1 mk
Volumes (MCQ)
14 Surface Areas and Any question on Surface Areas VSA 1 mk
Volumes (MCQ)
15 Statistics Any concept from Statistics VSA 1 mk
(MCQ)
16 Probability Any concept from Probability VSA 1 mk
(MCQ)
17 Polynomials • Find the sum or product of zeroes/ VSA 1 mk
• Write a quadratic polynomial, given
sum and product of zeroes/
• Find the zeroes of a quadratic
polynomial/
• Find dividend, given quotient,
remainder and divisor.
18 Pair of Linear Equations • Problems based on the existence of VSA 1 mk
in Two Variables solutions of a pair of linear
equations in two variables (Table
3.4)/
• Find the value of k for which the
given pair of linear equations has a
unique solution or no solution or
infinitely many solutions.
19 Areas Related to Circles • Find length of arc of a circle/ VSA 1 mk
• area of sector of a circle
(figure may be provided)
(Do not substitute for 𝜋 )
20 Probability Find probability of given events VSA 1 mk
Section B
21 #Real Numbers a) Without performing ‘long division’ SA I 2 mks
method, to find whether the given
rational number is terminating or non-
terminating and to wite its decimal
expansion.

OR
b) Prove a ± √𝑏 is irrational.
22 #Real numbers a) Find HCF of two numbers using SA I 2 mks
Euclid’s Division Algorithm.
OR
b) Find LCM of two numbers by the
prime factorisation method.

23 Statistics Find mode of grouped data. SA I 2 mks
24 Introduction to Given a trigonometric ratio, to find the SA I 2 mks
Trigonometry value of the other trigonometric ratio
using k method.
25 Introduction to Evaluate given expression by SA I 2 mks
Trigonometry substituting the known values of
trigonometric ratios.
26 Triangles Numerical application based on any SA I 2 mks
one of the four theorems on Triangles.
27 Coordinate Geometry Problem based on the concept of SA I 2 mks
• Distance formula/
• Section formula
28 Coordinate Geometry Problem based on the concept of area SA I 2 mks
of a triangle
Section C
29 Polynomials Divide a cubic polynomial p(x) by a SA II 3 mks
linear polynomial g(x) and write the
result in the form
p(x) = q(x) × g(x) + r(x)
30 #Pair of Linear a) Find the solution of the pair of SA II 3 mks
Equations in Two linear equations by Elimination
Variables method
OR
b) Find the solution of the pair of linear
equation by substitution method
31 Quadratic Equations Find roots of the quadratic equation by SA II 3 mks
Factorisation method.
32 Quadratic Equations Find roots of the quadratic equation by SA II 3 mks
using quadratic formula.
33 Arithmetic Progressions Given an AP, to find the nth term and SA II 3 mks
sum of n terms
34 Constructions Construct tangents to a circle from an SA II 3 mks
external point.
35 Constructions Construct similar triangles as per given SA II 3 mks
scale factor.
36 #Triangles Proof of any one theorem SA II 3 mks
• B.P.T./
• Pythagoras Theorem/
• converse of Pythagoras theorem
(Any two to be asked)
37 Some Applications of Problem with figure showing SA II 3 mks
Trigonometry • an angle of elevation/
• an angle of depression
38 Circles • Proof of Theorem 10.2 / SA II 3 mks
• Numerical applications
39 Areas Related to Circles Find area of shaded region. SA II 3 mks

40 Surface Areas and Word problem on concept of volume of SA II 3 mks
Volumes combination of two solids.

Section D
41 Statistics Find Mean by Direct method. (Given six LA 4 mks
class intervals)
42 Pair of Linear Equations Find solution of a pair of linear LA 4 mks
in Two Variables equations in two variables by graphical
method.
# - Internal choice to be provided

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