Goa Board Class 12 Sample Paper 2027 Mathematics (Voc)

FOR GOA CLASS 12 PREPARATION

Goa Board Class 12
Sample Paper 2027
Mathematics (Voc)
EXAM YEAR TYPE SUBJECT

Goa Class 12 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

.
.co s e m

s em l a
a ag
GOA BOARD OF SECONDARY & HIGHER SECONDARY EDUCATION
ALTO – BETIM, GOA

PROFORMA FOR ANALYSIS OF QUESTION PAPER 2026 onwards

o m
o m . c
. c
Subject: Mathematics (Voc.)
Marks Allotted: 50 se
Year of Examination: April 2026 onwards
m
em a
Duration: 2 hrs Class: XII Computer Technique
s g l
g la a
a
1. Sections if any: - YES – Section A, B, C and D.

2. Total No. of questions and marks: -
No. of questions No. of questions to be Total marks for all the Maximum marks for
set in the paper attempted questions set in the attempted questions
paper
m
25 25
m .co 50 50

s e
3. Study of options:
l a
g paper:- -NO-
a
(a) Overall options in the whole question
(b) Overall options within the sections: - -NO-
(c) Overall options within a question: - -NO-
(d) Internal option within the question: - -NO-
(e) Comparability options: --NO-

4. Instructions for examiners: - Evaluate as per pattern

m
m .co
5. Directions in individual question: - -NIL

.co
m 6. Allocation of marks question-wise and part-wise: - s e m
s e g la
g la Section A: Q.Nos. 01 to 10 – 1 mark each
a
a Section B: Q.Nos. 11 to 18
Section C: Q.Nos. 19 to 22
– 2 marks each
– 3 marks each
Section D: Q.Nos. 23 to 25 – 4 marks each

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 1 of 16

7. General format
(a) Arrangement of question, numbering and printing etc.
Section A Section B Section C Section D
1 11 19 23
2 12 20 24
3 13 21 25
4 14 22
5 15
6 16
7 17
8 18
9
10

8. Question-wise Analysis
Sr. Obj Content Area Major Form of Language Definiteness Difficulty Marks Time
no. ecti area of content the of of the level of allotted in
Part ve topic questions Questions answers the min.
no. questions
1 K Matrices M.C.Q. Definite Easy 1 3
2 U Matrices M.C.Q. Definite Easy 1 3
3 A Matrices M.C.Q. Definite Average 1 3
4 A Matrices M.C.Q. Definite Average 1 3
5 A Matrices M.C.Q. Definite Easy 1 3
6 U Derivative VSA Definite Easy 1 3
7 U Derivative VSA Definite Easy 1 3
8 K Integration VSA Definite Easy 1 3
9 K Integration VSA Definite Easy 1 3
10 K Definite Integrals VSA Definite Easy 1 3
11 U Numerical Methods SA1 Definite Easy 2 4
ENGLISH

12 K Probability SA1 Definite Easy 2 4
13 U Probability SA1 Definite Average 2 4
14 U Derivative SA1 Definite Difficult 2 4
15 U Derivative SA1 Definite Average 2 4
16 U Derivative SA1 Definite Average 2 4
17 U Integration SA1 Definite Average 2 4
18 A Definite Integrals SA1 Definite Average 2 4
19 U Continuity SA2 Definite Difficult 3 7
20 A Matrices SA2 Definite Average 3 7
21 U Integration SA2 Definite Difficult 3 7
22 A Definite Integrals SA2 Definite Average 3 7
23 A Numerical Methods LA Definite Average 4 10
24 A Correlation & LA Definite Average 4 10
Regression
25 S L.P.P LA Definite Average 4 10

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 16

.
.co s e m

s em l a
a ag
A) Weightage to Learning Outcomes
Sr. No. Learning Outcomes Marks Percentage of Marks

1. Knowledge 6 12%

2. Understanding 18 36%

m
co
3. Application 22 44%

4. Skill
. c om 4 8%
em .
e m l as
l as ag
g
a to Content/Subject Units
B) Weightage
Question For
Sr. No. Units Marks Percentage
marks

1. Numerical Methods 2+4 6 12%

2. Correlation & Regression 4 4 8%

m
c. o
3. Matrices 1+1+1+1+1+3 8 16%

e m
s
4. Probability 2+2 4 8%

l a
ag
5. Continuity 3 3 6%

6. Derivatives 1+1+2+2+2 8 16%

7. Integration 1+1+2+3 7 14%

8. Definite Integrals & Application 1+2+3 6 12%

9. Linear Programming 4 4 8%

m
m
Total 50
c. o 100%
m .co s e m
s e g la
g la C) Coverage of topics a
a No. of topics in the syllabus Topics covered Percentage
9 9 100%

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 3 of 16

D) Weightage to form of questions
Sr. Form of questions Marks for No. of Total Percentage
No. each question questions Marks
1. M.C.Q. 1 5 5 10%
2. Very Short Answer Type (VSA) 1 5 5 10%
3. Short Answer Type (SA1) 2 8 16 32%
4. Short Answer Type (SA2) 3 4 12 24%
5. Long Answer Type (LA) 4 3 12 24%
Total 25 50 100%

The expected time for different types of question would be as follows:

Sr. Form of questions Approx. Time No. of Approx. Time for
No. for each questions each form of
question in (n) question in mins
mins(t) (n x t)
1. M.C.Q. 3 5 15
2. Very Short Answer Type (VSA) 3 5 15
3. Short Answer Type (SA1) 4 8 32
4. Short Answer Type (SA2) 7 4 28
5. Long Answer Type (LA) 10 3 30
Total 25 120

As the total time is calculated on the basis of the number of questions required to be answered
and the length of their anticipated answers, it would, therefore be advisable for the candidates to
budget their time properly by cutting out the superfluous words and be within the expected time
limits.

Scheme of Options
There will be no overall choice. However, there is an internal choice in Section C for 3 questions
of 4 marks category.

E) Definiteness of Questions:
Sr. No. Definiteness No. of questions Marks Percentage
1. Definite 25 50 100%
2. Partly Definite 0 0 0
3. Not Definite 0 0 0

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 16

.
.co s e m

s em l a
a ag
F) Weigh Difficulty level of questions:
Sr. No. Level of difficulty No. of question Marks Percentage
1. Easy 10 12 24%
2. Average 12 30 60%
3. Difficult 3 8 16%

m
om
A question may vary in difficulty level from individual to individual. As such, the assessment in
. co
. c
respect of each question will be made by the paper setter on the basis of general anticipation
em
e m
from the group as a whole taking the examination. This provision is only to make the paper
l as
l as
balanced in its weightage, rather than to determine the pattern of marking at any stage.
ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 5 of 16

Goa Board of Secondary & Higher Secondary Education, Alto, Betim - Goa

BLUE PRINT
Subject: Mathematics(Voc.) Timing :2hours Std: XII Computer Technique

Objective Knowledge Understanding Application Skill Total
S.N Contents/Units MCQ VSA SA-1 SA-II LA MCQ VSA SA-1 SA-II LA MCQ VSA SA-I SA-II LA VSA SA-I SA-II LA Total
(1) (1) (2) (3) (4) (1) (1) (2) (3) (4) (1) (1) (2) (3) (4) (1) (2) (3) (4) (50)
1. Numerical 1(2) 1(4) 2(6)
Methods
2. Correlation & 1(4) 1(4)
Regression
3. Matrices 1(1) 1(1) 3(1) 1(3) 6(8)

4. Probability 1(2) 1(2) 2(4)

5. Continuity 1(3) 1(3)

6. Differentiation 2(1) 3(2) 5(8)

7. Integration 2(1) 1(2) 1(3) 4(7)

8. Definite 1(1) 1(2) 1(3) 3(6)
Integration
9. Linear 1(4) 1(4)
Programming
Total 5(6) 10(18) 9(22) 1(4) 25(50)

Note: Figures outside the brackets indicate the no. of questions and those inside the brackets indicate the marks.

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 16

.
.co s e m

s em g l a
a a
Syllabus for the Academic Year 2026 onwards
Goa Board of Secondary and Higher Secondary Education
Alto Betim, Goa

Course: Std. XII Vocational-Computer Techniques
Subject: Mathematics (Voc.)
m
om . co
Theory
. c e m
e m l as
Marks
s
Sr. Topic and Sub Topics
No
a
l Methods g
a 6
Alloted
1
• a
g
Numerical
Construct Forward and Backward difference tables. (Only problems)
• Lagranges Interpolation (Only problems)
• Inverse Interpolation (Only problems)
2 Correlation and Regression 4
• Correlation.
• Definition and calculation of the correlation coefficient.
• Positive, negative and perfect correlation.
m
• Use of scatter diagram in interpreting the values of the correlation coefficients.

.co
• Calculations of regression coefficients and the equation of two lines of regression
m
by method of least squares.
s e
3 Matrices
l a 8

ag
• Matrix as a rectangular arrangement of numbers.
• Types of matrices: Row, Column, Zero, Square, Diagonal, Scalar, Unit, Symmetric,
Singular, Non-Singular, Triangular, transpose of a matrix, determinant of a matrix,
adjoint of a matrix.
• Equality of matrices
• Algebra of matrices: addition, subtraction, scalar multiplication, multiplication,
commutativity and associativity of matrix operation.
• Inverse of a matrix by Adjoint method.
• Application to solving simultaneous equations in three variables using adjoint
m
c. o4
m method.
.co
em
Probability 4

e m Random experiment and finite sample space, event, elementary events,
las
las mathematical definition of probability of an event
ag
ag 5 Continuity
• Continuity of a function at a point
3

• Left hand side and right hand side limits
• Meaning of x  a, x  a+, x  a-
• Continuity of a function at a point over an interval
• Properties of continuous function (without proof)

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 7 of 16

6 Derivatives 8
• Derivative of a function, its geometric and physical significance
• Derivative of the sum, difference, product and quotient of a function
• Derivative of a function – chain rule (uvw)
• Derivatives of composite functions with reference to algebraic, logarithmic,
exponential, trigonometric functions
• Differentiation of implicit function, logarithmic differentiation
7 Integration 7
• Integration as the inverse process of differentiation. Indefinite integrals
• Properties of integrals
• Integrals involving algebraic, trigonometric, logarithmic and exponential function
• Integral of composite function
𝑓 ′ (𝑥)
• Integral of ∫ 𝑑𝑥
𝑓(𝑥)
• Integration by parts using LATE. (Inverse trigonometric functions are not
included)
8 Definite Integral and Applications 6
• Definition
• Evaluation of definite integrals
• Properties of definite integrals (first four)
• Trapezoidal rule
• Simpson’s rule
9 Linear Programming 4
• Linear inequalities in two variables and the graph of its solution
• System of linear inequalities in two variables and the graph of its solution set
• Meaning of linear programming and its importance, meaning of constraints,
objective function, optimization, convex set (polygon) of the property that a
linear function (objective function) over a convex polygon takes on its maximum
value at other vertex of the polygon

Linear Programming problem and its solution by graphical method.

References : 1. A NEW APPROACH TO MATHEMATICSAND STATISTICS
Higher Secondary Std : XII Science paper-I
S.G. Chitale, Dr. Mrs. N.A. Joshi

2. A NEW APPROACH TO MATHEMATICSAND STATISTICS
Higher Secondary Std: XII Science paper-II
S.G. Chitale, Dr. Mrs. N.A. Joshi

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 16

.
.co s e m

s em l a
a Internal Scheme (Practical) ag
Marks allotted for First term, and Second term practical examination
First term 50

Second term 50

Total 100

m
om . co
List of Practical’s
. c e m
e m l as
a s
First Term(50 marks)
l of Correlation
Second Term(50 marks)
ag
a g
1. Coefficient 7. Trapezoidal Rule

2. Regression of X on Y 8. Simpsons rule

3. Regression of Y on X 9. Lagrange’s Interpolation

4. Addition of two matrices 10. Lagrange’s Inverse Interpolation

5. Subtraction of two matrices
m
6. Multiplication of two matrices
m .co
s e
a
Note: The above topics should be journalised and should contain the following:
l
ag
i. Algorithms
ii. Programs using Python programming language
iii. Inputs
iv. Outputs

Goa Board Examination (50 marks) Duration: 2 hrs.

m
c. o
1 Numerical Methods 6
m
.co
(1 question from the below mentioned sub topic of 2 marks)

e
• Construct Forward/Backward difference table and identify any two values m
e m (1 question from the below mentioned sub topics of 4 marks each) la
s
las ag
ag • Lagrange’s Interpolation
• Inverse Interpolation (Only problems)
2 Correlation and Regression 4
(1 question from any of the below mentioned sub topic of 4 marks)
• Calculation of the correlation coefficient.
• Calculations of regression coefficients and the equation of two lines of regression by
method of least squares.

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 9 of 16

3 Matrices 8
(5 questions of 1 mark each from the below sub topics)
• Matrix as a rectangular arrangement of numbers.
• Types of matrices: Row, Column, Zero, Square, Diagonal, Scalar, Unit, Symmetric,
Singular, Non-Singular, Triangular, transpose of a matrix, determinant of a matrix,
adjoint of a matrix.
• Equality of matrices
• Algebra of matrices: addition, subtraction, scalar multiplication, multiplication,
commutativity and associativity of matrix operation.
• Inverse of a matrix by Adjoint method. (1 question of 3 marks)
• Application to solving simultaneous equations in three variables using adjoint method .
4 Probability 4
2 questions of 2 marks each.

5 Continuity 3
1 question of 3 marks

6 L.P.P 4
(1 question from the below mentioned sub topics of 4 marks each)
• Maximize problem
• Minimize problem
7 Derivatives 8
(2 questions of 1 mark and 3 questions of 2 marks from any of the below mentioned sub-
topics)
• Derivative of the sum, difference, product and quotient of a function
• Derivative of a function-chain rule
• Derivative of composite functions with reference to algebraic, logarithmic,
exponential, trigonometric functions
• Logarithmic Differentiation, Differentiation of implicit functions

8 Integration 7
(2 questions of 1 mark, 1 question of 2 marks and 1 question of 3 marks from any of the
below mentioned sub topics)
• Integration as the inverse process of differentiation. Indefinite integrals
• Properties of integrals
• Integrals involving algebraic, trigonometric, logarithmic and exponential function
• Integral of composite function
𝑓 ′ (𝑥)
• Integral of ∫ 𝑑𝑥
𝑓(𝑥)
• Integration by parts using LATE. (Inverse trigonometric functions are not included)
9 Definite Integral 6
• Evaluation of definite integrals – 1 question of 1 mark
• Trapezoidal rule – 1 question of 2 marks
• Simpson’s rule – 1 question of 3 marks
Total 50

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 16

.
.co s e m

s em l a
a ag

m
om . co
. c e m
em l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 11 of 16

Goa Board of Secondary and Higher Secondary Education
Alto Betim, Porvorim – Goa
Model Paper 2026 onwards
Std: XII Computer Technique Maximum Marks: 50
Sub: Mathematics (Voc.) Duration : 2 hours
No. of Questions: 25
Instructions: i. All questions are compulsory
ii. Write the question number of the corresponding answers clearly.
iii. There are four sections in this question paper (A,B,C&D)
iv. Section A contains 10 questions of 1 mark each.
v. Section B contains 8 questions of 2 marks each.
vi. Section C contains 4 questions of 3 marks each.
vii. Section D contains 3 questions of 4 marks each.
viii. Figures to the right indicate full marks.
ix. Graph should be drawn on the answer paper itself.

Section A
Question numbers from 1 to 10 carry 1 mark each.
1. A diagonal matrix in which all diagonal elements are equal is called:
• Identity Matrix
• Scalar Matrix
• Null Matrix
• Skew-Symmetric Matrix

2. If [𝑎 − 𝑏 0] = [1 0] then value of a is:
2 𝑏 2 1

• 0
• 1
• 2
• -2

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 16

.
.co s e m

s em l a
a ag
2 𝑥
3. If [ ] is a singular matrix then x is equal to:
−3 6
• 0
• 4
• -3
m
• -4
om . co
. c e m
m as
s2e 4 g l
a
l −1 −2] then A is:
4. if 𝐴 = [
g
2
a
a 0 0
• [ ]
0 0
1 0
• [ ]
0 0
4 16
• [ ]
1 4
4 8
m
.co
• [ ]
−2 −4

e m
l as
5. If A = [
1 4
2 5 ag I is an identity matrix is:
] then A + 5I, where

2 4
• [ ]
2 10
6 4
• [ ]
2 10
2 5
• [ ]
3 6
m
.co
5 0
• [
m ]
.co
0 5
e m
e m as
s 6. Find the derivative of sin(x + 4x) with respect to x. gl
la a
2

ag
3
7. Find the derivative of 3x with respect to x.

1
8. Evaluate ∫( + 3x 2 ) dx
x

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 13 of 16

9. Evaluate ∫ sec2 (2x + 1) dx

2
10. Evaluate ∫0 (2x + 4)dx

Section B
Question numbers from 11 to 18 carry 2 marks each.
11. Construct a forward difference table for the following data:

X 5 10 15 20 25
Y 3 5 2 0 5

Hence identify Δ2y10 , Δ3y10

12. A card is drawn from a pack of 52 playing cards. Find the probability of getting a
queen or a king.

13. Two unbiased dice are thrown. Find the probability that the product of numbers
on their upper face is greater than 20.

14. Differentiate e4x. sin4x with respect to x.

dy
15. Find if x2 + y2 = 8xy
dx

dy
16. If y = (log x) x , find
dx

5sinx
17. Evaluate ∫ dx
15+5cosx

4
18. Evaluate ∫1 (2x)dx using Trapezoidal rule when n = 3

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 16

.
.co s e m

s em l a
a ag
Section C
Question numbers from 19 to 22 carry 3 marks each.
19. If f is continuous on [0,15] where

m
3x 2 + 5x
om
f(x) = { ax + 13b
0≤x<5
5 ≤ x < 10 . co
. c e m
e m x 2 − 3x 10 ≤ 𝑥 ≤ 15
l as
as ag
Findaglvalue of a and b.
the

1 3
20. Find the inverse of [ ] using adjoint method.
1 4

21. Evaluate∫ 𝑥. 𝑠𝑖𝑛𝑥 𝑑𝑥 m
m .co
s e
g l a
4
a
22. Evaluate ∫(2x + 1) dx using Simpson s rule when n = 4 ′

0

Section D
Question numbers from 23 to 25 carry 4 marks each.
m
m .co
.co m
23. For the following table
m s e
s e x 0 2 4
g la
g la f(x) 4 6 8 a
a
Using Lagrange’s Inverse Interpolation formula, find the value of x when f(x)=7.

m . c
c. o s e m
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 15 of 16

24. Obtain the regression line of y on x for the following data:
x 6 7 8 9

y 5 4 3 2

25. Solve the L.P.P. by graphical method.
Maximise Z = 3x + 5y
subject to x ≤ 4, y ≥ 2, 2x +3y ≤ 6
and x ≥ 0, y ≥ 0

**********

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 16 of 16