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WORKSHOP FOR MATHEMATICS TEACHERS
ACADEMIC SUPPORT GROUP (ASG)
PRESENT SITUATION
 Poor result of Mathematics is the cause of decline in Board result.
 Improvement in Mathematics result is essential for improvement of class X
result.
 Responsibility for improvement lies on the Mathematics teachers.
NEED OF THE HOUR
 To improve the result quantitatively i.e. increase the number of students passing.
 To pull up the students obtaining 20 marks or so to the pass marks level.
 To improve the result qualitatively i.e. enable students to clear competitive exams.
WEIGHTAGE TO SUBJECT UNIT
Coordinate
G eometry
8%
Algebra
Statistics
26%
12%
Mensuration
10%
Commercial
Mathematics
Trigonometry
12%
10%
G eometry
22%
BLUE PRINT
Time: 3 Hours
M.M 100
CONTENT AREA
I. Algebra
1. Linear Equations
2. Polynomials
3. Rational Expression
4. Quadratic Equation
5. Arithmetic Progression
NUMBER OF QUESTIONS
OF
3 Marks 4 Marks 6 Marks
26 (8)
7 (2)
3 (1)
3 (1)
7 (2)
6 (2)
1
1
1
1
2*
1
1
-
-
Sub Total
II. Commercial Mathematics
1. Instalments
2. Income Tax
Sub Total
26 (8)
6
2
-
12(3)
6(2)
6 (1)
12 (3)
2
2
-
1
1
III. Geometry
1. Similar Triangles
2. Circles
3. Constructions
Sub Total
22 (5)
9 (2) 1
9 (2)
1*
4 (1) 22 (5) 2
IV. Mensuration
V. Trigonometry
VI. Statistics
VII. Coordinate Geometry
Sub Total
10 (2)
10 (2)
12(3)
8 (2)
40 (9)
GRAND TOTAL
-
100 (25) 10
1
1
1*
1
2
1
3
2
7
1*
1
2
10
5
1*
Summary:
Number of Questions of 6 Marks: 5
4 Marks: 10
3 Marks: 10
Weightage to Difficulty Level of Questions
S.No
Estimated Difficulty Level of Questions
Percentage of Marks
1
2
3
Easy
Average
Difficult
15%
70%
15%
Scheme of Options
 All questions are compulsory i.e. there is no overall choice in the question paper.
 However, internal choices have been provided in two questions of 3 marks each,
two questions of 4 marks each and two questions of 6 marks each.
 These choices have been given from within the same topic and in questions
which test higher mental abilities of students.
ALGEBRA
Sub-Topic : Linear Equations in two Variables
Value Points :– 7 (3+4)
Ratin
Points to be
g/
Emphasised
Mark
s
1. Solve the i. Solving the
i. In Elimination
i. Should change Easy
equation
method, while
the sign of terms
Simultaneous (any method) 2 subtracting the
of second
3
linear
second equation from equation from
equations
ii. Writing answer the first equation the first while
as x =--students do not change subtracting
the signs of terms of
y =--1 the second equation. ii. Answer should
ii. They do not write be written
answer separately.
separately as x =-----and y=----2. Graphical i. Preparing the
i. Students use
i. Marking both Easy
Method
tables for each
separate Graph sheet the axis correctly
equation
½+½ for each equation
ii. Finding the
4
ii. Plotting the
ii. Do not write the
co- ordinates of
graph correctly for solution as Answer point of
each equation
iii. Some times
intersection of the
1+1
students mark x axis lines plotted
iii. Writing the
as y axis & vice versa iii. Finding the
solution as
& so plot the points point of
answer as x=----, wrongly
intersection of
y=--any plotted line
1
with x- axis or yaxis correctly.
ALGEBRA
Sub-Topic : G.C.D. & L.C.M. OF Polynomials
Value Points – 3 (1)
Type of
Common Mistakes
Marking
Points to be
Rating/
Expected
committed by
Scheme
Emphasized
Marks
Questions
students
1. Find the i. Factorization i.. While splitting the i. Splitting of the middle Easy
G.C.D. and of polynomials middle term they do term for factorization
3
L.C.M.
1+ 1
not write signs (+ or -)
ii Writing
correctly
G.C.D.
and/or L.C.M.
1
Type of
Expected
Questions
Common Mistakes
Marking Scheme committed by
students
2. Finding
the
constants a
and b if
G.C.D. is
given
i. Factorisation i. While using
of G.C.D 1 remainder theorem
ii. Finding value they do not substitute
of ‘a’
1 the value of x in the
iii.Finding
equation correctly ,
value of ‘b’ 1 e.g. for an equation
x2+x-12 if x-3 is a
factor, then value of x
should be substituted
as (3)2 +(3) – 12
instead of writing
directly as 9+3-12
3. Based on i. Writing the i. Do not write the
formula formula
formula correctly
G.C.D. X correctly
ii. Do not write the
L.C.M
1
answer in simplified
= p(x) ii. Simplifying form
X q(x)
& getting
correct
answer
2
i.Proper use of remainder Average
theorem i.e. if f(a)= 0,
then (x - a) is ‘a’ factor
of f(x)
ii.Enough practice should
be given on using
remainder theorem for
finding a & b
i.Enough practice should
be given to use the
formula correctly
ii. After factorisation the
answer should be in
lowest form
ALGEBRA
Sub-Topic : Rational Expressions
Value Points – 3 (1)
Type of
Expected
Questions
Reduce to
the
lowest
form
Common Mistakes
committed by
students
i.Factorisation of
They do not write the
Polynomials
2 answer in simplified
form i.e. lowest term
ii. Writing the answer
in simplified form 1
Marking Scheme
Points to be
Emphasised
Rating/
Marks
i. Answer should Average
be written in
lowest terms
ii. Practise should
be given in
factorisation of
polynomials by
splitting themiddle
term
ALGEBRA
Sub-Topic : Quadratic Equations
Value Points – 7 (3+4)
Type of
Expected Marking Scheme
Questions
Common
Mistakes
committed by
students
Points to be
Emphasised
Rating/
Marks
1. Solve the i. Writing the values
i. Do not write +
equation of a, b, c
1 or – signs with
ii. Writing the
the values of a, b
formula and
and c
substituting the values ii. Do not write
of a, b, c correctly 1 the value of sq.
iii.Simplifying and
root of
arriving at correct
discriminant (D)
answer
1
correctly
1. Word
i. Assuming variables i. Students are
Problem on ½
unable to even
Quadratic ii. Forming the
form the
equation or Equation
1 equations
linear
iii. Arriving at
equation
Quadratic equation 1
(internal
iv. Factorisation
1
choice)
v. Writing the answer ½
i. Substituting the
Average
correct values of a,
b, c in D =b2- 4ac
ii. Finding the square
root of the number
i.They must be given Difficult
enough practice in
forming the equation
ALGEBRA
Sub-Topic : Arithmetic Progression (AP)
Value Points – 6 (3+3)
Type of
Expected
Questions
1.Finding the
nth
term
Common Mistakes
Marking Scheme committed by
students
i. Use of correct i. They do not use the
formula 1
formula correctly
ii. Correct
ii. Calculation
substitution of
mistakes
values
iii. In writing the nth
1
term they forget to
iii. Finding the
subtract one from n
required term
e.g. for finding 20th
1
term they write
a20=a+20d instead of
a20 =a+19d
Finding the
Sum of
n terms i.e.
Sn
i. Writing ‘a’ and Sometimes they use
‘d’ from the given last term ‘l’ as ‘n’
A.P.
1
ii. Writing the
formula of Sn 1
iii. Finding Sn as
solution
1
Points to be
Emphasised
Rating/Marks
i. Learning and
application of
the correct
Easy
formula
3
ii. Short method
should be used to
find the nth term
if sum to n terms
is given
Stress should be Easy
given on the
3
application of
correct formula
COMMERCIAL MATHEMATICS
Sub Topic: Instalments
Value Points: 6 (3+3)
Types of
expected
questions
1. Finding the
amount of
instalment
2. Finding the
rate of interest
3. Finding the
total amount
paid or sum
borrowed
Marking Scheme Common
Mistakes
committed by
students
Question will
i. Incorrect use
usually involve
of Instalment
three steps
3 formulae
Points to be
Emphasised
Rating/
Marks
i. Practice to be
Easy
given in calculations
6
ii. Instalment question
will contain 3 or 4
ii. Calculation instalments
mistakes
iii. In questions
involving compound
interest maximum
number of instalments
would be three
COMMERCIAL MATHEMATICS
Sub Topic: Income Tax
Value Points: 6 (1)
Types of
expected
questions
Marking Scheme
Common
Mistakes
committed by
students
1. Find the
i. Usually the
i. Calculation
total income question will have mistakes
tax to be paid major 6 steps of
ii. Advance Tax is
calculations
multiplied by 12
2.Find the tax
6
Instead of 11
to be paid in
iii. Education
the last month
CESS is applied
after subtracting
the advance tax
iv. Education
CESS is
subtracted instead
of adding
Points to be
Emphasised
Rating /
Marks
i. Student should be Easy
taught to subtract
6
correctly for e.g.
* 190000
10000
80000 (wrong)
190000
10000
180000 (right)
ii. Education CESS to
be calculated on the
total tax due
GEOMETRY
Sub-Topic : Similar Triangles
Value Points – 9 (3+6)
Type of
Common Mistakes
Expected
Marking Scheme
committed by students
Questions
1.Problem on i.Correct figure ½ i.They do not draw the
Similar
ii. Proof
2 ½ figure correctly
triangles
ii.Proofs are not
relevant to the figure
2. Theorem
with
rider
i.Figure, given, to
prove,
construction
½each
ii. Proof
2
iii. Rider
2
GEOMETRY
Sub-Topic : Circle
Value Points – 9 (3+6)
Type of
Expected
Marking Scheme
Questions
1. Problem
i.Correct figure
based
½
on circle
ii. Proof
2½
2. Theorem
i. Figure, given,
with rider
to prove,
construction ½
each
ii.Proof
2
iii. Rider
2
Points to be
Emphasised
Rating/
Marks
i.Correct use of
relevant similar
triangle theorem
Difficult
i.Sometimes the
i.They should
students write the
draw the figure
theorem without
first.
drawing the figure,
ii. Explanation
hence get no marks
should be given
ii.Proof is not relevant according to
to the figure
the figure drawn
iii. They do not show
the angles in the figure
mentioned in the proof
Theorem
part is
easy
4
Common Mistakes
Points to be
Rating/
committed by
Emphasised
Marks
students
i They do not draw Correct use of
Difficult
the figure correctly relevant theorem in
ii. Proofs are not
circle
relevant to the figure
i.Sometime they write i. They should draw Theorem
the theorem without the figure first.
part
drawing the figure
ii. Explanation should easy
ii. Proof is not
given according to
4
relevant to the figure the figure
iii. Both thetheorem
would be out of 10
starred theorem, so
repeated practice of
writing the theorem is
required with correct
figure
GEOMETRY
Sub-Topic : Constructions
Value Points – 4(1)
Type of
Expected
Questions
Marking
Scheme
Construction i. Correct
construction 3
ii. Writing the
steps of
construction 1
Common Mistakes
Points to be Emphasised
committed by students
i.They do not construct
angles with the help of
compass
ii.They do not draw
angle correctly
iii. They do not draw
neat figures
Rating/
Marks
i. They should use
Easy
sharpened pencils
4
ii. Enough practice should
be given for all the
constructions in the class
itself
iii. Angle should be
constructed with the help
of compass only
iv. Use of protracter (D) is
not allowed
MENSURATION
Value Points: 10 (4+6)
Type of
expected
questions
Marking Scheme
1.Conversion For 4 marks
of solids
question
i. Formula and
substitution of
values
1
ii. Solving the
2. Mixed
problem
3
figure
For 6 marks
question
3.Frustrum iii. Formula and
substitution of
values
1
iv. Solving the
problem
5
Common Mistakes
committed by
students
Points to be
Emphasised
Rating/ Marks
i. Same units are not
used
ii. Solve the question
without drawing the
figure
iii. Units are not
specified with the
answers
iv. Students use
wrong formula
v. Make calculation
mistakes
i. All the
Difficult
formulae are to
be learnt by
heart
ii Area unit to be
specified as
square of the
unit and the
volume be as
cube of the unit
TRIGONOMETRY
Value Points: 10 (4+6)
Type of
expected
questions
Marking Scheme
Common Mistakes
committed by the
students
Points to be
Emphasised
1. Proving Solution usually
of
involves 4 steps.
identities Each step carries 1
mark
i. Do not use of the
Students should be
basic identities
made to learn the basic
correctly e.g. sin2θ
identities thoroughly
=1-cos2θ
ii. Make mistakes in
using correct T- ratios
during simplification
2.Complem i. Correct change of i.. They write sin
i. Comp. angles to be
entary
complementary
550 = sin (900-550)
applied directly.
angles
angles
2
ii. Wrong values are sin550 = cos (900-550)
(Internal
ii. Solution
1
substituted for sin300, ii. Values of T- ratios
choice in Q1 iii. Answer
1
sin600 etc.
of 00, 300, 600, 450, 900
& 2)
are to be memorised.
TRIGONOMETRY
Type of
Marking Scheme Common Mistakes
expected
committed by the
questions
students
height &
Distance
i. Correct figure 1 i. Angle nearer to 900 is
smaller than the angle
ii. Solving the
farther than 900
problem
4 ii. Angle of depression is
not marked in the figure
iii. Writing the
if it is mentioned in
answer
1 the question
iii. Unit of distance is
not changed, if required
in the question
Rating/
Marks
Difficult
Easy
4
Points to be Emphasised Rating
/marks
a. Students should be told Easy
that angle of depression part is
is equal to angle of
figure
elevation
1 mark
b. If in a question angle
of depression is
mentioned it should be
marked in the figure
c. Angle nearer to 900
should be greater than the
angle farther than 900
d. Questions would not
involve more than two
right angled triangles
e. Answer should be
marked with proper unit
as it carries one mark
STATISTICS
Sub-Topic : Mean
Value Points – 4(1)
Type of
Expected
Questions
1. Finding
the
mean for
discrete or
continuous
data
Common Mistakes
Rating/M
Marking Scheme
committed by the Points to be Emphasised
arks
students
i. Writing correct
i.They do not write i.They should learn
Easy
value of xi, fixi 1½ the formulae
the formulae
4
ii. Finding sum of fi ii. Calculation
ii.Lots of practice should
, fixi
1 mistakes in finding be given for calculating
iii.Correct formula the values of fixi, fixi and totalling
½
sum of fixi
iv.Finding mean
correctly
½
1.Finding i.Forming equations They add the value i.They should be properly
the
in missing
of ‘p’ along with guided and given enough
missing
frequencies
2 the data e.g. if sum practice
frequencies ii. Solving the
of fixi is 250+10p, ii. Any method of finding
equations and
they write it as
the mean can be adopted
finding the missing 260p
frequencies
2
STATISTICS
Sub-Topic : Pie Chart
Value Points – 4(1)
Type of
Marking
Expected
Scheme
Questions
Reading the Pie i.Finding the
chart
data using the
central angle 4
Drawing the Pie i.Finding the
chart with the Central angles
given data
from the given
data
2
ii.Drawing the
Pie chart
correctly 2
Common Mistakes
committed by the
students
They divide the
central angle with
the data and
multiply with 360o
Points to be Emphasised
Rating /
Marks
Central angle of the pie Easy
chart should be divide by 4
360o and multiplied by
the data
i. They do not make i.They should be guided
correct central
to make acute angles first
angles specially
ii. Beautification is not
when it is obtuse or required
more than 180o
iii. They should name the
ii. They spend more region correctly in the
time in beautifying chart
the pie chart
STATISTICS
Sub-Topic : Probability
Value Points – 4(1)
Type of
Expected Marking Scheme
Questions
Finding i.Total outcomes
the
ii. Favourable
probability outcomes
1
iii. Finding
probability
2
Common Mistakes committed Points to be
by students
Emphasised
Rating
/Marks
i.They do not write the
total outcomes of the
event
ii.They do not write the
formula
iii. They do the counting of
outcomes in case of cards
wrongly e.g. in case of cards
numbered from 15 to 30, they
count it as 15 instead of 16
Easy
4
They should be
given enough
practice to write
total outcomes,
favourable
outcomes, the
formula and
then the
probability
CO-ORDINATE GEOMETRY
Value Points – 8 (4+4)
Type of Expected
Questions
Marking Scheme
1.Finding a point on i. Formula
1
x-axis equidistant ii. Solution
2½
from two points
iii. Writing answer
2.Showing the
½
points are collinear
3. Proving a
quadrilateral to be a
Rectangle, square,
parallelogram etc
Common
Mistakes
Points to be
Emphasised
i. They do not
write formula
correctly
ii. Make Mistakes
in calculation
iii. They do not
find Sq. root
correctly
i. More practice
Easy
should be given for 4
writing and
applying the
formula correctly
ii. The students
should learn to
calculate square
root correctly
Finding the value of i.Taking ratio p : 1 i. They use
‘k’ when three
and finding the ratio distance formula
points are collinear 3
instead of section
using section
ii. Finding the value formula for doing
formula
of ‘k’
1
this question
which involves
lengthy
calculations
Rating /
Marks
i. They should use Average
section formula for 2
doing this
question.
TOPICS TO BE EMPHASISED
1. Finding the mean (Statistics)
2. Finding the missing frequencies (Statistics)
3. Reading & Plotting PIE - CHART (Statistics)
4. Use of Distance and Section Formula (Co-ordinate Geometry)
5. All Starred Theorems (Geometry)
6. Graphical Solution of Linear Equations (Algebra)
7. Instalments (Commercial Mathematics)
8. Income Tax (Commercial Maths)
9. Factorisation – by splitting the middle term
10. Constructions (6)
11. Complementary Angles (Trigonometry)
Wow!! Getting 65% in Mathematics is SO EASY!!