Units and Topics
#  Unit/Topic  Marks 

1  Commercial Mathematics   
2  Algebra   
3  Geometry   
4  Mensuration   
5  Trigonometry   
6  Statistics   
7  Probability   
Total   
Syllabus
 Concept of Compound Interest
 Use of Formula
A = P (1+ r /100)^{n}
 Finding CI from the Relation CI = A – P
 Interest compounded halfyearly included.
 Using the formula to find one quantity given different combinations of A, P, r, n, CI and SI; difference between CI and SI type included.
 Rate of growth and depreciation
Note: Paying back in equal installments, being given rate of interest and installment amount, not included.
(a) Compound interest as a repeated Simple Interest computation with a growing Principal. Use of this in computing Amount over a period of 2 or 3years.
(b) Use of formula A = P (1+ r /100)^{n}.
Finding CI from the relation CI = A – P.
 Interest compounded halfyearly included.
 Using the formula to find one quantity given different combinations of A, P, r, n, CI and SI; difference between CI and SI type included.
 Rate of growth and depreciation.
Note: Paying back in equal installments, being given rate of interest and installment amount, not included.
 Shares and Dividends Examples
 Shares and Dividends
(a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium.
(b) Formulae
 Income = number of shares*rate of dividend*FV.
 Return = (Income / Investment)*100.
Note: Brokerage and fractional shares not included
(a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium.
(b) Formulae
 Income = number of shares*rate of dividend*FV.
 Return = (Income / Investment)*100. Note: Brokerage and fractional shares not included
 Introduction to Banking
 Computation of Interest
 Computation of interest for a series of months
 Recurring Deposit Accounts: computation of interest using the formula
 Bank
 Bank
 Types of bank account
(a) Savings Bank Accounts.
Types of accounts. Idea of savings Bank Account, computation of interest for a series of months.
(b) Recurring Deposit Accounts: computation of interest using the formula:
 Sales Tax, Value Added Tax, and Good and Services Tax
 Computation of Tax
Computation of tax including problems involving discounts, listprice, profit, loss, basic/cost price including inverse cases
 Concept of Discount
 Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
 Goods and Service Tax (Gst)
 Gst Tax Calculation
 Input Tax Credit (Itc)
 Coordinates Expressed as (x,y)
 Distance Formula
 Section Formula
 The Midpoint of a Line Segment (Midpoint Formula)
Coordinates expressed as (x,y) Distance between two points, section, and Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines.
(a) Distance formula.
(b) Section and Midpoint formula (Internal section only, coordinates of the centroid of a triangle included).
 Quadratic Equations
 Introduction and Standard Form of a Quadratic Equation  ax^{2} + bx + c = 0, (a ≠ 0)
 Solutions of Quadratic Equations by Factorization
 Nature of Roots
 Nature of Roots Based on Discriminant
 two distinct real roots, two equal real roots, no real roots
 Solutions of Quadratic Equations by Using Quadratic Formula and Nature of Roots

Two distinct real roots if b^{2} – 4ac > 0

Two equal real roots if b^{2} – 4ac = 0

No real roots if b^{2} – 4ac < 0
(a) Quadratic equations in one unknown. Solving by:
 Factorisation.
 Formula.
(b) Nature of roots,
Two distinct real roots if b^{2} – 4ac > 0
Two equal real roots if b^{2} – 4ac = 0
No real roots if b^{2} – 4ac < 0
(c) Solving problems
 Factor Theorem
 Remainder Theorem
 Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem
Note: f (x) not to exceed degree 3
(a) Factor Theorem.
(b) Remainder Theorem.
(c) Factorising a polynomial completely after obtaining one factor by factor theorem.
Note: f (x) not to exceed degree 3.
 Concept of Proportion
 Proportion
 Continued or mean proportion
 Proportionality law
 Componendo and Dividendo Properties
 Alternendo and Invertendo Properties
 Direct Applications
 Concept of Ratio
(a) Duplicate, triplicate, subduplicate, subtriplicate, compounded ratios.
(b) Continued proportion, mean proportion
(c) Componendo and dividendo, alternendo and invertendo properties.
(d) Direct applications.
 Linear Inequations in One Variable
 For x ∈ N , W, Z, R
 Solving Algebraically and Writing the Solution in Set Notation Form
 Representation of Solution on the Number Line
Linear Inequations in one unknown for x_{ E} N, W, Z, R. Solving
 Algebraically and writing the solution in set notation form.
 Representation of solution on the number line.
 Arithmetic Progression  Finding Their General Term
 Arithmetic Progression  Finding Sum of Their First ‘N’ Terms.
 Simple Applications of Arithmetic Progression
 Finding their General term.
 Finding Sum of their first ‘n’ terms.
 Simple Applications.
 Geometric Progression  Finding Their General Term.
 Geometric Progression  Finding Sum of Their First ‘N’ Terms
 Simple Applications  Geometric Progression
 Finding their General term.
 Finding Sum of their first ‘n’ terms.
 Simple Applications.
 Introduction to Matrices
(a) Order of a matrix. Row and column matrices.
(b) Compatibility for addition and multiplication.
(c) Null and Identity matrices.
 Addition and Subtraction of Matrices
 Multiplication of Matrix
Multiplication of a 2*2 matrix by
 a nonzero rational number
 a matrix
 Matrices Examples
(a) Order of a matrix. Row and column matrices.
(b) Compatibility for addition and multiplication.
(c) Null and Identity matrices.
(d) Addition and subtraction of 2*2 matrices.
(e) Multiplication of a 2*2 matrix by
 a nonzero rational number
 a matrix.
 Reflection Examples
 Reflection Concept
(a) Reflection of a point in a line:
 x=0, y =0, x= a, y=a, the origin.
(b) Reflection of a point in the origin.
(c) Invariant points.
 Reflection of a Point in a Line
x=0, y =0, x= a, y=a, the origin.
 Reflection of a Point in the Origin.
 Invariant Points.
(a) Reflection of a point in a line:
x=0, y =0, x= a, y=a, the origin.
(b) Reflection of a point in the origin.
(c) Invariant points.F
 Slope of a Line
 Concept of Slope
 Equation of a Line
 Various Forms of Straight Lines
 General Equation of a Line
 Slope – Intercept Form
 y = mx+c
 Two  Point Form
 (yy_{1}) = m(xx_{1})
 Geometric Understanding of ‘m’ as Slope Or Gradient Or tanθ Where θ Is the Angle the Line Makes with the Positive Direction of the x Axis
 Geometric Understanding of c as the yintercept Or the Ordinate of the Point Where the Line Intercepts the y Axis Or the Point on the Line Where x=0
 Conditions for Two Lines to Be Parallel Or Perpendicular
 Simple Applications of All Coordinate Geometry.
(c) Equation of a line:
Slope –intercept form y = mx+c
Two point form (yy_{1}) = m(xx_{1})
Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis.
Geometric understanding of c as the yintercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.
Conditions for two lines to be parallel or perpendicular. Simple applications of all of the above.
 Introduction of Loci
 Definition
 Meaning
 Loci Examples
 Constructions Under Loci
 Theorems Based on Loci
(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.
(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.
(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.
Loci : Definition, meaning, Theorems based on Loci.
(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.
(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.
(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Areas of Sector and Segment of a Circle
 Area of the Sector and Circular Segment
 Length of an Arc
 Tangent Properties  If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments
 Tangent Properties  If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection
 Tangent to a Circle
Theorem  The tangent at any point of a circle is perpendicular to the radius through the point of contact.
 Number of Tangents from a Point on a Circle
Theorem  The Length of Two Tangent Segments Drawn from a Point Outside the Circle Are Equal
 Chord Properties  a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord
 Chord Properties  the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)
 Theorem: Equal chords of a circle are equidistant from the centre.
 Converse: The chords of a circle which are equidistant from the centre are equal.
 Chord Properties  There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line
 Arc and Chord Properties  the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle
 Theorem: Angles in the Same Segment of a Circle Are Equal.
 Arc and Chord Properties  Angle in a Semicircle is a Right Angle
 Arc and Chord Properties  If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse
 Arc and Chord Properties  If Two Chords Are Equal, They Cut off Equal Arcs, and Its Converse (Without Proof)
 Arc and Chord Properties  If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal
 Cyclic Properties
 Opposite Angles of a Cyclic Quadrilateral Are Supplementary
 The Exterior Angle of a Cyclic Quadrilateral is Equal to the Opposite Interior Angle (Without Proof)
 Tangent Properties  If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
(a) Chord Properties:
 A straight line drawn from the center of a circle to bisect a chord which is not a diameter is at right angles to the chord.
 The perpendicular to a chord from the center bisects the chord (without proof).
 Equal chords are equidistant from the center.
 Chords equidistant from the center are equal (without proof).
 There is one and only one circle that passes through three given points not in a straight line.
(b) Arc and chord properties:
 The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle.
 Angles in the same segment of a circle are equal (without proof).
 Angle in a semicircle is a right angle.
 If two arcs subtend equal angles at the center, they are equal, and its converse.
 If two chords are equal, they cut off equal arcs, and its converse (without proof).
 If two chords intersect internally or externally then the product of the lengths of the segments are equal.
(c) Cyclic Properties:
 Opposite angles of a cyclic quadrilateral are supplementary.
 The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).
(d) Tangent Properties:
 The tangent at any point of a circle and the radius through the point are perpendicular to each other.
 If two circles touch, the point of contact lies on the straight line joining their centers.
 From any point outside a circle two tangents can be drawn and they are equal in length.
 If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
 If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.
Note: Proofs of the theorems given above are to be taught unless specified otherwise.
 Circumscribing and Inscribing a Circle on a Regular Hexagon
 Circumscribing and Inscribing a Circle on a Triangle
 Construction of Tangents to a Circle
 Construction of Tangent to the Circle from the Point Out Side the Circle
 To construct the tangents to a circle from a point outside it
 Circumference of a Circle
 Circumscribing and Inscribing Circle on a Quadrilateral
(a) Construction of tangents to a circle from an external point.
(b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.
 Concept of Symmetry
 Concept of Lines Symmetry
 Figures with one Line of Symmetry
 Figures with two Line of Symmetry
 Figures with more Line of Symmetry
(a) Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamondshaped figure.
(b) Being given a figure, to draw its lines of symmetry. Being given part of one of the figures listed above to draw the rest of the figure based on the given lines of symmetry (neat recognizable free hand sketches acceptable).
 Similarity of Triangles
 Similarity Triangle Theorem
If in a two triangles corresponding angles are equal then their corresponding sides are in same ratio hence two triangle are similar
 Axioms of Similarity of Triangles
 Areas of Similar Triangles Are Proportional to the Squares on Corresponding Sides
Axioms of similarity of triangles. Basic theorem of proportionality.
(a) Areas of similar triangles are proportional to the squares on corresponding sides.
(b) Direct applications based on the above including applications to maps and models.
 Circumference of a Circle
 Circle  Direct Application Problems Including Inner and Outer Area
 Surface Area of a Right Circular Cone
 Surface Area of a Sphere
 Surface area of a sphere
 Hemisphere
 Hollow Hemisphere
 Volume of a Cylinder
 Volume of a Combination of Solids
 Surface Area of Cylinder
 Right Circular Cylinder
 Hollow Cylinder
Area and circumference of circle, Area and volume of solids – cone, sphere.
(a) Circle: Area and Circumference. Direct application problems including Inner and Outer area..
(b) Threedimensional solids  right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of two solids included.
Note: Frustum is not included.
Areas of sectors of circles other than quartercircle and semicircle are not included.
 Trigonometric Ratios of Complementary Angles
 Trigonometric Identities
 Heights and Distances  Solving 2D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
 Trigonometry
(a) Using Identities to solve/prove simple algebraic trigonometric expressions.
sin^{2} A + cos^{2} A = 1
1 + tan^{2} A = sec^{2} A
1+cot^{2} A = cosec^{2} A; 0< A<90^{0}
(b) Trigonometric ratios of complementary angles and direct application:
sin A = cos(90  A),cos A = sin(90 – A)
tan A = cot (90 – A), cot A = tan (90 A)
sec A = cosec (90 – A), cosec A = sec(90 – A)
(c) Heights and distances: Solving 2D problems involving angles of elevation and depression using trigonometric tables.
Note: Cases involving more than two right angled triangles excluded.
 Median of Grouped Data
 Ogives (Cumulative Frequency Graphs)
 Concepts of Statistics
 Graphical Representation of Data as Histograms
 Construction of a histogram for continuous frequency distribution
 Construction of histogram for discontinuous frequency distribution.
 Graphical Representation of Ogives
 Finding the Mode from the Histogram
 Finding the Mode from the Upper Quartile
 Finding the Mode from the Lower Quartile
 Finding the Median, upper quartile, lower quartile from the Ogive
 Calculation of Lower, Upper, Inter, SemiInter Quartile Range
 Concept of Median
 Mean of Grouped Data
 Mean of Ungrouped Data
 Median of Ungrouped Data
 Mode of Ungrouped Data
 Mode of Grouped Data
 Mean of Continuous Distribution
Statistics – basic concepts, , Histograms and Ogive, Mean, Median, Mode.
(a) Graphical Representation. Histograms and ogives.
Finding the mode from the histogram, the upper quartile, lower Quartile and median from the ogive.
Calculation of inter Quartile range.
(b) Computation of:
Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean*, median class and modal class for grouped data. (both continuous and discontinuous).
 Basic Ideas of Probability
 Probability  A Theoretical Approach
 Classical Definition of Probability
 Type of Event  Impossible and Sure Or Certain
 assume that all the experiments have equally likely outcomes, impossible event, sure event or a certain event, complementary events,
 Sample Space
 Type of Event  Complementry
 Simple Problems on Single Events
Not using set notation
 Random Experiments
 Random experiments
 Sample space
 Events
 Definition of probability
 Simple problems on single events (tossing of one or two coins, throwing a die and selecting a student from a group)