## Unit 1: Commercial Mathematics

Compound Interest Practise Now

(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 3-years.

(b) Use of formula A=P(1+r/100)^{n}. Finding CI from the relation CI = A - P.

Interest compounded half-yearly 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.

Sales Tax and Value Added Tax Practise Now

Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases.

Quadratic Equations Practise Now

(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.

Reflection

(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.

Ratio and Proportion Practise Now

(a) Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios.

(b) Continued proportion, mean proportion.

(c) Componendo and dividendo, alternendo and invertendo properties.

(d) Direct applications.

(c) Equation of a line:

Slope − intercept form y = mx + c

Two- point form (y-y1) = m(x-x1) 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 y-intercept/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.

## Unit 3: Geometry

Symmetry

(a) Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamond-shaped 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

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 semi-circle 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.

Note: Proofs of the theorems given above are to be taught unless specified otherwise.
Constructions

Construction of tangents to a circle from an external point.

Circumscribing and inscribing a circle on a triangle and a regular hexagon.

## Unit 4: Mensuration

Area and circumference of circle, Area and volume of solids − cone, sphere

(a)CirclePractise Now

Area and Circumference. Direct application problems including Inner and Outer area.

(b)Three-dimensional 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 quarter-circle and semicircle are not included.

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).

*Mean by all 3 methods included:

Direct :∑f/∑fx.

Short-cut : A+ ∑fd/∑f , where d = x - A

Step-deviation: A+ ∑ft/∑f *i where t=(x-A)/i.

## Unit 7:Probability

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)