## Unit 1: Pure Arithmetic

Irrational Numbers

(a) Rational, irrational numbers as real numbers, their place in the number system. Surds and rationalization of surds.

(b) Irrational numbers as non-repeating, nonterminating decimals.

(c) Classical definition of a rational number p/q,p, q ∈ Z, q ≠ 0. Hence, define irrational numbers as what cannot be expressed as above.

(d) Simplifying an expression by rationalising the denominator.

## Unit 2:Commercial Mathematics

Profit and Loss

The meaning of Marked price, selling price and discount, thus giving an idea of profit and loss on day to day dealings. Simple problems related to Profit and Loss and Discount, including inverse working.

Compound Interest

Compound Interest as a repeated Simple Interest computation with a growing Principal.

Linear Equations and Simultaneous (linear) Equations Practise Now

Solving algebraically (by elimination as well as substitution) and graphically.

Solving simple problems based on these by framing appropriate formulae.

Indices/ Exponents

Handling positive, fractional, negative and “zero” indices.

Simplification of expressions involving various exponents

a^{m} * a^{n} = a^{(m+n)},
a^{m} / a^{n}= ^{(m-n)}, (a^{m})^{n} = ^{mn} etc use of laws of exponents.

Logarithms

Logarithmic form vis-a-vis exponential form: interchanging.

Laws of Logarithms and its use. Expansion of expression with the help of laws of logarithm

eg. y=(a^{4}*b^{2})/c^{2}

log y = 4 log a + 3 log b - 3 log c etc. .

and its converse.

Equal intercept theorem: proof and simple application.

Similarity, conditions of similar triangles

As a size transformation.

Comparison with congruency, keyword being proportionality.

Three conditions: SSS, SAS, AA. Simple applications (proof not included).

Applications of Basic Proportionality Theorem.

Pythagoras Theorem Practise Now

Proof and Simple applications of Pythagoras Theorem and its converse.

Rectilinear Figures

Rectilinear figures or polygons, Different kinds of polygons and its names interior and exterior angles and their relations. Types of regular polygons parallelograms, conditions of parallelograms, Rhombus, Rectangles. Proof and use of theorems on parallelogram.

(a) Sum of interior angles of a polygon.

(b) Sum of exterior angles of a polygon.

Triangles with equal areas on the same bases have equal corresponding altitudes.

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

## Unit 5:Statistics

Introduction, collection of data, presentation of data, Graphical representation of data, Mean, Median of ungrouped data.

(i) Understanding and recognition of raw, arrayed and grouped data.

(ii) Tabulation of raw data using tally-marks.

(iii) Understanding and recognition of discrete and continuous variables.

(iv) Mean, median of ungrouped data.

(v) Class intervals, class boundaries and limits, frequency, frequency table, class size for grouped data.

(vi) Grouped frequency distributions: the need to and how to convert discontinuous intervals to continuous intervals.

(vii)Drawing a histogram and frequency polygon.

## Unit 7:Trigonometry

Trigonometric Ratios: sine, cosine, tangent of an angle and their reciprocals

Trigonometric ratios of standard angles- 0, 30, 45, 60, 90 degrees. Evaluation of an expression involving these ratios

Simple 2-D problems involving one right-angled triangle

Concept of sine and cosine being complementary with simple, direct application

## Unit 8:Co-ordinate Geometry

Cartesian System, Plotting a point in the plane for given coordinates

Dependent and independent variables.

Ordered pairs, co-ordinates of points and plotting them in the Cartesian Plane.

Graphs of x=0, y=0, x=a, y=a, x=y, y= mx+c including identification and conceptual understanding of slope and y-intercept.

Recognition of graphs based on the above.