Mathematics

1. Goods and Services Tax (GST)

Computation of GST on intra-state and inter-state transactions, input tax credit and the final price paid by the consumer.

2. Banking

Recurring deposit accounts: computing maturity value, interest earned and the monthly deposit.

3. Shares and Dividends

Nominal and market value of shares, dividend, income, rate of return and change of shares.

4. Linear Inequations

Solving linear inequations in one variable over the set of natural numbers, whole numbers, integers and real numbers, with representation on the number line.

5. Quadratic Equations

Solving quadratic equations by factorisation and by formula, the nature of roots, and word problems that reduce to a quadratic equation.

6. Ratio and Proportion

Proportion, continued proportion, mean proportion, componendo and dividendo, alternendo and invertendo, and their applications.

7. Factorisation of Polynomials

Remainder theorem and factor theorem, and factorising polynomials of degree three.

8. Matrices

Order of a matrix, addition and subtraction, multiplication by a scalar, matrix multiplication, and identity and null matrices.

9. Arithmetic and Geometric Progression

Finding the nth term and sum of an arithmetic progression, and the nth term of a geometric progression.

10. Reflection

Reflection of a point in the axes, in the origin and in lines parallel to the axes; invariant points.

11. Section and Distance Formula

Distance between two points, section formula, midpoint and centroid of a triangle.

12. Equation of a Straight Line

Slope and intercept, the various forms of a straight line, and conditions for parallel and perpendicular lines.

13. Similarity

Similar triangles, the basic proportionality theorem, and the relation between areas of similar figures.

14. Loci

The locus of a point satisfying a given condition, and constructions based on standard loci.

15. Circles

Angle properties, cyclic properties, tangent properties and the intersecting chords theorem.

16. Constructions

Constructing tangents to a circle, circumscribing and inscribing circles on a triangle and a regular hexagon.

17. Cylinder, Cone and Sphere

Surface area and volume of a cylinder, cone, sphere and hemisphere, including combinations and conversions of solids.

18. Trigonometric Identities

Proving identities using the standard relations between trigonometric ratios, and ratios of complementary angles.

19. Heights and Distances

Two-dimensional problems involving one or two right-angled triangles, angles of elevation and angles of depression.

20. Statistics

Mean, median, mode and quartiles for raw, discrete and grouped data.

21. Graphical Representation

Histograms and ogives (cumulative frequency curves), and reading the median and quartiles from an ogive.

22. Probability

Random experiments, sample space, and the probability of simple single events.