Classes 9-12
Mathematics for Classes 9 to 12, including Intermediate: algebra, trigonometry, coordinate geometry, functions and proof.
Middle Years is the longest of the three programmes and the last. It runs from algebraic expressions and identities through equations, factorisation, surds and polynomials, then into coordinate geometry, trigonometry, logarithms and progressions.
It closes with the material Intermediate and entrance papers assume. That is mathematical induction and quadratic equations, sets and relations, intervals and inequalities, and finally functions, graphs and the straight line.
Both CBSE and the Andhra Pradesh state syllabus are covered.
This is for a student in Classes 9 to 12, including Intermediate. The mathematics here does not yield to memory alone. An identity applied the wrong way round, or a sign convention half remembered, will produce wrong answers for a year. It suits a student who wants the method to make sense, and who is working towards board examinations or entrance preparation.
Classes run live online over Zoom, in batches of up to ten students, and in person at our Poranki centre.
At this level one unresolved doubt does not stay where it started. A sign convention misunderstood in trigonometry reappears in coordinate geometry and again later. So questions are taken as they arise, and online a teacher can watch the working of ten students as it forms.
A free demo class can be booked on this website, by phone, or on WhatsApp at +91 90599 12593.
Tests are frequent, and written in the form the board and entrance papers use, so the method of answering is practised alongside the mathematics. How we teach →
Practice is continuous at this stage, because fluency is what the examination measures. The practice quizzes on this site cover the same chapters and can be attempted as often as a student likes.
6 lessons
Algebraic expressions from the ground up: what they are, the five types, how to find the degree of a term, how to put numbers back in place of the letters, and how to add, subtract and multiply whole expressions.
6 lessons
The distributive laws and the standard algebraic identities for squares and cubes of binomials and trinomials, with proofs, expansions and finding values.
6 lessons
What a linear equation in one variable is, how to solve it by balancing and transposing, how to handle brackets, fractions and decimals, and how to turn word problems into equations.
6 lessons
Linear equations in two variables and their straight-line graphs, how to tell whether a pair has one, none or infinitely many solutions, and the substitution, elimination and cross multiplication methods.
6 lessons
What a formula and its subject are, how to rearrange a formula with inverse operations, fractions, brackets, squares and roots, what to do when the subject appears twice, and how to answer do-as-directed questions.
9 lessons
Factorisation of algebraic expressions: the H.C.F of monomials, factorising with identities, splitting the middle term, and dividing expressions.
8 lessons
What surds are, the laws of surds, rationalising factors, simplifying and raising surds to powers, multiplying with identities, rationalising denominators, values of expressions, and square roots of surds.
7 lessons
The fourteen laws of exponents, with negative and fractional exponents, letters in the exponent, exponential equations, chains of equal powers, and mixed problems with decimals, surds and identities.
11 lessons
Polynomials from the first definitions to factorisation: terms and degree, zeros and roots, the quadratic formula, long and synthetic division, the remainder and factor theorems, and the factors of xⁿ ± aⁿ.
7 lessons
Time and work, from one day's work to teams that change, sharing wages and comparing workers, followed by boats and streams: downstream and upstream speeds and the equations they lead to.
9 lessons
Geometry with proofs: angles and parallel lines, congruent triangles, isosceles triangles and inequalities, parallelograms, the mid-point theorem, similar triangles, Pythagoras' theorem, and chords, angles and tangents of circles.
7 lessons
Areas and volumes beyond the basics: Heron's formula, arcs, sectors and segments of circles, and the surface areas and volumes of cuboids, cylinders, cones, spheres and solids built from them.
5 lessons
Points as pairs of numbers: the Cartesian plane, the distance formula, the section and midpoint formulas, the centroid and area of a triangle, and testing quadrilaterals with coordinates.
10 lessons
Angles in degrees, grades and radians, the six trigonometric ratios, identities, signs in the quadrants, standard and allied angles, domains, ranges and graphs, and problem-solving concepts.
9 lessons
What a logarithm is, the twelve laws of logarithms with proofs, simplifying expressions, solving logarithmic equations, graphs of log functions, and common logarithms with characteristic and mantissa.
13 lessons
Sequences and series, arithmetic and geometric progressions with their general terms, sums, properties and means, arithmetico-geometric series, and harmonic progressions with the harmonic mean.
5 lessons
The principle of mathematical induction and how to set out a proof, with induction proofs of sum formulas, divisibility results, inequalities, recursive sequences, products and counting results.
9 lessons
Quadratic equations and their roots: factorisation, completing the square, the quadratic formula, the discriminant, sum and product of roots, equations that reduce to quadratics, and word problems.
10 lessons
Sets and how to write them, subsets and power sets, Venn diagrams and set operations, the laws of sets, counting with cardinal numbers, survey problems, and relations with their domain, range, inverse and types.
7 lessons
16 lessons
16 lessons
9 lessons
Matrices from the start: order and types, addition and multiplication, transpose, determinants and their properties, adjoint and inverse, and solving linear equations.
8 lessons
Tell us about your child and we will call you back about Middle Years.
Rather talk now?