Classes 9-12

Middle Years

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.

Who is this for?

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.

What students learn

Expand and factorise confidently, and recognise which identity an expression is asking for.
Solve linear, simultaneous and quadratic equations, and rearrange a formula to isolate what is asked.
Say what the roots of a quadratic will be like before solving it.
Simplify surds and rationalise a denominator without a worked example to copy.
Use trigonometric ratios and identities on height and distance problems.
Find the equation of a straight line from the information a question actually gives.
Use logarithms to turn a hard multiplication into an easy addition.
Write a proof by mathematical induction, set out in steps a marker can follow.
Read sets, intervals, inequalities and function notation as fluently as ordinary algebra.
Sketch a graph from an equation, and read an equation back from a graph.

By the end of this programme

Set up and solve linear, simultaneous and quadratic equations, and describe the nature of the roots.
Turn a worded problem into algebra, and rearrange a formula to isolate the quantity asked for.
Apply trigonometric ratios and identities, and work in the coordinate plane up to the straight line.
Write a proof by induction, set out step by step.
Read the set, interval and function notation Intermediate and entrance papers use.

How the programme runs

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 and assessment

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 at home

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.

Courses in this programme

5 lessons

Algebraic Expressions and Their Uses

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.

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