Mathematics Theory Notes

Perimeter

Perimeter is simply the distance you would walk if you traced the whole outside edge of a shape and came back to where you started.

Square Root

Every time you know the area of a square and want to find the length of one side, you are taking a square root.

Fractions

Half a cup of flour, a third off the price, a quarter tank of petrol, splitting a bill three ways — fractions are how we talk about parts…

Binomial Expressions

Every time a builder works out the area of a plot whose sides are given as expressions, or a shopkeeper mentally squares 103 to price a…

Congruence of Triangles

Every time two machine parts must fit, two roof beams must carry the same load, or a tiled floor must repeat a pattern without a single…

Area

Look at a circular kokis mould, a hand-held fan opened part-way, a slice cut from a birthday cake, or a pie-shaped plot of land marked out…

Factors of Quadratic Expressions

Multiplying two brackets to get a quadratic is easy — you learned it in Grade 9.

Triangles

Look at almost any built thing that has to stay standing — a roof truss, a bridge girder, the A-frame of a step ladder, the gable of a…

Inverse Proportion

When more workers join a job it finishes sooner; when a bus goes faster it arrives earlier.

Data Representation

Every day the world hands you raw numbers — election results, a family budget, the marks of a whole class — and raw numbers are hard to…

LCM of Algebraic Expressions

The moment you try to add two algebraic fractions with different denominators — say (1)/(2x) + (1)/(3y) — you hit a wall until you can find…

Algebraic Fractions

Every formula that divides one changing quantity by another is an algebraic fraction: speed as (distance)/(time), a profit margin as…

Percentages

Every time you see "20% off" on a shirt in a Pettah shop, a bank offer "8% interest per annum", or a bill that adds "15% VAT", you are…

Equations

Almost every real decision that involves an unknown amount hides an equation.

Parallelograms I

Look at a garden gate, a folding clothes-drying rack, or the criss-cross scissor-lift on a lorry — they all hold their shape because of…

Parallelograms II

In Lesson 15 you learned what a parallelogram is and the neat properties that follow from it.

Sets

Every time a survey asks "how many students play cricket, how many play football, and how many play both?" you are really being asked a…

Logarithms I

Some numbers in the real world grow by multiplying, not by adding — the strength of an earthquake on the Richter scale, the loudness of…

Logarithms II

Before calculators sat in every schoolbag, engineers building bridges, astronomers charting stars, and accountants closing the year's books…

Linear Relationships

Almost every real cost you meet has a "starting amount" and a "rate".

Rate

Every time a bus timetable promises you'll reach Colombo in three hours, every time you glance at a fuel gauge and wonder if you'll make it…

Formulae

A formula is a rule written in symbols, and the whole point of a rule is that you can use it whichever way you need.

Triangle Angle Theorems

Look at the roof of a house, the truss of a bridge, or the frame of a bicycle — you will find triangles everywhere, because a triangle is…

Linear Inequalities

So much of real life is not "exactly equal to" — it is "at least", "no more than", "under the limit".

Frequency Distributions

Imagine a teacher marks 200 exam papers.

Chord-Centre Theorem

Circles are everywhere in real life — the rim of a bicycle wheel, the arch of a bridge, the plan of a circular paddy plot being surveyed.

Constructions

Every time a mason marks the corners of a house so the walls meet squarely, or a carpenter cuts a picture frame whose opposite sides match…

Surface Area and Volume

How much paint covers a cylindrical water tank?

Probability

Every day you weigh chances without noticing: will it rain before you reach home, which cricket team is likelier to win, is it worth buying…

Real Numbers

Real numbers form the foundation of all quantitative mathematics at the O/L level.

Indices and Logarithms - I

Indices (also called exponents or powers) provide a shorthand way of writing repeated multiplication.

Indices and Logarithms - II

This lesson extends the basic laws of indices and logarithms to more advanced applications, including solving exponential and logarithmic…

Surface Area of Solids

The surface area of a solid is the total area of all its external faces or surfaces.

Volume of Solids

Volume is the measure of the amount of three-dimensional space occupied by a solid object.

Areas of Plane Figures between Parallel Lines

This lesson focuses on finding the area of plane figures that lie between two parallel lines.

Share Market

The share market is a platform where shares of publicly listed companies are bought and sold.

The Midpoint Theorem

The Midpoint Theorem is a fundamental result in Euclidean geometry that establishes a relationship between the midpoints of two sides of a…

Graphs

A graph is a visual representation of the relationship between two variables.

Equiangular Triangles

Equiangular triangles are triangles in which all three interior angles are equal.

Data Representation and Interpretation

Data representation and interpretation is the process of organizing, displaying, and drawing conclusions from numerical information.

Geometric Progressions

A Geometric Progression (GP) is a sequence of numbers where each term after the first is obtained by multiplying the previous term by a…

Pythagoras' Theorem

Pythagoras' Theorem describes a fundamental relationship between the three sides of a right-angled triangle.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles.

Matrices

A matrix is a rectangular arrangement of numbers (or other mathematical objects) enclosed in square brackets.

Inequalities

An inequality is a mathematical statement that compares two expressions using inequality symbols.

Cyclic Quadrilaterals

A cyclic quadrilateral is a quadrilateral whose four vertices all lie on a single circle.

Tangents

A tangent is a straight line that touches a circle at exactly one point.