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What is the Zero of a Polynomial?

Graph of a Linear Equation in 2 variables

The diagonals of a parallelogram always bisect each other

How to identify the coordinates of a point on the cartesian plane?

Line drawn through the center of a circle to bisect a chord is perpendicular to it

Space race – Transitivity of parallel lines

The sum of either pair of opposite angles of cyclic quadrilateral is 180°

How to construct a triangle given its base, a base angle and sum of other two sides?

How to construct a triangle given its base, a base angle and difference of other two sides?

Concept Outline – Number Systems

Objective Questions – Number Systems

HOTs – Number Systems

Case Study Questions – Number Systems

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Number Systems

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Whole Numbers, Integers, and the Number Line

What are Rational Numbers?

Converting Fractions to Decimal Numbers | Successive Magnification of decimals

How to convert Terminating decimals into Fractions?

How to convert Recurring decimals into Fractions?

What are Irrational Numbers?

How to plot Irrational Numbers on a number line?

Laws of exponents: Product rule | Quotient rule

Laws of exponents: Power of power rule

Laws of exponents: Power of product rule

Laws of exponents: Fractional exponent rule

What are Real Numbers?

How to Rationalise the Denominator of a Real Number?

Plotting Irrational Numbers using the Semi Circle Method

Solved Examples

Polynomials

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What Are Polynomials?

Polynomial Equations and their Graphs

What is the Zero of a Polynomial?

How can we add, subtract and multiply two polynomials?

Polynomial Long Division

Remainder theorem and Factor theorem

Quadratic Factorisation

How to find the roots of a cubic polynomial?

Difference of squares identity | a² – b² = (a + b)(a – b)

Perfect squares identity | (a + b)² = a² + b² + 2ab

Product of binomials identity | (x + a) (x + b) = x² + (a + b)x + ab

Square of trinomials (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

Cube of binomials identity | (a+b)³ = a³ + b³ + 3a²b + 3ab²

Sum of Cubes identity | a³ + b³ = (a + b) (a² – ab + b²)

Difference of Cubes identity | a³ – b³ = (a – b) (a² + ab + b²)

Sum of 3 cubes identity | x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – xz)

Solved Examples

Coordinate Geometry

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What is the Cartesian system of coordinates?

How to identify the coordinates of a point on the cartesian plane?

How to plot points on a cartesian plane?

Solved Examples

Linear Equations in Two Variables

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What are linear equations in 2 variables?

Equations of Lines parallel to the x-axis and y-axis

Graph of a Linear Equation in 2 variables

Solved Examples

Introduction to Euclid’s Geometry

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Euclid’s Definitions

What are axioms and postulates?

Euclid’s Postulates (1 – 4)

Two distinct lines cannot have more than one point in common

Euclid’s 5th Postulate

Solved Examples

Lines and Angles

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What role do lines and angles play in our daily lives?

Points, Lines, Angles and a little bit of snooker!

Linear pair postulate and vertically opposite angles

What happens when a transversal intersects 2 parallel lines? The story of Eratosthenes

Alternate interior angles theorem

Alternate exterior angles theorem

Converse of alternate interior angles theorem

Converse of Alternate exterior angles theorem

Stuck in space with the Co-Interior Angles Theorem

Resurrection of Lord Dracula | Co-Exterior Angles Theorem

Cast your spell carefully: Converse of Co-Interior Angles theorem

Election Chaos at Dragonstone | Converse of Co-Exterior Angles Theorem

Space race – Transitivity of parallel lines

Solved Examples

Triangles

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What are triangles and why do we love them?

Angle sum property of triangles | Exterior angle property

What is congruence and why do we care?

ASA Congruence Criterion

AAS Congruence Criterion

SSS Congruence Criterion

RHS Congruence Criterion

Isosceles Triangle Property

Converse of Isosceles Triangle Property

Longer side inequality theorem

Converse of the Longer side inequality theorem

Triangle inequality theorem

Solved Examples

Quadrilaterals

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What are Quadrilaterals and why do we care?

What are the conditions for a quadrilateral to be a parallelogram?

A diagonal of a parallelogram divides it into two congruent triangles

If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram

In a parallelogram, opposite angles are equal

If in a quadrilateral, each pair of opposite angles is equal then it is a parallelogram

The diagonals of a parallelogram always bisect each other

If the diagonals of a quadrilateral bisect each other then it is a parallelogram

A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel

Space-Colosseum Escape | Midpoint Theorem of a Triangle

Arc Reactor | Converse of the Midpoint Theorem of a Triangle

Solved Examples

Areas of Parallelograms and Triangles

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Finding the areas of parallelograms and triangles

Figures on the Same Base and Between the Same Parallels

Parallelograms that stand on the same base and lie between the same parallels are equal in area

Triangles that share the same base and lie between the same parallel lines have equal area

Two triangles having the same base (or equal bases) and equal areas lie between the same parallels

Solved Examples

Circles

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So What Exactly Is a Circle?

Anatomy of a circle: Chords, Perpendiculars & Central angles

Equal chords of a circle subtend equal angles at its center

Chords that subtend equal angles at the center are also equal in length

Perpendicular drawn from the center of a circle to any of its chords splits it into 2 equal parts

Line drawn through the center of a circle to bisect a chord is perpendicular to it

Chords that are equal in length are also equidistant from the center

Chords that are equidistant from the center are also equal in length

There is one and only one circle passing through 3 given non-collinear points

What are inscribed angles and why do we care?

Relationship between central angles and inscribed angles | Angle subtended in a semi-circle

Angles subtended by a chord in the same segment are always equal to each other

Converse of Angles in the same segment of a circle are equal

Cyclic Quadrilaterals: The Good, Bad and Ugly

The sum of either pair of opposite angles of cyclic quadrilateral is 180°

If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic

Solved Examples

Constructions

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Geometric constructions 101

How to construct the Perpendicular bisector of a given line?

How to construct the angle bisector of a given angle?

Constructing angles worth 30°, 45°, 60°, 90° and 120°

What are unique triangles and how do we construct them?

How to construct a triangle given its base, a base angle and sum of other two sides?

How to construct a triangle given its base, a base angle and difference of other two sides?

How to construct a triangle given its perimeter and its two base angles?

Bonus: B for base, A for angle and SU for sum | New congruence criteria

Bonus content: B for base, A for angle and DF for difference | A new congruence criteria

Bonus content: A for angle, A for angle and P for perimeter | A new congruence criteria

Solved Examples

Heron’s Formula

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Heron’s Formula

The Bermuda Triangle: Can Heron’s Formula Unlock Its Secrets?

Solved Examples

Surface Areas and Volumes

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Types of 3D solids: Prisms, Pyramids & Spheres

What exactly is the surface area of an object?

Surface area of Cubes and Cuboids

Surface area of a Cylinder

Surface area of a Cone

Surface area of Spheres & Hemispheres

Introducing Volumes: The ‘Eureka’ story

Volume of Cubes and Cuboids

Volume of a Cylinder

The Nargle Chase | Volume of a Cone

The Zombie Apocalypse | Volume of a Sphere and a Hemisphere

Solved Examples

Statistics

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What is Statistics and why do we care?

Types of data: Primary vs Secondary

Understanding Range and Raw data

What are Tally Marks?

Grouped frequency distribution

Seeing Data: What is Data Visualisation?

What is a Bar Graph?

What is a Histogram?

What is a Frequency Polygon?

Mean, Median, and Mode: Measures of Central Tendency

Solved Examples

Probability

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The Monty Hall Problem | Introduction to Probability

The Sorting Hat’s Guide to Experimental Probability

Solved Examples

Sample Papers

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Sample Paper 1: Solution

Sample Paper 2: Solution

Sample Paper 3: Solution

Math in Action

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