Understanding coefficients in Quadratic Equations

Refresher on Basic Inequalities

Solving Quadratic Inequalities and representing the solution on the number line – Portion of the curve below the x-axis

Solving Quadratic Inequalities and representing the solution on the number line – Portion of the curve above the x-axis

Practice Question 1 – Solving Quadratic Inequalities and representing the solution on the number line

Practice Question 2 – Solving Quadratic Inequalities and representing the solution on the number line

How are the roots of the quadratic equation related to the sign of the discriminant

Summary – How are the roots of the quadratic equation related to the sign of the discriminant

How are the roots of the quadratic equation related to its discriminant when the discriminant is greater than 0

How are the roots of the quadratic equation related to its discriminant when the discriminant is equal to 0

How are the roots of the quadratic equation related to its discriminant when the discriminant is less than 0

Conditions for a quadratic equation to have two distinct real roots and how this relates to a case where a line intersects a given curve at two points

Practice Question 3a – Conditions for a quadratic equation to have two distinct real roots and how this relates to a case where a line intersects a given curve at two points

Practice Question 3b – Conditions for a quadratic equation to have two distinct real roots and how this relates to a case where a line intersects a given curve at two points

Conditions for a quadratic equation to have two equal real roots and how this relates to a case where a line is a tangent to a given curve

Practice Question 4a – Conditions for a quadratic equation to have two equal real roots and how this relates to a case where a line is a tangent to a given curve

Practice Question 4b – Conditions for a quadratic equation to have two equal real roots and how this relates to a case where a line is a tangent to a given curve

Conditions for a quadratic equation to have no real roots and how this relates to a case where a line does not intersect a given curve

Practice Question 5a – Conditions for a quadratic equation to have no real roots and how this relates to a case where a line does not intersect a given curve

Practice Question 5b – Conditions for a quadratic equation to have no real roots and how this relates to a case where a line does not intersect a given curve

Conditions for a quadratic equation to have real roots and how this relates to a case where a line intersects a given curve

Practice Question 6a – Conditions for a quadratic equation to have real roots and how this relates to a case where a line intersects a given curve

Practice Question 6b – Conditions for a quadratic equation to have real roots and how this relates to a case where a line intersects a given curve

Conditions for quadratic expression to be always positive when a>0

Practice Question 7a – Conditions for quadratic expression to be always positive when a>0

Conditions for quadratic expression to be always negative when a<0

Practice Question 7b – Conditions for quadratic expression to be always negative when a<0

Conditions for quadratic expression to be always positive when a>0 (or always negative when a<0) - Thinking Questions

Completing The Square

Practice Question 8a – Completing The Square, a>0

Practice Question 8b – Completing The Square, a>0

Practice Question 8c – Completing The Square, a<0

Practice Question 8d – Completing The Square, a<0

What are Surds

What are Surds – Rules of Surds

Practice Question 1a – Simplifying of Surds

Practice Question 1b – Simplifying of Surds

Practice Question 1c – Simplifying of Surds

Practice Question 1d – Simplifying of Surds

Practice Question 1e – Simplifying of Surds

Practice Question 1f – Simplifying of Surds

Practice Question 2a – Simplifying of Surds (Addition and Subtraction of Surds)

Practice Question 2b – Simplifying of Surds (Addition and Subtraction of Surds)

Practice Question 3a – Simplifying of Surds (Multiplication of Surds)

Practice Question 3b – Simplifying of Surds (Multiplication of Surds)

Conjugate Surd

Rationalizing the Denominator and Division of Surds

Practice Question 4a – Simplifying of Surds (Division of Surds and Rationalizing the Denominator)

Practice Question 4b – Simplifying of Surds (Division of Surds and Rationalizing the Denominator)

Practice Question 4c – Simplifying of Surds (Division of Surds and Rationalizing the Denominator)

Practice Question 4d – Simplifying of Surds (Division of Surds and Rationalizing the Denominator)

Practice Question 4e – Simplifying of Surds (Division of Surds and Rationalizing the Denominator)

Practice Question 4f – Simplifying of Surds (Division of Surds and Rationalizing the Denominator)

Practice Question 5a – Division of Surds and Rationalizing the Denominator (Questions involving Area)

Solving Equations involving Surds

Practice Question 6a – Solving Equations Involving Surds

Practice Question 6b – Solving Equations Involving Surds

Practice Question 6c – Solving Equations Involving Surds

Practice Question 6d – Solving Equations Involving Surds

Equality of Surds

Practice Question 7a – Solving for unknowns using Equality of Surds

Practice Question 7b – Solving for unknowns using Equality of Surds

Laws of Indices

What is a Function (Recap)

Euler’s Number, e

Exponential Function

Graph of Exponential Function

Graph of Natural Exponential Function

Logarithmic Function

Graph of Logarithmic Function

Graph of Natural Logarithmic Function

Logarithms

Common Logarithms

Natural Logarithms

Practice Question 1a – Converting to Logarithmic Form and Index Form

Practice Question 1b – Converting to Logarithmic Form and Index Form

Practice Question 1c – Converting to Logarithmic Form and Index Form

Practice Question 1d – Converting to Logarithmic Form and Index Form

Practice Question 2a – Solving Logarithmic Equations

Practice Question 2b – Solving Logarithmic Equations

Practice Question 3 – Evaluating Logarithmic Expressions

Laws of Logarithms (Power Law)

Practice Question 4a – Using Power Law

Practice Question 4b – Using Power Law

Laws of Logarithms (Product Law)

Practice Question 5a – Using Product Law

Practice Question 5b – Using Product Law

Laws of Logarithms (Quotient Law)

Practice Question 6a – Using Quotient Law

Practice Question 6b – Using Quotient Law

Laws of Logarithms (Change-of-Base Law)

Practice Question 7a – Using Change-of-Base Law

Practice Question 7b – Using Change-of-Base Law

Logarithmic Equations

Practice Question 8 – Solving Logarithmic Equations

Practice Question 9 – Solving Logarithmic Equations using Substitution

Exponential Equations

Solving Exponential Equations by taking logarithms on both sides

Solving Exponential Equations by taking common logarithms on both sides (Using lg)

Solving Exponential Equations by taking natural logarithms on both sides (Using ln)

Solving Exponential Equations by taking natural logarithms on both sides (Using ln)

Practice Question 10a – Solving Exponential Equations by taking logarithms on both sides

Practice Question 10b – Solving Exponential Equations by taking logarithms on both sides

Practice Question 10c – Solving Exponential Equations by taking logarithms on both sides

Practice Question 10d – Solving Exponential Equations by taking logarithms on both sides

Practice Question 10e – Solving Exponential Equations without taking logarithms on both sides

Practice Question 11 – Application of Exponential and Logarithmic Functions

What are Polynomials

What are Polynomials – Degree of Polynomials

What are Polynomials – How to denote Polynomials

What are Polynomials – Adding, Subtracting and Multiplying Polynomials

What are Polynomials – Finding coefficient of a particular term without expanding polynomials

Practice Question 1 – Adding, subtracting and multiplying Polynomials

Practice Question 2 – Evaluating Polynomial with a given x value

What are identities

Practice Question 3 – Finding unknown(s) in an identity in x

Sum of Cubes and Difference of Cubes

Dividing Polynomials

Practice Question 4 – Dividing Polynomials

Remainder Theorem

Practice Question 5 – Remainder Theorem

Factor Theorem

Practice Question 6a – Factor Theorem

Practice Question 6b – Factor Theorem

Solving Cubic Equations

Practice Question 7 – Solving Cubic Equations

What are Partial Fractions

What are Partial Fractions – Degree, Proper, Improper and Long Division

Partial Fractions – Linear Factor

Practice Question 1 – Linear Factor

Partial Fractions – Repeated Linear Factor

Practice Question 2 – Repeated Linear Factor

Partial Fractions – Quadratic Factor which cannot be factorised

Practice Question 3 – Quadratic Factor which cannot be factorised

Linear Factor, Repeated Linear Factor and Quadratic Factor

Partial Fractions – Using Long Division first if the fraction is improper

Practice Question 4 – Using Long Division first if the fraction is improper

What is Binomial Theorem

The Combination Calculation – An Intuition

The Combination Calculation

The Binomial Expansion of (a+b) to the power of n

Finding a specific term in the expansion of (a+b) to the power of n

Practice Question 1 – The Binomial Expansion of (a+b) to the power of n

Practice Question 2a – Finding a specific term in the expansion of (a+b) to the power of n

Practice Question 2b – Finding a specific term in the expansion of (a+b) to the power of n

The Binomial Expansion of (1+b) to the power of n

Practice Question 3 – The Binomial Expansion of (1+b) to the power of n

Finding a specific term in the expansion of (1+b) to the power of n

Practice Question 4 – Finding a specific term in the expansion of (1+b) to the power of n

What is Coordinate Geometry

Midpoint of the line joining two points

Practice Question 1 – Midpoint of the line joining two points

The shoelace formula with 3 points (Vertices)

The shoelace formula with 4 points (Vertices)

Practice Question 2 – The shoelace formula

Parallel and Non-Parallel Lines

Practice Question 3 – Parallel and Non-Parallel Lines

Perpendicular Lines

Practice Question 4 – Perpendicular Lines

What is Linear Law

Linear Law Y=mX+c

Linear Law Y=mX+c with examples

Linear Law Y=mX+c with more examples

Practice Question 1 – Linear Law

Application of Linear Law

Practice Question 2 – Application of Linear Law

Practice Question 3a – Linear Law (Using Logarithm)

Practice Question 3b – Linear Law (Using Logarithm)

Circles

Practice Question 2a – Circles

Practice Question 2b – Circles

Trigonometric Ratios of Acute Angles and Special Angles 𝜃

Trigonometric Ratios of Complementary Angles

General Angles 𝜃 and Basic Angle 𝛼

Practice Question 1a – General Angles 𝜃 and Basic Angle 𝛼

Practice Question 1b – General Angles 𝜃 and Basic Angle 𝛼

Trigonometric Ratios of General Angles 𝜃 (ASTC)

Practice Question 2a – Trigonometric Ratios of General Angles 𝜃 (ASTC)

Practice Question 2b – Trigonometric Ratios of General Angles 𝜃 (ASTC)

Practice Question 2c – Trigonometric Ratios of General Angles 𝜃 (ASTC)

Practice Question 2d – Trigonometric Ratios of General Angles 𝜃 (ASTC)

Practice Question 2e – Trigonometric Ratios of General Angles 𝜃 (ASTC)

Practice Question 2f – Trigonometric Ratios of General Angles 𝜃 (ASTC)

Basic Trigonometric Equations

Practice Question 3a – Basic Trigonometric Equations

Practice Question 3b – Basic Trigonometric Equations

Graphs of the Sine Function – Properties

Graphs of the Sine Function, a>0

Graphs of the Sine Function, a<0

Practice Question 4a – Graphs of the Sine Function

Practice Question 4b – Graphs of the Sine Function

Graphs of the Cosine Function – Properties

Graphs of the Cosine Function, a>0

Graphs of the Cosine Function, a<0

Practice Question 5a – Graphs of the Cosine Function

Practice Question 5b – Graphs of the Cosine Function

Graphs of the Tangent Function – Properties

Graphs of the Tangent Function, a>0

Graphs of the Tangent Function, a<0

𝑡𝑎𝑛 𝜃 = 𝑠𝑖𝑛 𝜃 / 𝑐𝑜𝑠 𝜃 where 𝑐𝑜𝑠 𝜃 ≠ 0

Secant, Cosecant and Cotangent Functions

Trigonometric Identities (1)

Trigonometric Identities (2)

Trigonometric Identities (3)

Practice Question 1 – Using the identities

Further Trigonometric Equations

Practice Question 2a – Further Trigonometric Equations

Practice Question 2b – Further Trigonometric Equations

Practice Question 2c – Further Trigonometric Equations

Practice Question 2d – Further Trigonometric Equations

Addition Formulae sin(A+B)

Addition Formulae sin(A-B)

Addition Formulae cos(A+B)

Addition Formulae cos(A-B)

Addition Formulae tan(A+B)

Addition Formulae tan(A-B)

Practice Question 1a – Addition Formulae

Practice Question 1b – Addition Formulae

Practice Question 1c – Addition Formulae

Double Angle Formulae sin(2A)

Double Angle Formulae cos(2A)

Double Angle Formulae tan(2A)

Practice Question 2a – Double Angle Formulae

Practice Question 2b – Double Angle Formulae

Practice Question 2c – Double Angle Formulae

R-Formulae

Practice Question 3a – R-Formulae

Practice Question 3b – R-Formulae

Intuitive Approach , Let’s talk about gradient of a line (Positive Slope)

Intuitive Approach , Let’s talk about gradient of a line (Negative Slope)

Intuitive Approach , Let’s talk about gradient of a Curve

Intuitive Approach , when gradient of a curve is always positive

Intuitive Approach , when gradient of a curve is always negative

Intuitive Approach , when gradient is always 0

Intuitive Approach , when gradient of a curve goes from negative to positive

Intuitive Approach , when gradient of a curve goes from positive to negative

Differentiation – Gradient of a Curve at a Point

Definitions and Standard notations in Differentiation

Practice Question 1 – Differentiation – Gradient of a Curve at a Point

Power Rule

Derivative of ax, where a is a constant

Derivative of a constant, c

Practice Question 2a – Power Rule

Practice Question 2b – Power Rule

Practice Question 2c – Power Rule

Chain Rule

Practice Question 3a – Chain Rule

Practice Question 3b – Chain Rule

Practice Question 3c – Chain Rule

Product Rule

Practice Question 4a – Product Rule

Practice Question 4b – Product Rule

Practice Question 4c – Product Rule

Quotient Rule

Practice Question 5a – Quotient Rule

Practice Question 5b – Quotient Rule

Practice Question 5c – Quotient Rule

Recap Relationship between Gradient Function dydx and Tangent

Equation of Tangent

Practice Question 1 – Equation of Tangent

Equation of Normal

Practice Question 2 – Equation of Normal

Rates of Change

Practice Question 1a – Rates of Change

Practice Question 1b – Rates of Change

Practice Question 1c – Rates of Change

Connected Rates of Change (Chain Rule)

Practice Question 2a – Connected Rates of Change (Chain Rule)

Practice Question 2b – Connected Rates of Change (Chain Rule)

What are Stationary Points

Practice Question 1a – Stationary Points

Practice Question 1b – Stationary Points

Types of Stationary Points

Maximum and Minimum Turning Point (First Derivative Test)

Practice Question 2 – Maximum and Minimum Turning Point (First Derivative Test)

Stationary Point of inflexion (First Derivative Test)

Practice Question 3a – Stationary Point of inflexion (First Derivative Test)

Practice Question 3b – Stationary Point of inflexion (First Derivative Test)

First Derivative Test (Summary)

Maximum and Minimum Turning Point (Second Derivative Test)

Stationary Point of inflexion (Second Derivative Test, Cases When It Is Inconclusive)

Maximum and Minimum Turning Point (Second Derivative Test, Cases When It Is Inconclusive)

Second Derivative Test (Summary)

Maximum and Minimum Values

Maximum and Minimum Values (Why only one stationary point?)

Practice Question 4a – Maximum and Minimum Values

Practice Question 4b – Maximum and Minimum Values – Application Question

Derivative of sin x

Derivative of cos x

Derivative of tan x

Practice Question 1a – Derivatives of sin x, cos x and tan x

Practice Question 1b – Derivatives of sin x, cos x and tan x

Practice Question 1c – Derivatives of sin x, cos x and tan x

Practice Question 1d – Derivatives of sin x, cos x and tan x

Practice Question 1e – Derivatives of sin x, cos x and tan x

Practice Question 1f – Derivatives of sin x, cos x and tan x

Practice Question 1g – Derivatives of sin x, cos x and tan x

Practice Question 1h – Derivatives of sin x, cos x and tan x

Derivative of sin(ax+b), where a and b are constants

Derivative of cos(ax+b), where a and b are constants

Derivative of tan(ax+b), where a and b are constants

Practice Question 2a – Derivatives of sin(ax+b), cos(ax+b) and tan(ax+b)

Practice Question 2b – Derivatives of sin(ax+b), cos(ax+b) and tan(ax+b)

Practice Question 2c – Derivatives of sin(ax+b), cos(ax+b) and tan(ax+b)

Practice Question 2d – Derivatives of sin(ax+b), cos(ax+b) and tan(ax+b)

Derivative of sin x raised to the power of n, where n is a constant

Derivative of cos x raised to the power of n, where n is a constant

Derivative of tan x raised to the power of n, where n is a constant

Practice Question 3a – Derivatives of sin x raised to the power of n, cos x raised to the power of n and tan x raised to the power of n

Practice Question 3b – Derivatives of sin x raised to the power of n, cos x raised to the power of n and tan x raised to the power of n

Practice Question 3c – Derivatives of sin x raised to the power of n, cos x raised to the power of n and tan x raised to the power of n

Practice Question 3d – Derivatives of sin(ax+b) raised to the power of n, cos(ax+b) raised to the power of n and tan(ax+b) raised to the power of n

Practice Question 3e – Derivatives of sin(ax+b) raised to the power of n, cos(ax+b) raised to the power of n and tan(ax+b) raised to the power of n

Practice Question 3f – Derivatives of sin(ax+b) raised to the power of n, cos(ax+b) raised to the power of n and tan(ax+b) raised to the power of n

Derivative of e to the power of x

Derivative of e to the power of ax+b, where a and b are constants

Practice Question 4a – Derivative of e to the power of ax+b

Practice Question 4b – Derivative of e to the power of ax+b

Practice Question 4c – Derivative of e to the power of ax+b

Practice Question 4d – Derivative of e to the power of ax+b

Practice Question 4e – Derivative of e to the power of ax+b

Practice Question 4f – Derivative of e to the power of ax+b

Derivative of ln x

Derivative of ln(ax+b), where a and b are constants

Practice Question 5a – Derivative of ln(ax+b)

Practice Question 5b – Derivative of ln(ax+b)

Practice Question 5c – Derivative of ln(ax+b)

Practice Question 5d – Derivative of ln(ax+b)

The Reverse of Differentiation

Indefinite Integral of ax^n

Indefinite Integral of ax^n – My Way of Teaching

Indefinite Integral of ax^n – Example Revisited

Practice Question 1a – Indefinite Integral of ax^n

Practice Question 1b – Indefinite Integral of ax^n

Practice Question 1c – Indefinite Integral of ax^n

Practice Question 1d – Indefinite Integral of ax^n

Practice Question 1e – Indefinite Integral of ax^n

Practice Question 1f – Indefinite Integral of ax^n

Practice Question 1g – Indefinite Integral of ax^n

Practice Question 1h – Indefinite Integral of ax^n

Indefinite Integral of (ax+b)^n

Indefinite Integral of (ax+b)^n – My Way of Teaching

Practice Question 2a – Indefinite Integral of (ax+b)^n

Practice Question 2b – Indefinite Integral of (ax+b)^n

Practice Question 2c – Indefinite Integral of (ax+b)^n

Practice Question 2d – Indefinite Integral of (ax+b)^n

Definite Integral, How to evaluate Definite Integral

Definite Integral, An Example (My Way Of Teaching)

Practice Question 3a – Definite Integral

Practice Question 3b – Definite Integral

Practice Question 3c – Definite Integral

Practice Question 3d – Definite Integral

Results on Definite Integrals (1)

Results on Definite Integrals (2)

Results on Definite Integrals (3)

Practice Question 4a – Results on Definite Integral

Practice Question 4b – Results on Definite Integral

Practice Question 4c – Results on Definite Integral

Practice Question 4d – Results on Definite Integral

Indefinite Integral of sin x

Indefinite Integral of cos x

Indefinite Integral of sec x raised to the power of 2

Practice Question 1a – Indefinite Integrals of sin x, cos x and sec x raised to the power of 2

Practice Question 1b – Indefinite Integrals of sin x, cos x and sec x raised to the power of 2

Practice Question 1c – Indefinite Integrals of sin x, cos x and sec x raised to the power of 2

Practice Question 1d – Definite Integrals of sin x, cos x and sec x raised to the power of 2

Practice Question 1e – Definite Integrals of sin x, cos x and sec x raised to the power of 2

Practice Question 1f – Definite Integrals of sin x, cos x and sec x raised to the power of 2

Indefinite Integral of sin(ax+b), a not equal to 0

Indefinite Integral of cos(ax+b), a not equal to 0

Indefinite Integral of sec(ax+b) raised to the power of 2, a not equal to 0

Practice Question 2a – Indefinite Integrals of sin(ax+b), cos(ax+b) and sec(ax+b) raised to the power of 2

Practice Question 2b – Indefinite Integrals of sin(ax+b), cos(ax+b) and sec(ax+b) raised to the power of 2

Practice Question 2c – Indefinite Integrals of sin(ax+b), cos(ax+b) and sec(ax+b) raised to the power of 2

Practice Question 2d – Definite Integrals of sin(ax+b), cos(ax+b) and sec(ax+b) raised to the power of 2

Practice Question 2e – Definite Integrals of sin(ax+b), cos(ax+b) and sec(ax+b) raised to the power of 2

Practice Question 2f – Definite Integrals of sin(ax+b), cos(ax+b) and sec(ax+b) raised to the power of 2

Indefinite Integral of e to the power of x

Practice Question 3a – Indefinite Integral of e to the power of x

Practice Question 3b – Definite Integral of e to the power of x

Indefinite Integral of e to the power of ax+b, a not equal to 0

Practice Question 4a – Indefinite Integral of e to the power of ax+b

Practice Question 4b – Indefinite Integral of e to the power of ax+b

Practice Question 4c – Indefinite Integral of e to the power of ax+b

Practice Question 4d – Definite Integral of e to the power of ax+b

Practice Question 4e – Definite Integral of e to the power of ax+b

Indefinite Integral of x^-1, x>0

Practice Question 5a – Indefinite Integral of x^-1

Practice Question 5b – Definite Integral of x^-1

Indefinite Integral of (ax+b)^-1, ax+b greater than 0 and a not equal to 0

Practice Question 6a – Indefinite Integral of (ax+b)^-1

Practice Question 6b – Indefinite Integral of (ax+b)^-1

Practice Question 6c – Definite Integral of (ax+b)^-1

Practice Question 6d – Definite Integral of (ax+b)^-1

Using Definite Integral to find Area (x-axis) (1)

Using Definite Integral to find Area (x-axis) (2)

Practice Question 1a – Using Definite Integral to find Area (x-axis)

Practice Question 1b – Using Definite Integral to find Area (x-axis)

Practice Question 1c – Using Definite Integral to find Area (x-axis)

Practice Question 1d – Using Definite Integral to find Area (x-axis)

Practice Question 1g – Using Definite Integral to find Area (x-axis)

Using Definite Integral to find Area (y-axis) (1)

Using Definite Integral to find Area (y-axis) (2)

Practice Question 2a – Using Definite Integral to find Area (y-axis)

Practice Question 2b – Using Definite Integral to find Area (y-axis)

Practice Question 2c – Using Definite Integral to find Area (y-axis)

Practice Question 2d – Using Definite Integral to find Area (y-axis)

Practice Question 2e – Using Definite Integral to find Area (y-axis)

Definite Integral : Area Bounded by a Curve And Line(s)

Practice Question 3a – Definite Integral : Area Bounded by a Curve And Line(s)

Practice Question 3b – Definite Integral : Area Bounded by a Curve And Line(s)

Introduction to Kinematics

Distance

Displacement

Average Speed

Speed and Velocity

Speed and Velocity – With Illustrations

Acceleration

Acceleration – With Illustrations

Practice Question 1a – Kinematics

Practice Question 1b – Kinematics

Practice Question 1c – Kinematics

Practice Question 1d – Kinematics

Displacement, Velocity and Acceleration

Practice Question 2 – Kinematics

Midpoint Theorem

Practice Question 1a – Midpoint Theorem

Alternate Segment Theorem (Tangent-Chord Theorem)

Practice Question 2a – Alternate Segment Theorem (Tangent-Chord Theorem)