numberskill’s board-casts are free math tuition lessons on YouTube. These videos are based on Singapore’s GCE O levels and A levels (H2) math syllabus. numberskill’s YouTube channel was added to YouTube EDU, a free source of quality educational content from around the globe. Check out numberskill's YouTube channel!

Consider this scenario:

You have a math test tomorrow but your next math tuition class is on the day after tomorrow. Worse, you forgot how to solve rates of change problems. You tried reading the textbook but you forgot what your teacher taught in class. Looks like you’re not going to do well for the dreadful math test. Ever felt as helpless as this?

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Board-cast is for FREE, for ALL. Through Board-casts, Gary hopes to help students who can’t afford the time or money to go for math tuition classes. It is also a practical way to give back to society and to spread knowledge of math to all who want to learn beyond the shores of Singapore.

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Integration - How to integrate a rational function?

Binomial Theorem – An Introduction to the binomial theorem and its relation to the Pascal’s triangle.

Binomial Theorem – The binomial expansion formula.

Binomial Theorem – Example 1 – A basic binomial expansion question to get used to the formula.

Binomial Theorem – Expansion in Ascending or Descending powers of x.

Binomial Theorem – The General Term formula.

Binomial Theorem – Example 2 – Finding the term independent of x.

Binomial Theorem – The nCr formula.

Binomial Theorem – Example 3 – A binomial question that requires the use of the nCr formula.

Binomial Theorem – Example 4 – Expanding 3 terms in a binomial question.

Binomial Theorem – Example 5 – Challenging question with power unknown.

Binomial Theorem – Example 6 – Super Challenging binomial question.

Binomial Theorem - Challenging binomial theorem question.

Partial Fractions – Introduction

Partial Fractions – What is partial fraction?

Partial Fractions – Example 1 (partial fractions with linear factors)

Partial Fractions – Example 2 (partial fractions with repeated linear factor)

Partial Fractions – Example 3 (partial fractions with non-factorizable quadratic factor)

Partial Fractions – Improper Fractions

Partial Fractions – The Cover-Up Rule

Partial Fractions – Example 4 (Cover-Up Rule)

Sum of roots, product of roots – Introduction

Sum and Product of Roots – Example 1

Sum and Product of Roots – Find quadratic equations using sum and product of roots – Example 2

Sum and Product of Roots – Example 3

Sum and Product of Roots – Example 4

Sum and Product of Roots – Example 5

Quadratic Equations and Inequalities – Introduction

Quadratic Equations and Inequalities – Example 1 (2 Real and Distinct Roots)

Quadratic Equations and Inequalities – Example 2 (Repeated Root)

Quadratic Equations and Inequalities – Example 3 (No Real Root)

Quadratic Equations and Inequalities – Maximum and Minimum Functions

Quadratic Equations and Inequalities – How to complete the square

Quadratic Equations and Inequalities General Formula

Quadratic Equations and Inequalities – Example 4 (Complete the square and sketch)

Quadratic Equations and Inequalities – Example 5 (Complete the sqaure and sketch)

Quadratic Equations and Inequalities – Example 6 (Complete the sqaure)

Quadratic Inequalities – How to solve quadratic inequalities

Quadratic Inequalities – Example 7 (basic)

Quadratic Inequalities – Example 8

Quadratic Inequalities – Example 9 (important)

Quadratic Inequalities – Example 10 (challenging)

Quadratic Inequalities – Example 11 (line intersect curve)

Quadratic Inequalities – Example 12 (line is tangent to curve)

Polynomials – Introduction of Identities

Identities – Example 1 (Expansion and Substitution method)

Identities – Example 2 (Best method)

Identities Example 3 Example using best method

Polynomials – Long Division of Polynomials

Polynomials – The Remainder Theorem

Polynomials – The Remainder Theorem – Example 4 (Basic)

Polynomials – The Remainder Theorem – Example 5 (Basic)

Polynomials – The Remainder Theorem – Example 6 (simultaneous equations)

Polynomials – The Remainder Theorem – Example 7 (same remainder)

Polynomials – The Factor Theorem – Introduction

Polynomials – The Remainder and Factor Theorem – Example 8

Polynomials – The Remainder and Factor Theorem – Example 8 (con’t using long division)

Polynomials – The Remainder and Factor Theorem – Example 8 (con’t using synthetic division)

Polynomials – The Remainder and Factor Theorem – Example 9 (challenging)

Polynomials – Factorization of cubic expressions with example

Polynomials – Factorization of cubic expressions Example 10

Matrices – Order of a matrix and square matrix

Matrices – Addition and Subtraction of matrices

Matrices – Multiplication of matrices

Matrices – Matrix multiplication Example 1

Matrices – Matrix equation Example 2

Matrices – Matrix multiplication (uncommon) Example 3, 4

Matrices – Identity Matrix and Determinant of a Matrix

Matrices – The inverse matrix

Matrices – Using matrices to solve simultaneous equations

Matrices – Example 5 (no solution, infinite number of solutions)

Matrices – Matrices Example 6 Word problem

The inverse matrix and the use of matrix to solve simultaneous equations are no longer in the A math syllabus.

Trigonometry – The Basic Angle, Reference Angle, Acute Angle

Trigonometry – Signs of Trigonometry Ratios

Trigonometry – Example 1

Trigonometry – Some Special Angles

Trigonometry – Example 2

Trigonometry – Example 3 (draw triangle type)

Trigonometry – Example 4 (draw triangle type)

Trigonometry – The Sine Curve

Trigonometry – The Cosine Curve

Trigonometry – The Tangent Curve

Trigonometry – Example 1 – Sketch the graph of y = 2 cos x – 1

Trigonometry – Example 2 (modulus curves)

Trigonometry – Example 3 – Sketch y = tan 2x

Basic Differentiation for O levels.

Differentiation Example 1

Differentiation Example 2 (reciprocal of x)

Differentiation Example 3

Differentiation Example 4 (word problem)

Differentiation Example 5 (word problem)

Differentiation – A Lesson on Chain Rule

Differentiation – Examples on Chain Rule

Differentiation – Product Rule

Differentiation – Product Rule Example 1

Differentiation – Product Rule Example 2

Differentiation – A lesson on Quotient Rule

Differentiation – Quotient Rule Example 1

Relative Velocity was taken out of the Singapore GCE O levels Additional Math syllabus since 2007.

Relative Velocity – Introduction

Relative Velocity – Parallel Motion – Example 1

Relative Velocity – Parallel Motion – Example 2

Relative Velocity – Parallel Motion – Example 3

Relative Velocity – Parallel Motion – Example 4

Relative Velocity – Motion in air and water – main concept

Relative Velocity – Relative velocity of motion in water (animation)

Relative Velocity – Motion in air and water Example 1 – River crossing

Relative Velocity – Motion in air and water Example 2 – River crossing

Relative Velocity – Motion in air and water Example 3 – Aircraft with return trip

Relative Velocity – Motion in air and water Example 4 – Interception

Relative Velocity – Relative motion of 2 moving objects

Relative Velocity – Relative motion of 2 moving objects Example 2

Relative Velocity – Relative motion of 2 moving objects Example 3 (Interception)

Relative Velocity – Relative motion of 2 moving objects Example 4 (wind speed)

Functions – Composite Functions Part 1

Functions – Composite Functions Example

Functions – Example 2 (inverse function)

Functions – Example 3 (JJC – composite function)

Functions – Example 4 (HCJC – transformation of graph)

Functions – Example 5 (NJC – composite and inverse function)

Functions – Example 6 (PJC – sketch, composite and inverse function)

Functions – Example 7 (RJC – domain and range of a composite function)

Functions – Example 8 (YJC – one to one, inverse and composite function)

3D Vectors for A Levels – An Introduction

Vectors – Unit Vector

Vectors – Directional Cosines

Vectors – Ratio Theorem and Mid-point Theorem

Vectors – Dot Product or Scalar Product

JC math tuition - H2 A levels Math - Distance between 2 planes in vectors

A Levels H2 math - Vectors 2007/TJC/1/4 (Challenging question on ratio theorem)

A Levels H2 math tuition - Vectors 2008/DHS/2/5

Differentiation by First Principle

Differentiation by First Principle – Examples

JC math tuition- Integration by parts

Challenging question on binomial series that students always ask during H2 math tuition

A Levels H2 math tuition - Mathematical Induction question with hence parts

JC math tuition - Normal Distribution 2011/AJC/P2/Q9

JC math tuition - How to find volume of revolution bounded by 2 curves