Math is a challenging subject and a key skill required for many university programs, careers and also just in daily life. This course will help you deeply understand the key topics found in high school Math to 1) make excellent grades 2) go on to study or use Math in the future.
Deeply Understand Key High School Math Topics and Achieve Exam Success
Understand key ideas, techniques and how to apply them
Solve a wide range of Math problems
Confidently take tests and exams
Prepare for using Math in the future
Understanding is the key for Math success. Understand it, Ace it!
Successful Math students understand the material, struggling students try to learn it. This course helps you understand the most important high school Math topics and apply that understanding to answer a wide range of problems. I’ve taught frustrated students who knew every theorem and equation but were unable to answer exam questions. Why? Because you can never anticipate how a Math question will be presented. But if you truly understand the material it doesn’t matter, you can still nail your answers!
This course focuses on the second half of high school Math, for 15-17 year olds. Regardless of where you live there's a set of key Math topics that you’ll be studying. The topics I cover are: Algebra, Functions, Graphs of Functions, Log and Exponential Functions, Trigonometric Functions, Trigonometric Identities, Polynomials, Differential Calculus, Integral Calculus, Circles and Vectors. I’ve designed classes based on my experience of working with students who have struggled with this material. I know why they’ve found these ideas difficult to grasp, but I’ve helped them master them and I can help you too!
Why this Course?
This course has been carefully designed based on my experience of successfully teaching students with wide-ranging abilities. Take this course and you'll understand these ideas in ways that I know work. You'll also benefit from over 700 carefully selected practice questions which will increase your confidence and prepare you to nail tests and exams.
What to Expect on this Course
The course is laid out in an easy to use structure with a section for each topic and individual classes within that section. I’ve ordered topics to maximise your learning based on my experience of teaching them.
Each lesson delivers one key idea or technique. I start with the theory and move onto examples to show you how to answer common question types. You can reinforce your learning through a range of practice questions with solutions.
Take this course and you’ll walk away confident in your understanding of key high school Math material and just might look forward to taking your next Math test.
Learn how to simplify algebraic expressions by combining terms. Master the rules for working with negatives, and learn how to multiple two brackets together.
At the end of this lecture you'll be able to confidently factorise trinomial algebraic expressions into two brackets. You'll also learn how to recognise differences of squares and how to factorise them into two brackets.
Learn how to simplify algebraic fractions using common techniques such as common factors and factorising into two brackets.
Master the technique of adding and subtracting algebraic fractions by using a technique similar to adding and subtracting numeric fractions.
At the end of this lecture you'll be able to confidently change the subject of equations and formulae - an important technique in algebra.
This class helps you understand that a function is a relationship between variables. Understanding what functions are is important in being able to work with them confidently.
This class teaches you the role that variables play in functions which is crucial for understanding and working with functions successfully.
At the end of this class you'll understand what the domain of a function is and how to write the domain of a function. You'll also learn the common restrictions on the domain of a function.
This class teaches you how to confidently compose two functions as well as the correct notation for writing composite functions.
Take this class to understand what the inverse of a function is and master the technique for finding the inverse of any given function.
Take this class to understand how to make a sketch of the graph of a function from its equation. You'll also learn to confidently identify the graphs of linear, quadratics and cubic functions.
When the equation of a function changes so does its graph. Take this class to learn to identify different types of changes to the equation of a function and how to sketch the graph of the function after it's been changed.
Master the technique for finding the co-ordinates of the points where a graph crosses the x-axis and the y-axis by letting x=0 or y=0. This is a key technique when sketching the graphs of functions.
Master the technique of setting the equations of functions equal to find the points where their graphs intersect.
In this class you'll learn the standard equation of a straight line and understand why it represents the equation of a linear function. You'll be able to find the equation of a selection of straight lines which will be expanded upon in later classes.
In this class you'll learn what the gradient of a straight line is and how it fits with the equation of a straight line. You'll be able to confidently find the gradient of a straight line using any two points on the line.
In this class you'll learn how to identify a quadratic function by its equation. You'll also learn some key facts about quadratic functions such as their general algebraic form, the shape of their graphs and about their symmetry.
In this class you'll learn to draw the graph of a quadratic function from its equation and you'll be able to identify key facts about those graphs such as their shape, their turning points and where they cross the axes.
In this class you'll learn about the roots of quadratic functions which are the points where the graph crosses over the x-axis. You'll understand the three types of root and how to use the technique of factorisation to find the roots of a given quadratic.
This class demonstrates how to use the discriminant to determine what kind of roots a quadratic function has. This technique is called finding the nature of the roots and is used to show whether a quadratic function has zero, one or two roots.
Understand how to use the roots of a quadratic function to find its turning point in the cases where the function has one or two roots.
Master the technique of completing the square which you can use to find the co-ordinates of the turning point of a quadratic function. This technique is particularly useful where the quadratic has no roots to help with finding the turning point.
In this class we look at example quadratic functions to reinforce your understanding of the various techniques you've learnt in this section. This includes determining the nature of the roots, finding the roots, finding the turning point and determining the shape of the graph.
This class introduces you to exponential and logarithmic functions. By the end of this class you'll understand the relationship between these functions and be introduced to the general shape of their graphs.
At the end of this lecture you'll understand the general shape and key features of the graph of an exponential function and a logarithmic function. You'll also better understand the relationship between their graphs and be able to identify key points.
To work with exponential and logarithmic functions you have to be able to use the correct notation. By the end of this class you'll confidently write expressions involving exponentials and logarithms.
One of the most important features of working with logarithms is knowing the laws of logarithms. By the end of this class you'll have mastered the laws of logarithms which is essential for solving equations with exponentials or logarithms in them.
By the end of this lecture you'll be familiar with the Sin, Cos, and Tan functions and how they can be used to link angles and lengths of sides of triangles.
In this class you'll come to understand the Sine function by becoming familiar with its graph. You'll become familiar with the general shape of the Sine function, its maximum and minimum values, where it crosses the axes and the interval on which it repeats - key knowledge if you want to be successful in trigonometry.
In this class you'll come to understand the Cosine function by becoming familiar with its graph. You'll become familiar with the general shape of the Sine function, its maximum and minimum values, where it crosses the axes and the interval on which it repeats - key knowledge if you want to be successful in trigonometry.
In this class you'll come to understand the Tangent function by becoming familiar with its graph. You'll become familiar with the general shape of the Sine function, its maximum and minimum values, where it crosses the axes and the interval on which it repeats - key knowledge if you want to be successful in trigonometry.
Although it would be nice to always work with the most basic forms of the Sine and Cosine functions, its crucial that you become confident with variations too. By the end of this class you'll understand the various ways in which the Sine and Cosine functions can be manipulated and how those changes impact on the graph of those functions.
Using the theory from the previous class, this class demonstrates through several examples how to sketch the graph of the Sine or Cosine function when they have been manipulated. For example, how to sketch y=Sin2X or y=3CosX+2
Trigonometry questions are often written using radians rather than degrees. By the end of this class you'll understand what a radian is and how to convert degrees to radians, a key skill for trigonometry success.
In this class you'll master several techniques for working out the exact value of trig functions. You'll learn to use the graph of the function to do this as well as known values and the CAST method.
In this class you'll learn what the trig addition formulas are and how to use them. This is an important skill which you'll need for solving trigonometric equations.
In this class you'll learn what the trig double angle formulas are and how to use them. This is an important skill which you'll need for solving trigonometric equations.
This class helps you understand what polynomial expressions are and you'll learn what is meant by polynomial factors.
The factor and remainder theorems help you to determine whether an expression is or is not a factor of a polynomial. By the end of this class you'll master the technique of using the factor and remainder theorems.
In this class you'll learn to master the technique of synthetic division which is used in factorising polynomials fully if one factor is already known. This is a key technique in working with polynomial expressions.
In this class we put together the techniques you've learnt in this section to fully factorise polynomials using the factor / remainder theorem and synthetic division together.
Differential Calculus is all about derivatives of functions. This class helps you understand what is meant by the derivative of a function before you learn how to find derivatives using various techniques presented in this section.
To work with derivatives you need to be able to use the correct notation. By the end of this class you'll have mastered the appropriate notation required for Differential Calculus.
The power rule is the primary rule used to find the derivative of functions. In this class you'll learn what the power rule looks like and how to use it correctly to find the derivative of applicable functions.
The chain rule is used to find the derivative of composite functions (which are usually identified by being in a bracket with a power above it). This class teaches you how to use the chain rule with confidence.
Learn how to find the derivatives of the Sin(aX) and Cos(aX) functions.
Differentiation can be used to solve a wide variety of types of question. In this class we look at one of the most common applications of differentiation which is to find the equation of a tangent to a curve at a given point.
One of the most important points of any function is where it changes direction. Such points (maximums, minimums and points of inflection) are called stationary points. In this class learn how to use the derivative of a function to find the stationary points.
As well as finding stationary points we also want to know what type they are (maximum, minimum or point of inflection). This is called finding the nature of the stationary point. In this class you'll learn how to use a nature table to demonstrate what kind of stationary point a function has.
In this class you'll learn what notation must be used for integration and you'll learn the first rule for finding the integral of a given function - the power rule.
In this class you'll learn how to find the integral of the Sin(aX) and Cos(aX) functions.
The chain rule for integration, often called the reverse chain rule, can be used to find the integral of certain types of functions. In this class you'll learn how to use the reverse chain rule to find the integral of relevant functions.
This class introduces the idea of a definite integral. By the end of this class you'll understand what a definite integral is and will have mastered the technique for finding them.
A key application of definite integrals is to find the area underneath a curve. In this class you'll learn how to use definite integrals to find the area under a given curve and between two points on the x-axis known as limits.
In this class we run through several examples of integration question which require the use of the various techniques you've learnt in this section - the power rule, integrating trig functions, the reverse chain rule, and definite integrals.
Gary is a Mathematician turned philosopher. Educated in the UK and the US he has a first class honours degree in Pure Mathematics and a Master’s degree in Environmental Philosophy.
Following a successful career in the oil industry Gary engaged his passion for nature and undertook post-graduate research at The University of Edinburgh, working with leading experts in their fields.
He is particularly interested in the relationship between humans and the rest of nature and loves sharing his knowledge and ideas with others.
When he’s not philosophizing or teaching Math you’re likely
to catch him on a mountain, in a forest or on his yoga mat.
Learn more on his website or FaceBook page.