# Secondary Maths - Brightstorm: Core 3 Videos

#### Brightstorm: Core 3 Videos

Collection Author: Craig Barton - Maths AST and creator of www.mrbartonmaths.com (TES Name: mrbartonmaths)

Brightstorm produces videos that explain key mathematical concepts and provide sample solutions on a wide range of mathematical topics. They have become an official TES Partner, and have kindly agreed to share their videos on our website.

Brightstorm is a US company, and hence its videos are based around the USA curriculum. However, I have spent some time mapping their hundreds of high-quality videos to the UK curriculum. What I particularly like are that many of the videos are aimed at post-16 students, studying AS, A2 and even Further Mathematics. Good quality videos, help and support for these courses tends to be few and far between. I also like the clarity and concise nature of the explanations and solutions – the teachers in the videos certainly know their stuff, and are able to convey this in an accessible way.

These videos could be used in the classroom, or better still by students at home. There is certainly scope to participate in the “flipped classroom”, whereby students use the videos at home to learn a concept, and then time is spent in the classroom working through problems with the teacher to make sure they have understood all the important concepts.

As the videos are American, it is important to get your head around some key terminology differences. The main ones are:

• Exponent = Power / Indices
• Rectangular = Cartesian Co-ordinates (i.e. x-y axis)
• Anti-differentiation = Integration

This particular collection of videos is appropriate for the Core 3 A2 Module. I have mapped it to the OCR specifications, so you may find slight differences of your follow another exam board and have to dip into the other modules.

#### Functions

Introduction to Functions

• Concise video on how to define a function. Key terms: function, dependent variable, independent variable

Function Notation

• Concise video on how to define function notation. Key terms: function notation, f(x)

Polynomial Function

• Concise video on how to evaluate a polynomial in function notation. Key terms: function notation, f(x), polynomial, constant, linear, quadratic, cubic

Domain and Range

• Concise video on how to define domain and range. Key terms: domain, range

Introduction to Rational Functions

• Concise video on how to define rational functions, and how to identify their domain and zeros. Key terms: rational functions polynomials domain zeros

Definition and Doman of a Rational Expression

• Concise video on how to define a rational expression. Key terms: rational expression, domain

Composition of Functions

• Concise video on how to calculate the composition of functions. Key terms: composition, f(g(x))

Graphing a Rational Equation

• Concise video on how to graph a basic rational equation. Key terms: graphing a rational expression, 1/x, asymptotes

Continuous Functions

• Concise video on how to determine whether a function f(x) is continuous everywhere on its domain. Key terms: limits, definition of continuous function, domain of a function, power functions, exponential functions, logarithmic functions

Continuity

• Concise video on how to determine whether a function f(x) is continuous at a particular point x=a. Key terms: limits, definition of a function continuous at a point, domain of a function

• Concise video on how to know when to include a absolute value when simplifying a square root. Key terms: absolute value, square roots, even root, odd power

Limits of Rational Functions

• Concise video on how to evaluate the limit of k/x^n as x goes to infinity (or negative infinity). Key terms: rational functions limits infinity

Limits at a Glance

• Concise video on how to quickly find the limit of a rational function as x goes to infinity. Key terms: rational functions polynomials degree limits infinity

Limits and End Behaviour

• Concise video on how to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph. Key terms: limits, rational functions, limit at infinity, limit at negative infinity, horizontal asymptotes, end behavior

Evaluating Limits Algebraically: Part 1

• Concise video on how to evaluate the limit of a function using continuity. Key terms: limits, definition of continuous function, domain of a function, rational functions

Evaluating Limits Algebraically: Part 2

• Concise video on how to evaluate the limit of a function at points where it is not continuous. Key terms: limits, definition of continuous function, domain of a function, rational functions, factoring polynomials, holes

Limits: A Numerical Approach

• Concise video on how to estimate a limit using a table of values. Key terms: limits, functions, table of values, numerical approach, undefined

Limits: A Graphical Approach

• Concise video on how to determine one-sided and two-sided limits from the graph of a function. Key terms: one-sided limits, two-sided limits, limit does not exist, piecewise functions, left-hand limit, right-hand limit, graph, graphical approach

Infinite Limits and Vertical Asymptotes

• Concise video on how to use one-sided limits to find a vertical asymptote. Key terms: one-sided limits, infinity, limit does not exist, rational functions, left-hand limit, right-hand limit, table of values, numerical approach, vertical asymptote

#### Trigonometry

• Concise video on how to derive the sine of a sum formula. Key terms: cosine of a difference formula, the cofunction identities, the sine of a sum formula

The Double Angle Formuale

• Concise video on how to use the sine and cosine addition formulas to prove the double-angle formulas. Key terms: the sine of a sum formula, the cosine of a sum formula, the sine double-angle formula, the cosine double-angle formula

Other Forms of the Cosine Double Angle Formula

• Concise video on how to derive two more cosine double-angle formulas. Key terms: the Pythagorean identity, the cosine double-angle formulas

The Half Angle Identities

• Concise video on how to use the power reduction formulas to derive the half-angle formulas. Key terms: the power reduction formulas, the half-angle formulas, quadrants

Graphing the Reciprocal Trigonometric Functions

• Concise video on how to use the unit circle to derive identities that are useful in graphing the reciprocal trigonometric functions. Key terms: identities, the unit circle, the cofunction identities, the add Π identities

The Inverse Sine Function

• Concise video on how to restrict the domain of sine so it will have an inverse function. Key terms: inverse functions, one-to-one, inverse sine, arcsine

The Inverse Cosine Function

• Concise video on how to restrict the domain of cosine so it will have an inverse function. Key terms: inverse functions, one-to-one, inverse cosine, arccosine

Using the Inverse Trigonometic Functions

• Concise video on how to evaluate expressions like tan(sin-1 (4/5)). Key terms: sine, cosine, tangent, inverse sine, inverse cosine, inverse tangent, the unit circle

Find the Equation of Sine and Cosine Waves

• Concise video on how to identify the graph of a stretched cosine curve. Key terms: sine, cosine, period, amplitude, intercepts, turning points

Trigonometric Equations that require Factoring

• Concise video on how to solve a sine equation by factoring: 4 sin2 x = 2. Key terms: trigonometric equations, factoring, the unit circle, principal solutions, periodicity

#### The functions e and ln

Properties of Logarithms

• Concise video on how to evaluate logarithms when the argument is a recognizable power of the base. Key terms: logarithmic functions, exponential functions, inverse functions, identities, the common logarithm

The Number e and the Natural Logarithm

• Concise video on how the number e is defined. Key terms: exponential functions, graphing exponential functions, tangent lines, the definition of e

Exponential Functions

• Concise video on how to graph exponential functions. Key terms: exponential functions, graphs of exponential functions, asymptote

Exponential Growth and Decay

• Concise video on how to find the doubling time of a population when the growth rate is given. Key terms: exponential growth, exponential functions, doubling time, logarithmic functions, the natural logarithm, round-off error

#### Differentiation

The Chain Rule

• Concise video on how to differentiate a composite function. Key terms: composite function, composition, inside function, outside function, differentiation

Derivatives of Exponential Functions

• Concise video on how to use the definition of the derivative to find a derivative formula for exponential functions. Key terms: limits, derivative, definition of the derivative, difference quotient, exponential functions, natural logarithm

The Chain Rule: The General Exponential Rule

• Concise video on how to differentiate a composite function when the outside function is exponential. Key terms: chain rule, composite functions, composition, exponential functions

The Chain Rule: The General Power Rule

• Concise video on how to differentiate a composite function when the outside function is a power function. Key terms: chain rule, composite functions, power functions, power rule, differentiation

Derivatives of Logarithmic Functions

• Concise video on how to infer the derivative of the natural log function using a calculator investigation. Key terms: derivative formula, limits, derivative, the number e, numerical approximation of the derivative, natural logarithm

Chain Rule: The General Logarithmic Rule

• Concise video on how to differentiate a composite function when the outside function is the natural logarithm. Key terms: chain rule, logarithmic functions, properties of logarithms, derivative of natural log

An Important Limit

• Concise video on how to interpret the value of a limit important in the derivative of exponential functions. Key terms: limits, natural logarithm, numerical approximation

The Product Rule

• Concise video on how to differentiate a product of two functions. Key terms: differentiation, derivative formula, power functions, the product rule of derivatives

The Quotient Rule

• Concise video on how to differentiate a quotient of two functions. Key terms: differentiation, quotient rule, product rule, derivatives

Instantaneous Rates of Change

• Concise video on how to estimate the instantaneous rate liquid is pouring out of a container at t=4 by computing average rates of change over shorter and shorter intervals of time. Key terms: average rate of change, instantaneous rate of change, change in quantity, change in time, limits

#### Integration

The Fundamental Theorem of Calculus

• Concise video on how to use the fundamental theorem of calculus to evaluate a definite integral. Key terms: fundamental theorem of calculus, definite integral, antiderivative, continuity

Anti-Differentiation (Integration)

• Concise video on how to find an antiderivative of a function. Key terms: antiderivative, derivative

Definition of Anti-derivatives

• Concise video on how to define an antiderivative. Key terms: differentiation, antiderivative, derivative

Definition of Indefinite Integrals

• Concise video on how to define an indefinite integral. Key terms: indefinite integral, antiderivative, antidifferentiation

Indefinite Integrals

• Concise video on how to solve an indefinite integral using the properties of indefinite integrals. Key terms: indefinite integral, antiderivative, antidifferentiation, differentiation

The Definite Integral

• Concise video on how to define the definite integral. Key terms: definite integral, approximating area under the curve, left-hand sums, right-hand sums, limits

Complicated Definite Intervals

• Concise video on how to solve complex indefinite integral using the properties of indefinite integrals. Key terms: indefinite integral, antiderivative, antidifferentiation, differentiation

Definite Integrals and Area

• Concise video on how to use definite integrals to find the area between a curve or under a curve. Key terms: definite integral, area problems, area between curves

Definite Integrals as Net Change

• Concise video on how to use the fundamental theorem of calculus to compute the net change of a quantity. Key terms: definite integral, net change, rate of change, net change theorem, fundamental theorem of calculus

Average Value of a Function

• Concise video on how to find the average value of a function over an interval [a,b]. Key terms: average value, antidifferentiation, limits of integration, functions, area under a curve