# Secondary Maths - Brightstorm: Core 3 Videos

**TES Secondary Maths resource collections**

**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:

- Radical = Square Root
- 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**

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

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

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

- 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

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

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

- 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

- 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

- 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

- 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

- 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

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

- 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

- 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

- 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

- 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

- 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**

- 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

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

- 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**

- 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

- 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

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

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

- 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

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

- 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

- 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

- 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