• Some Assumed Knowledge

◦ 1 – Arithmetic operations, fractions, factoring, polynomial long division, solving equations, completing the square, the quadratic formula, binomial theorem, surds, inequalities, interval notation, absolute values

◦ 2 – The existence of a root, trigonometric functions

  • Functions

◦ 1 – The concept, domain, range, codomain

◦ 2 – Linear functions, polynomials, exponentials, trigonometric, hyperbolic, limits

◦ 3 – Composition of functions, inverse functions, logarithmic functions, inverse trigonometric functions

  • Complex Numbers

◦ 1 – Introduction, addition, subtraction, multiplication, division, plotting, solving equations, modulus

◦ 2 – Polar form, converting between polar and cartesian, multiplying, dividing

◦ 3 – De Moivre’s theorem, Euler’s identity, exponential form, nth roots

◦ 4 – Graphing regions

  • Vectors

1 – Introduction, addition and scalar multiplication, length, i, j, k unit vectors

2 – Scalar/dot product, projection vectors

3 – Vector/cross product, triple product

4 – Lines and planes, equations, intersections, distance from a point to a plane, angle between planes

5 – Applications, geometry, science and engineering

  • Differentiation

1 – Rates of change, first principles, graphing the derivative function

2 – Rules

3 – Graphing, turning/stationary points, inflection points

4 – Tangent line approximation, linearization, Newton’s method, optimisation, related rates

5 – Implicit differentiation

  • Integration

◦ 1 – Area under a curve, Riemann sums, properties

◦ 2 – The fundamental theorem of calculus

◦ 3 – Substitution, by parts, involving trig, partial fractions, numerical methods

◦ 4 – Position, velocity, acceleration, areas between curves, volumes of revolution, accumulation of change, work, hydrostatic pressure, force

Learning and Practicing Mathematics via the Internet

The Khan Academy, available at http://www.khanacademy.org/, has over 2600 videos, many of which are mathematics. You can watch videos without logging in, but signing up only requires a Google account or a Facebook account and means your activity is recorded so that points and badges are earned by watching videos.

When each problem in the video is presented you should pause the video and attempt to solve the problem yourself. Once you have had an attempt or two, continue watching the video to see the approach taken by the presenter. At the end of the video you can often click the green ‘Practice this concept’ button above and to the right of the video.

Some of the videos start very basic and progress, some are just basic as an introduction for the next video, but if you can’t understand something in the video, there is help available. You could leave a comment on the post that sent you to the video, leave a comment on the video in the Khan Academy, search YouTube (http://patrickjmt.com/http://rootmath.org/ and AlRichards314 are all good channels) or the Khan Academy for another explanation or search the following websites for explanations:





Another amazing collection of material designed to educate the public is MIT OpenCourseWare, go on have a browse. Possibly most useful to you is the

Single variable calculus notes

Application of calculus java apps

A group that call themselves the world wide centre of mathematics has a good series of long lectures on calculus, you can find their collections here.

There are also some decent textbooks available online


Calculus of one real variable

Calculus (wikibooks)

Algebra (wikibooks)

Single variable calculus (MIT)

Calculus with applications (MIT)

Algebra 1 (FlexBook)

Calculus (FlexBook)

GAIM 1 – Getting Ahead in Mathematics 1 – MATH1110 University of Newcastle, Australia

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