Revision notes.

Try this with Mathematics Specialist

1. Close your notes and write the main idea in two sentences from memory.
2. Reopen the source and correct the first mistake or omission you find.
3. Add one example and one question to test whether you can apply the idea.

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Topics in the resource inventory

• Modulus, argument, polar form and de Moivre's theorem for integral powers
• Addition as vector addition, multiplication as rotation and dilation, and complex-number geometry
• Loci and regions in the complex plane: circles, rays, perpendicular bisectors and |z - a| = k|z - b|
• nth roots of unity and of complex numbers; factor and remainder theorems, conjugate roots and polynomial equations
• Composition of functions: when f(g(x)) is defined, its domain and range
• One-to-one functions, inverse functions and the reflection property
• Absolute value, y = 1/f(x), y = |f(x)|, y = f(|x|) and rational functions with vertical, horizontal and oblique asymptotes
• 3D vector algebra, scalar product and vector proofs of geometric results
• Lines, line segments, spheres and parametric curves; do the paths cross or do the particles meet?
• Cross product, planes and systems of three linear equations with their geometric interpretation
• Vector functions of time: velocity, acceleration, distance travelled, projectile and circular motion
• Integration with trigonometric identities and the substitution u = g(x), including exact definite integrals
• Integral of 1/x, f'(x)/f(x) and partial fractions
• Areas between curves in x and in y, volumes of solids of revolution about either axis, and numerical integration
• Implicit differentiation, related rates and the increments formula
• Separable differential equations and slope fields
• Formulating differential equations: exponential, logistic and other growth-rate models
• Rectilinear motion with variable acceleration, v dv/dx, and simple harmonic motion
• The sample mean as a random variable: distribution of X-bar and the central limit theorem
• Confidence intervals for a population mean: construction, sample size, width and interpretation