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GCE Advanced Level Section 01
MECHANICS 2:
- DYNAMICS: Laws of motion; connected particles; resultant; F = ma; momentum; impulse
- KINEMATICS: Use of vectors; displacement, velocity and acceleration; displacement/time and velocity/time graphs; application of the calculus; constant acceleration formulae; collision; interception; examination - style questions (with fully worked answers)
- STATICS: Forces; resolving forces; resultant force; equilibrium; friction; moments; centre of mass
- PROJECTILES: horizontal, vertical and symmetrical projection
- WORK
- ENERGY
- POWER
- IMPACT
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£3.00
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GCE Advanced Level Section 02
PURE:
- Simple Algebraic Division: factor theorem; remainder theorem
- Co-ordinate Geometry: the circle
- Series: geometric series; binomial series
- Trigonometry: sine/cosine rules; sine formula for area of a triangle
- Radians: Circle: sector area; arc length using radian formulae
- Sin, Cos and Tan Graphs
- Pythagorean Identities
- Solution of Trigonometric Equations
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£3.00
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GCE Advanced Level Section 03
PURE:
- Exponentials and Logarithms: laws of logarithms; solving logarithmic equations
- Differentiation: stationary points; maxima/minima; curve sketching; application to practical problems
- Integration: area under a curve; area between curve and straight line; numerical integration:trapezium/mid-ordinate/Simpsons rules
- The Calculus: practice questions (with fully worked answers)
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£2.40
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GCE Advanced Level Section 04
PURE:
- Algebra: factorization (including H.C.F.); simplifying (including L.C.M.; addition, subtraction, multiplication and division of algebraic fractional quantities; cancelling; solving equations
- Functions: domain; codomain; range; inverse function; composite function; one-one function; many-one function; modulus function; graphs of functions; combination of transformations on f(x)
- Practice Questions with fully worked answers
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£3.10
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GCE Advanced Level Section 05
PURE:
- Trigonometry: sec, cosec, cot, arcsin, arccos and arctan: graphs; Pythagorean identities; double angle formulae: (r, a) form; solving trigonometric equations
- Exponential and Logarithmic Functions: graphs
- Differentiation: exponential function (graph included); logarithmic function (graph included); trigonometric functions (sin x, cos x, tan x arcsin x, arccos x, arctan x, sec x, cosec x, cot x); angle sums and differences; product rule; quotient rule; chain rule
- Numerical Methods for Location of Roots of f(x) = 0: change of sign; iterative methods (including Newton-Raphson method)
- Practice Questions with fully worked answers
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£8.50
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GCE Advanced Level Section 06
PURE:
- Algebra: partial fractions; parametric equations of lines and curves; the binomial series (including the use of partial fractions for simplifying)
- Differentiation: implicit differentiation; connected rates of change; differentiation of exponential functions
- Parametric Equations of Lines and Curves: conversion between parametric and Cartesian forms
- Practice Questions with fully worked answers
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£2.00
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GCE Advanced Level Section 07
PURE:
- Integration: trigonometric functions; integration by substitution and by parts; volume of solid of revolution around the x - axis; integration using partial fractions; numerical integration using the trapezium rule
- Practice Questions with fully worked answers
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£2.00
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GCE Advanced Level Section 08
PURE:
- Differential Equations: separation of variables; general solutions; particular solutions; worked examples (with fully worked answers)
- Vectors: vectors in 2 and 3 dimensions; magnitude of a vector; addition, subtraction and scalar multiplication of vectors; position vector; distance between 2 points; vector equations of lines (r = a + tb and r = c + t(d - c), where t is a parameter; intersection of lines; scalar product; perpendicular vectors; parallel vectors; worked examples (with fully worked answers)
- Key Points: Vectors
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£1.40
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GCE Advanced Level Section 09
PURE:
- Summation of Finite Series: application of logarithms
- Differential Equations: first and second order
- Complex Numbers: Argand diagram; modulus
- Polar Co-ordinates (r, x)
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£3.50
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