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Course Content
Chapter-1. Logarithmic Functions and Indices.
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Lesson-1.1.1- The functions a^x and log b^x (where b is a natural number greater than one).
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Lesson-1.1.2- Use and properties of indices and logarithms, including change of base.
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Lesson-1.1.3- Simple manipulation of surds.
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Lesson-1.1.4- Rationalizing the Denominator.
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Chapter-2. The Quadratic Function.
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Lesson-2.1.1- The manipulation of quadratic expressions.
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Lesson-2.1.2- The roots of a quadratic equation.
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Lesson-2.1.3- Simple examples involving functions of the roots of a quadratic equation.
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Chapter-3. Identities and inequalities.
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Lesson-3.1.1- Simple algebraic division.
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Lesson-3.1.2- The factor and remainder theorems.
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Lesson-3.1.3- Solutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables.
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Lesson-3.1.4- Simple inequalities, linear and quadratic.
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Lesson-3.1.5- The graphical representation of linear inequalities in two variables.
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Chapter-4. Graphs
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Lesson-4.1.1- Graphs of polynomials and rational functions with linear denominators.
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Lesson-4.1.2- The solution of equations and transcendental functions by graphical methods.
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Chapter-5. Series
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Lesson-5.1.1- Use of the ∑ notation
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Lesson-5.1.2- Knowledge of the general term of an arithmetic series is required.
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Lesson-5.1.3- Use of the sum to n terms of an arithmetic series is required.
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Lesson-5.1.4- Knowledge of the general term of a geometric series is required.
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Lesson-5.1.5- Use of the sum to n terms of a finite geometric series is required.
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Lesson-5.1.6- Use of the sum to infinity of a convergent geometric series, including the use of r < 1 is required.
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Lesson-5.1.7- Proofs of the above are not required.
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Chapter-6. The Binomial Series.
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Lesson-6.1.1- Use of the binomial series (1 + x)^n
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Chapter-7. Scalar and Vector Quantities
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Lesson-7.1.1- The addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar.
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Lesson-7.1.2- Components and resolved parts of a vector.
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Lesson-7.1.3- Magnitude of a vector.
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Lesson-7.1.4- Position vector.
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Lesson-7.1.5- Unit vector.
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Lesson-7.1.6- Use of vectors to establish simple properties of geometrical figures.
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Chapter-8. Rectangular Cartesian Coordinates.
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Lesson-8.1.1- The distance between two points.
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Lesson-8.1.2- The point dividing a line in a given ratio.
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Lesson-8.1.3- Gradient of a straight line joining two points.
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Lesson-8.1.4- The straight line and its equation.
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Lesson-8.1.5- The condition for two lines to be parallel or to be perpendicular.
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Chapter-9. Calculus
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Lesson-9.1.1- Differentiation and integration of sums of multiples of powers of x (excluding integration of 1 x ),sin ,cos ,e^ax
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Lesson-9.1.2- Differentiation of a product, quotient and simple cases of a function of a function.
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Lesson-9.1.3- Applications to simple linear kinematics and to determination of areas and volumes.
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Lesson-9.1.4- Stationary points and turning points.
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Lesson-9.1.5- Maxima and Minima
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Lesson-9.1.6- The equations of tangents and normals to the curve y = f(x).
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Lesson-9.1.7- Application of calculus to rates of change and connected rates of change.
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Chapter-10. Trigonometry
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Lesson-10.1.1- Radian measure, including use for arc length and area of sector.
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Lesson-10.1.2- The three basic trigonometric ratios of angles of any magnitude (in degrees or radians) and their graphs.
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Lesson-10.1.3- Applications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes).
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Lesson-10.1.4- Use of the sine and cosine formulae.
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Lesson-10.1.5- The identity cos ^2 θ+sin^2 θ = 1
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Lesson-10.1.6- Use of the identity tanθ = sinθ/cosθ
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Lesson-10.1.7- Formal proofs of sin(A + B), cos(A + B) formulae will not be required.
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Lesson-10.1.8- Questions using the formulae for sin(A + B), cos(A + B), tan(A + B) may be set; the formulae will be on the formula sheet, for example: sin(A + B) = sinAcosB + cosAsinB
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Lesson-10.1.9- Long questions, explicitly involving excessive manipulation, will not be set.
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Lesson-10.1.10- Solution of simple trigonometric equations for a given interval.
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Edexcel OLevel Pure Math Revision Note & Solutions
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