We welcome foundation level students and students needing to refresh their core skills knowledge in the following areas:
Basic algebra: indices; algebraic expressions; arithmetic operations: addition, subtraction, multiplication; division of algebraic expressions; factor and remainder theorem
Equations and inequalities: solving linear equations; solving quadratic equations using: factorisation, discriminant method or completed square form; solving linear and quadratic inequalities
Functions: dependent and independent variables; domain and range; Real functions: sums, differences, product, quotient and function composition; inverse function; continuity of functions
Elementary functions and graphs including polynomials, exponential, logarithm and natural logarithm
Trigonometric functions and identities including solving equations
Basic Differential Calculus (one variable): definition of the derivative; derivatives of standard functions
Differentiation techniques: chain, product and quotient rules; implicit differentiation
Application of differentiation: maxima and minima of functions with curve sketching; Mean Value Theorem; tangent and normal lines to a curve; Taylor series
Basic Integral Calculus: definition of the integral as a limit of a sum and graphical principles of integration; Fundamental Theorem of Calculus; definite and indefinite integrals; integration of standard functions
Integration methods: Integration by substitution, integration using partial fractions, integration by parts
Applications of integration: areas under curves or between two curves; volumes of solid of revolution; numerical integration using Taylor series
University of Exeter LibGuide is licensed under CC BY 4.0
