Preparing for Engineering Mathematics

Skills	Learning Outcomes	Booklet	Worksheet	Further
Laws of Indices	perform calculations using indices state and use the laws of indices use scientific notation	HELM 1.2 Indices	MathCentre Indices	Indices and Powers
Laws of Logarithms	invert b = a^n using logarithms simplify expressions involving logarithms change bases in logarithms	HELM 6.3 Logarithms	MathCentre Logarithms	Logarithms
Simultaneous Equations	solve pairs of simultaneous linear equations	HELM 3.4 Simultaneous Equations	MathCentre Simultaneous Equations	Simultaneous Equations
Factorising Linear Equations	factorise simple expressions (Sections 1-4)	HELM Simple Factorising	Coventry MathsCentre Factorising	Factorising Quadratic Equations
Factorising Quadratic Equations	factorise quadratic expressions (Sections 3-5)	HELM Quadratic Factorisation	MathCentre Factorising	Quadratic Equations
Algebraic Fractions	add, subtract, multiply and divide algebraic fractions	HELM Algebriac Fractions	MathCentre Simplify Fractions	Algebraic Fractions
Trignometric Ratios	define trigonometric functions both in right-angled triangles express angles in degrees express angles in radians calculate all the angles and sides in any right-angled triangle given certain information define trigonometric functions generally sketch the graphs of the three main trigonometric functions: sin, cos, tan	HELM Trig Ratios	HELM Trig Functions	Trigonometric Ratios
Sine & Cosine Rules	solve triangles using the cosine formulae solve triangles using the sine formulae find areas of triangles	MathCentre Sin & Cos Rules	MathCentre Sin & Cos Rules	Sine & Cosine Rules
Differentiation	explain what is meant by the tangent to a curve explain what is meant by the gradient of a curve at a point (Sections 1-2)	HELM Differentiation	MathCentre Differentiation	Differentiation
Integration	evaluate simple integrals by reversing the process of differentiation use a table of integrals	HELM Integration	MathCentre Integration	Integration
Differentiation - Product and Quotient Rules	differentiate products and quotients of the standard functions differentiate a quotient using the product rule	HELM Product/ Quotient Rules	MathCentre Product/ Quotient Rules	Differentation - Product Rule Differentation - Quotient Rule
Integration - Definite Integrals	find simple definite integrals handle some integrals involving an infinite limit of integration	HELM Definite Integrals	MathCentre Definite Integrals	Integration - Definite Integrals
The Constant of Integrals	explain the need for a constant of integration when finding indefinite integrals	HELM Constant of Integrals
Factor & Remainder Theorems	use the remainder and factor theorems to find factors of polynomials	HELMFactor/ Remainder Theorems		Remainder & Factor Theorems
Partial Fractions	distinguish between proper and improper fractions express an algebraic fraction as the sum of its partial fractions	HELM Partial Fractions	MathCentre Partial Fractions	Integration using Partial Fractions
Integration by Substitution	make simple substitutions in order to find definite and indefinite integrals understand the technique used for evaluating integrals of the form f'(x)/f(x)dx use partial fractions to express an algebraic fraction in a simpler form and integrate it	HELM Int by Substitution	MathCentre Int by Substitution	Integration by Substitution
Integration by Parts	decide when it is appropriate to use the method known as integration by parts apply the formula for integration by parts to definite and indefinite integrals perform integration by parts repeatedly if appropriate	HELM Int by Parts	MathCentre Int by Parts	Integration by Parts

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Last updated: 9 May 2012