# 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
• factorise quadratic expressions (Sections 3-5)
Algebraic Fractions
• add, subtract, multiply and divide algebraic fractions
HELM Algebriac Fractions MathCentre Simplify Fractions Algebraic Fractions
Trigonometric Ratios
• define trigonometric functions both in right-angled triangles
• express angles in degrees and 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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