IGCSE Further Pure Mathematics revision checklist

International GCSE · Pearson Edexcel 4PM1

Getting started

• Algebra fluency: expanding and factorisingLesson →
• Algebra fluency: solving equationsLesson →
• Algebra fluency: indices, algebraic fractions and formulaeLesson →

1 Logarithmic functions and indices

• Exponential and logarithmic graphsLesson →
• Laws of logarithmsLesson →
• Change of base and solving equationsLesson →
• Surds and rationalising the denominatorLesson →

2 The quadratic function

• Factorising and completing the squareLesson →
• The discriminantLesson →
• Sum and product of rootsLesson →
• Forming equations from rootsLesson →

3 Identities and inequalities

• Algebraic divisionLesson →
• The factor and remainder theoremsLesson →
• Simultaneous equations and cubic equationsLesson →
• Linear and quadratic inequalitiesLesson →
• Regions and linear programmingLesson →

4 Graphs

• Graphs of polynomials and rational functionsLesson →
• Solving equations with graphsLesson →

5 Series

• Sigma notationLesson →
• Arithmetic seriesLesson →
• Geometric series and sum to infinityLesson →

6 The binomial series

• Binomial expansion for positive whole nLesson →
• Binomial series for any rational nLesson →

7 Scalar and vector quantities

• Vectors: components, magnitude and unit vectorsLesson →
• Vectors in geometryLesson →

8 Rectangular Cartesian coordinates

• Distance and dividing a lineLesson →
• Straight lines, parallel and perpendicularLesson →

9 Calculus

• Differentiating powers, sin, cos and eˣLesson →
• Product, quotient and chain rulesLesson →
• Integration and areasLesson →
• Volumes of revolutionLesson →
• Calculus in kinematicsLesson →
• Stationary points, maxima and minimaLesson →
• Tangents and normalsLesson →
• Rates of change and small changesLesson →

10 Trigonometry

• Radians, arcs and sectorsLesson →
• Trigonometric ratios of any angleLesson →
• Sine rule, cosine rule and 3D problemsLesson →
• Trigonometric identities and addition formulaeLesson →
• Solving trigonometric equationsLesson →