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Revise Edexcel GCSE (9-1) Mathematics Higher Revision Guide


Synopsis


Harry Smith

Summary

Chapter 1: Number

* Understand number systems: Decimal, binary, hexadecimal
* Simplify expressions: Expand, factorize, use BIDMAS
* Solve equations and inequalities: Linear, quadratic, simultaneous

Example: Solve 2x - 5 = 11. Answer: x = 8

Chapter 2: Algebra

* Manipulate algebraic expressions: Addition, subtraction, multiplication, division
* Solve equations and inequalities: Linear, quadratic, cubic
* Expand and factorize: Trinomials, quadratics, cubes

Example: Expand (2x + 3)(x - 1). Answer: 2x^2 + x - 6

Chapter 3: Ratio, Proportion, and Rates of Change

* Understand ratios and proportions: Equivalent fractions, scale factors
* Solve problems involving ratio, proportion, and rates of change: Simplifying, finding missing values
* Draw graphs of linear functions: Using the equation y = mx + c

Example: A map has a scale of 1:50,000. If the distance on the map between two points is 3 cm, find the actual distance. Answer: 1.5 km

Chapter 4: Geometry and Measures

* Measure and calculate angles: Using a protractor, trigonometry
* Find areas and volumes: Triangles, quadrilaterals, circles, spheres
* Pythagoras' Theorem: Calculating lengths in right-angled triangles

Example: A rectangular garden has a length of 5 m and a width of 3 m. Find its area. Answer: 15 m^2

Chapter 5: Probability

* Understand probability: Definitions, sample space
* Calculate probability: Theoretical, experimental
* Conditional probability and mutually exclusive events: Venn diagrams

Example: A bag contains 4 red marbles, 5 blue marbles, and 3 yellow marbles. What is the probability of drawing a blue marble? Answer: 5/12

Chapter 6: Statistics

* Summarize data: Mean, median, mode, range
* Draw and interpret graphs: Bar charts, pie charts, line graphs
* Estimate and interpret gradients: Finding the rate of change

Example: A survey of 100 students found the following data: Mean age = 15 years, Median age = 16 years, Mode age = 16 years, Range = 5 years.