GCSE Maths Paper 1 Higher Tier Revision

Introduction

• Focus on higher tier content for GCSE Maths Paper 1
• Additional resources: booklet, revision guide, checklist
• Personalized revision plan available through rapid revision program

Key Topics Covered

Reverse Percentages

• Problem: Determine original price before VAT
• Example: Price after 20% VAT is £600
  • Calculation: 120% = £600, find 100% by scaling down
  • Result: Original price is £500

Fraction Calculations

• Mixed numbers to improper fractions
• Find common denominators for operations
• Example: 21/5 - 8/3 results in 23/15

Recurring Decimals to Fractions

• Convert 0.73... to a fraction using algebra
• Multiply by 10 to eliminate recurring part
• Simplify to 11/15

Prime Factors and Lowest Common Multiple (LCM)

• Factor trees for prime factorization
• LCM through multiplication methods

Indices and Roots

• Negative and fractional indices rules
• Example: Simplifying 81^(-1/2) to 1/9

Surds

• Multiplying and simplifying surds
• Example: Express in form a√10

Standard Form

• Converting between standard form and ordinary numbers
• Calculations with standard form: addition, subtraction, multiplication, division

Expanding and Factorizing

• Single and double brackets
• Triple brackets for more complex expansion
• Factorizing quadratics and algebraic fractions

Simultaneous Equations

• Solving graphical simultaneous equations
• Using quadratic and linear equations

Geometry

Angles and Polygons

• Interior and exterior angles calculations
• Symmetry and ratio relationships

Parallel Lines and Transversals

• Angle rules: corresponding, alternate, and co-interior

Circle Theorems

• Understanding relationships and problem-solving using circle properties

Surface Area and Volume

• Cubes and spheres comparisons
• Using formulas for surface area and volume calculations

Trigonometry and Pythagoras

• Exact trigonometric values: sin, cos, tan
• SOHCAHTOA for triangle side calculations
• Pythagorean theorem applications

Vectors and Proofs

• Vector manipulation and ratio problems
• Proving mathematical statements with algebraic evidence

Ratios and Proportions

Sharing and Combining Ratios

• Adjust ratios for different quantities
• Examples: Packs of pens, houses and bungalows

Proportions

• Direct and inverse proportion applications
• Formula derivation and problem-solving

Probability and Statistics

Probability Tables

• Understanding and calculating probability distributions

Functions

• Finding inverse and composite functions
• Working with functional equations

Cumulative Frequency

• Plotting and interpreting cumulative frequency graphs
• Calculating interquartile range

Mean and Reverse Mean

• Calculating reverse means from given data

Capture-Recapture Method

• Estimating population size using proportional reasoning

These notes condense essential topics and methods required for higher tier GCSE Maths Paper 1. Refer to example problems and practice exercises to reinforce understanding and application of each concept.