AQA GCSE Higher Paper 2 Maths Lecture Notes

Overview

• Focus on solving a variety of maths problems using a calculator.
• Recommended approach: attempt each question before reviewing solutions provided in the lecture.

Key Topics Covered

Basic Maths Problems

• Form Conversion:
  • Example: Convert 30/12 into a simplified form (2.5).
• Triangular Numbers:
  • Given sequence: 6, 10, 15, 21. Next number by pattern (add 4, 5, 6, 7) = 28.
• Reciprocal:
  • Reciprocal of 4/7 is 7/4.

Percentage and Proportion

• Price Increase Problem:
  • Problem: Toy price increases by 12.5% to £19.53. Find original price.
  • Solution: Calculate original price using percentages.

Coin Problems

• Counting Coins:
  • Given different coins and total amount, solve for specific coin counts.
• Simplifying Ratios:
  • Example: Given a total and parts, simplify the ratio.

Geometry and Angles

• Polygon Angles:
  • Exterior angles of a polygon add up to 360 degrees. Example of finding exterior angle in octagon.

Probability

• Game Scenarios:
  • Dice and spinner game: Calculate probability of certain outcomes.

Algebra

• Co-efficient Problems:
  • Expand expressions and solve for unknowns (e.g., ax and bx values).
• Translation Vectors:
  • Identify movement in translation (e.g., 4 right, 3 down).

Volume and Surface Area

• Volume Calculation:
  • Calculate volume of a hemisphere and assess capacity.

Similar Shapes

• Prove Similarity:
  • Use scale factors to prove two rectangles are similar.

Complex Algebra

• Equation Rearrangement:
  • Solve to make a particular variable the subject of an equation.

Sequences

• Quadratic Sequences:
  • Work out expressions for nth term using the sequence of differences.

Circle Theorems

• Angle Calculations:
  • Use center and circumference relationships to find angles.

Finance

• Compound Interest:
  • Calculate minimum interest rate to reach a future value using the compound interest formula.

Iterative Methods

• Convergence:
  • Use iteration to find approximate solutions to equations.

Combinatorics and Probability

• Card Game Probabilities:
  • Assess chances of winning with different strategies.

Bounds and Approximations

• Upper and Lower Bounds:
  • Calculate bounds for expressions to find maximum or minimum possible values.

Simplifying Expressions

• Fractions and Simplification:
  • Simplify complex fraction expressions to identify constants.

Transformations

• Graphical Transformations:
  • Identify transformations such as vertical shifts and reflections on graphs.

Conclusion

• The paper covers a broad range of topics, emphasizing problem-solving skills in algebra, geometry, probability, and calculus using a calculator.
• Students should focus on understanding fundamental concepts and practicing with similar questions for better preparation.