AQA GCSE Maths Higher Non-Calculator Paper Overview

Introduction

• Complete paper walkthrough in under 25 minutes.
• Tips: Pause before attempting questions.

Key Questions and Solutions

Question 1: Fractions and Vectors

• Equivalent to 4.75:
  • 5 = 20/4 → 19/4 is the answer.
• Vector Representation of 'a':
  • 3 to the right, 2 down → (3, -2).
• Square and Cube Number:
  • A million (1000² and 100³).
• Reciprocal of 5/6:
  • Flip ⇒ 6/5.

Trigonometry

• Angle X using Cosine:
  • cos(x) = 9/18 = 1/2.
  • Use 30-60-90 triangle, 60° is the angle.

Scatter Graphs

• Correlation:
  • Graph A: Strong negative correlation.
  • Graph B: No correlation.

Venn Diagrams

• 80 People in Bands:
  • Singers not guitar players: 12.
  • Neither: 30.
  • Quarter of guitar players are also singers.
  • Diagram calculations provided.

Geometry

• Parallelogram Side Length:
  • Shorter side = 1/9 of perimeter.
  • Perimeter = 58.5 cm.
  • Longer side = 22.75 cm.

Sequences

• Geometric Progression:
  • Multiply by 4 between terms.
  • First and third terms: 2 and 8.
• Arithmetic Progression:
  • Add/subtract between terms.
  • Solved for P, P = 6.

Ratio and Proportions

• Holiday Cost:
  • Total = £2400. Ratio: 3:5 (deposit: monthly payments).
  • Monthly payments = £250.

Decimals

• Fraction to Decimal:
  • Use given conversion to calculate others.

Geometrical Shapes

• Wire Earring Length:
  • Circle radius = 21.
  • Quarter circle radius = 6.
  • Total length = 45π + 12.

Algebra

• Double Bracket Expansion:
  • Use comparing coefficients.
  • Smallest positive value for K: 3.

Quadratic Errors

• Correcting Solutions:
  • X = 7 is correct.
  • X = -2, not positive 2.

Indices and Roots

• Indices Laws Simplification:
  • Combine terms using indices laws.
• Cube Root Simplification:
  • Simplified to integer form.

Ratios

• Ratio of X to Y:
  • Derived from equations.

Iteration

• U2 and U3 Calculation:
  • U2 = 0.5, U3 = -8.

Graph Interpretation

• Formula Derivation:
  • Linear graph: Y = 3n + 20.

Simultaneous Equations

• Solving without Substitution:
  • Find X = 0.5, Y = -2.5.

Expressions

• Expression Simplification:
  • Find equivalent expressions.
• Power Zero Rule:
  • Any number to power zero = 1.

Order of Size

• Approximation:
  • Convert to decimals.

Proportionality

• Direct and Inverse Proportions:
  • Establish formulas using given conditions.

Cyclic Quadrilateral

• Proof of Non-Cyclic:
  • Opposite angles not adding to 180°.

Trigonometric Identities

• Sin and Cos between 90°-180°:
  • Determine true statements using graphs.

Histogram Completion

• Missing Bar Calculation:
  • Class width calculations, adjust height accordingly.

Rationalizing the Denominator

• Expression Simplification:
  • Multiply by root to simplify.

Advanced Algebra

• Surface Area and Volume Ratios:
  • Use area scale factor.
• Cubic Functions and Translation:
  • Expansion of cubic functions for translated graphs.

Conclusion

• Comprehensive paper review covering essential patterns and methods for solving higher-level GCSE math problems.