AQA GCSE Maths Higher Non-Calculator Paper Review

Introduction

• Covering a higher AQA paper in under 25 minutes.
• Advice: pause video to attempt questions before resuming.
• Aim: Save revision time by efficient problem-solving strategies.

Key Questions and Solutions

Fractions and Vectors

• Equivalent Fraction: 4.75 can be expressed as (\frac{19}{4}).
• Column Vector A: Moves 3 right, 2 down → ((3, -2)).

Numbers and Reciprocals

• Square & Cube Number: A million ((1000^2 = 100^3)).
• Reciprocal: Flip (\frac{5}{6}) to (\frac{6}{5}).

Trigonometry

• Angle X: Using cosine, (\cos(X) = \frac{9}{18} = \frac{1}{2}). Angle is 60 degrees.

Correlations in Graphs

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

Venn Diagrams

• Information: 80 people, 12 singers only, 30 neither.
• Solution: Venn diagram calculations result in 11 for both, remaining 33 only guitar players.

Parallelograms

• Length Calculation: Shorter side = 6.5 cm, (\frac{1}{9}) of perimeter.
• Longer Side: Final calculated length is 22.75 cm.

Progressions

• Geometric Progression: First term 2, Third term 8.
• Arithmetic Progression: (p = 6).

Ratio and Payments

• Holiday Cost: Deposit and payments are in ratio; calculations lead to £250 monthly payment.

Decimals

• Fraction Decimals: (\frac{33}{400}) as 0.0825.

Geometry and Circles

• Earring Problem: Radius of quarter circle shown as 6mm; total length is (45\pi + 12).

Algebra and Quadratics

• Quadratic Solution: First solution is correct; second solution requires correct substitution.

Indices and Roots

• Simplified Indices: (2^{11} \times 3^3 \times 5^6).
• Cube Root: Simplified as 44.

Equations and Ratios

• Ratio of x to y: Calculated as 6:1.

Iterative Sequences

• Iteration Values: U2 = 0.5, U3 = -8.

Graphs and Functions

• Graph Formula: Height formula (H = 20 + 3n).

Simultaneous Equations

• Solution: X = 0.5, Y = -2.5.

Simplification and Expressions

• Algebra: Expression results in (\frac{3x}{10}).

Powers and Order of Magnitude

• Power Zero: Expression with zero power equals one.
• Order: Approximated values for ordering.

Proportional Relationships

• Direct Proportionality: Equation from Y and X.
• Inverse Proportionality: Analysis through scenarios.

Cyclic Quadrilateral

• Proof: Verified and determined not cyclic by counterexample.

Trigonometry Graphs

• Sin/Cos Analysis: Determining value characteristics by angle.

Histograms

• Missing Bar Calculations: Height determined at 1.4.

Rationalization

• Rational Form: Simplified to (\frac{14\sqrt{7}}{7}).

Multiplication of Roots

• Root Products: Final calculated integer is 240.

Similar Cylinders

• Surface Area Ratios: Curved surface area maintains 9:25, height at 3:5.

Quadratic Factorization

• Difference of Squares: Simplified to squared terms.

Graph Translation

• Function Equation: Translated graph as (f(x) = x^3 - 12x^2 + 48x - 58).

Conclusion

• Complete walkthrough of AQA higher paper with emphasis on quick problem-solving techniques.