Overview
This lecture summarizes solutions and key concepts from an AQA GCSE Maths Foundation past paper, focusing on clear methods and concise reasoning for each question.
Basic Calculations & Conversions
- 0.02 × 100 = 2.
- X + X + X = 3X.
- 260 millimeters = 26 centimeters.
- -8 × 5 = -40.
- 4 apples at 35p each = £1.40; remaining £2.30 split across 5 bananas = 46p each.
Geometry & Symmetry
- A trapezium can have all sides different lengths.
- Triangle angles sum to 180°; exterior angle on straight line = 100°.
- Rotational symmetry of order 4: shape repeats 4 times in 360°.
Data & Ratios
- Pictograms: 1 circle = 4; total homework = 39 pieces, 19h 30m total time.
- Mini-bus problem: 159 passengers need 14 mini-buses (each with 12 seats).
- Tally chart criticisms: overlapping groups, not all data accounted for.
- Probability: missing probability = 0.45.
- Password ratio: numbers:letters:symbols = 1:3:2.
Algebra & Expressions
- Combine like terms: 6A - 7B - 2A = 4A - 7B, but if negative two, adjust accordingly.
- Index law: multiply numbers, add powers (3p² × 5p⁷ = 15p⁹).
- Solve: 5x + 6 > 3x + 15 → x > 4.5.
Fractions & Percentages
- Add fractions: common denominator, 5/6 + 1/4 = 17/12 = 1 5/12.
- Percentages: 43% of 2100 = 903.
Graphs & Slopes
- Fixed charge = 20p; gradient (cost per minute) = 8p.
- 7 minutes call: 20p + (8p × 7) = 76p.
Statistics & Averages
- Toffees median = 51 (above 50); mints median = 49 (not above 50).
Standard Form & Calculations
- 2,000 × 70,000 = 1.4 × 10⁸ (standard form).
- (1.8 × 10²) ÷ (3 × 10⁻¹) = 600 (ordinary number).
- Prime factors: 200 = 2³ × 5².
Worded & Multi-step Problems
- Reciprocal graph: y = 1/x.
- Distance problem: total AD = 49 miles.
- Trigonometry (sin 30°): x = 10 × 0.5 = 5 m.
- Factorize: x² + 7x + 10 = (x + 5)(x + 2).
Key Terms & Definitions
- Rotational Symmetry — Shape appears the same more than once as it rotates through 360°.
- Tally/Frequency Chart — Method for grouping and counting data occurrences.
- Index Law — When multiplying, add exponents.
- Median — Middle value in an ordered data set.
- Standard Form — Number written as a × 10ⁿ.
- Prime Factors — Prime numbers that multiply to give the original number.
Action Items / Next Steps
- Practice more past papers under timed, non-calculator conditions.
- Review key formulas: trigonometry, standard form, percentages, and index laws.
- Check criticisms and improvements for presenting data.