Overview
This lecture reviews key topics for the Edexcel Higher Paper 2 in GCSE Maths, covering concepts such as algebra, geometry, trigonometry, graph transformations, ratio, proportion, statistics, and Venn diagrams as outlined in a revision checklist.
Error Intervals and Bounds
- Error intervals use inequalities to show upper/lower bounds for rounded/truncated numbers.
- For rounding, lower bound is inclusive, upper is exclusive (e.g. 6.35 ≤ x < 6.45).
- Truncating means chopping off digits, not rounding; adjust intervals accordingly.
Algebra: Indices, Expanding, and Factorising
- Index laws: Add powers when multiplying, subtract when dividing, multiply powers in brackets.
- Simplify algebraic fractions by dividing coefficients and subtracting powers.
- Expand brackets by distributing terms; collect like terms when simplifying.
- Factorise by taking out common factors; for quadratics, find two numbers that multiply to c and add to b.
Solving Equations & Worded Algebra Problems
- Isolate variables by reversing operations; write solutions as fractions or decimals if not exact.
- For unknowns on both sides, move terms to one side to solve.
- Translate word problems into algebraic equations (define variables, relate ages or sums).
Geometry: Perimeter, Area, and Transformations
- Add expressions for perimeter; set equal when perimeters are related.
- Work with transformations: translation (vector notation), reflection (lines x= or y=), rotation, enlargement (scale factor and center—negative factors flip shapes).
Coordinate Geometry & Graphs
- Equation of a line: y = mx + c; parallel lines have equal gradients (m).
- Solve quadratic inequalities by factoring or graph analysis; represent solution intervals.
- Function notation: f(x), inverse functions (swap x/y, rearrange), and composite functions (substitute one into another).
Trigonometry & Graphs
- Draw sine, cosine, tangent graphs by plotting values; recognize key patterns and symmetries.
- Apply graph transformations: inside brackets affects x, outside affects y; negatives reflect over axes.
- Use sine/cosine rules for non-right angled triangles to find missing sides/angles.
Ratio, Proportion, and Currency
- Solve ratio problems by finding value per part.
- Direct and inverse proportion: Use appropriate formula (e.g. a = kb or a = k/b).
- Convert currencies using exchange rates; decide to multiply or divide based on required units.
Statistics & Probability
- Draw and interpret box plots: identify medians, quartiles, spread (IQR).
- Compare box plots using median and IQR for context-based conclusions.
- Use Venn diagrams for sets, unions (U), intersections (n), and complements (dash or ‘not in’).
Applied and Problem-Solving Questions
- Composite volume: split cross-sections into simpler shapes, sum areas, and multiply by depth.
- Capture-recapture: set up proportional equations to estimate totals.
- Interpret and fill Venn diagrams using given totals and overlaps; use algebra if overlaps are unknown.
Key Terms & Definitions
- Error Interval — Range of possible values after rounding/truncating.
- Index law — Rules for manipulating exponents.
- Translation — Shifting a shape by a vector.
- Enlargement — Resizing a shape from a center by a scale factor.
- Gradient (m) — Slope of a straight line.
- Inverse Function — Reverses the operation of a function.
- Composite Function — Applying one function to the result of another.
- Sine/Cosine/Tangent Rule — Formulas for missing sides/angles in triangles.
- Direct/Inverse Proportion — Relationships where one quantity increases or decreases with another.
- Interquartile Range (IQR) — Middle 50% spread in data.
- Venn Diagram, Union (U), Intersection (n), Complement (dash) — Set notation for probability/statistics.
Action Items / Next Steps
- Review full lessons for topics you feel less confident about using provided links.
- Practice similar exam questions, especially for transformations and functions.
- Complete any assigned revision checklists and worksheets.
- Prepare for Paper 3 by checking the release date and reviewing Paper 1 if needed.