Maths Grade 6-9 Revision Summary

Introduction

• The focus is on achieving grades 6 to 9 in math GCSE.
• Review content previously covered for grade 5.
• Conduct a personal subject analysis to ensure coverage of all topics.

Key Topics and Techniques

1. Indices

• Fractional Negative Indices:
  • Negative indices indicate reciprocals.
  • Fractional indices indicate roots and powers.
  • Simplify by flipping, rooting, then powering.

2. Bounds

• Error Intervals:
  • Calculate upper and lower bounds.
  • For maximum results in fractions, divide the upper bound by the lower bound.

3. Recurring Decimals

• Converting to Fractions:
  • Use algebraic methods.
  • Multiply out decimals to eliminate repeating parts.
  • Simplify final fractions.

4. Compound Interest

• Calculating Compound Interest:
  • Use formulas to determine growth over multiple interest periods.
  • Reverse calculations if necessary to find missing rates.

5. Sirds (Surds)

• Simplifying Sirds:
  • Rationalize denominators using conjugates.
  • Simplify expressions by multiplying out brackets and combining terms.

6. Standard Form

• Multiplying/Dividing in Standard Form:
  • Multiply/divide coefficients.
  • Add/subtract exponents.
  • Adjust format to maintain proper standard form.

Geometry and Trigonometry

7. Algebra

• Expanding Triple Brackets: Combine terms carefully.
• Factorization: Manage coefficients greater than one.
• Rearranging Formulae: Solve for specific variables.

8. Sequences

• Quadratic Sequences:
  • Recognize quadratic sequences by second differences.
  • Formulate nth terms using square numbers.

9. Graphs and Functions

• Completing the Square: Find vertex form for turning points.
• Simultaneous Equations: Solve graphical intersections algebraically.

10. Inequalities

• Quadratic Inequalities:
  • Identify regions above/below x-axis based on sign.
  • Solving involves finding roots and determining applicable sections.

11. Circle Theorems

• Tangent and Radius: Tangents are perpendicular to radii.
• Alternate Segment Theorem: Angles in alternate segments.

Probability & Statistics

12. Statistics

• Box Plots: Compare medians and interquartile ranges.
• Cumulative Frequency: Construct graphs to find medians and quartiles.
• Histograms: Calculate frequency density for uneven class widths.

13. Probability

• Tree Diagrams: Use for multi-step events, calculate conditional probabilities.
• Venn Diagrams: Organize complex relationships and intersections.

Advanced Topics

14. Algebraic Proofs

• Proof Techniques:
  • Use known identities and algebraic manipulation.
  • Show relationships and constants.

15. Transformations

• Coordinate Geometry: Describe transformations algebraically.
• Enlargements and Similar Shapes: Calculate scale factors and solve for unknowns.

Final Remarks

• Ensure to revise topics thoroughly.
• Engage in subject analysis to identify weak areas.
• Share resources and subscribe for regular updates.