IGCSE 0607 Maths Crash Course Notes

Overview

• Focus on 10 main topics for IGCSE 0607 Maths
• Master these topics to excel in exams (60-70% of questions)

1. GDC Skills

• Function: f(x) = x³ - 5x + 3
  • Sketching: Adjust window settings (-3 to 3, -10 to 15)
  • Identify intersections: 3 crossings on x-axis, 1 on y-axis
  • Minimum point coordinates:
    • Use GDC to find minimum, report in 3 significant figures (1.29, -1.30)
  • Describe symmetry:
    • Rotational symmetry (order 2) around the y-intercept (0, 3)
  • Solve equations using GDC:
    • Find intersection points with g(x) = 2x - 1
    • Report x-values (e.g., -2.90, 0.603, 2.29)
  • Inequalities:
    • Determine intervals where f(x) > g(x)

2. Statistics

• Mean mark estimation from grouped data
  • Calculate midpoints for categories
• Cumulative frequency:
  • Build cumulative frequency table
  • Plot graph for median and interquartile range calculations
  • Median estimation:
    • Interpolate between values on cumulative frequency graph
  • Interquartile range:
    • Find lower and upper quartiles from cumulative frequency graph
  • Passing marks estimation:
    • Determine minimum marks needed for passing

3. Coordinate Geometry

• Finding lengths and equations of lines
  • Use Pythagoras' theorem to find lengths
  • Equation of line: y = mx + c
• Perpendicular bisectors and gradients
  • Find equations for perpendicular lines
  • Identify intersection points of lines

4. Probability

• Tree diagrams for probability calculations
  • Calculate probabilities for events with replacement
  • Combine probabilities to find total probabilities for different scenarios

5. Percentage Calculations

• Reverse percentage problems
  • Calculate new prices from reduced prices
• Interest calculations (simple and compound)

6. Transformations

• Understand different transformation types: translation, reflection, rotation, stretch
  • Describe transformations accurately for marks

7. Functions

• Working with composite and inverse functions
  • Substitute values into functions
  • Solve function equations systematically

8. Sine & Cosine Rule, Bearings

• Solve triangles using sine and cosine rules
  • Work with bearings to find angles and lengths

9. Proportionality and Variation

• Understand direct and inverse variation
  • Set up proportionality statements
  • Solve for unknowns using initial conditions

10. Volume, Surface Area, and Similarity

• Calculate volumes of solids (cones, frustums)
  • Use similarity ratios to determine missing lengths
• Find areas of circular bases and curved surfaces

Conclusion

• Review each topic thoroughly
• Practice exam questions and past papers for better preparation
• Use the provided resources for deeper learning.