IGCSE 0607 Mathematics Crash Course Notes

Introduction

• Focus on 10 main topics that appear every year in IGCSE 0607 Mathematics.
• Mastering these topics prepares you for 60-70% of questions in the course.

1. GDC Skills

• Function Example: f(x) = x³ - 5x + 3
• Graphing Steps:
  • Input function into GDC (Graphing Display Calculator).
  • Adjust window settings to fit the question scale.
  • Identify cubic shape crossing points: crosses x-axis three times; y-axis once.
• Local Minimum Point:
  • Use GDC to analyze graph, find local min coordinates.
  • Round to three significant figures.
• Rotational Symmetry:
  • Identify and describe symmetry: rotational symmetry of order 2, center at (0, 3).
• Intersection with Linear Function:
  • For g(x) = 2x - 1, find intersection points using GDC.
  • Report x-values for each intersection accurately.
• Inequality Solutions:
  • Determine where f(x) > g(x) using intersection points.

2. Statistics

• Mean Calculation:
  • Use midpoints for grouped data (e.g., 0-10, 10-20).
  • Check class widths carefully to avoid errors.
• Cumulative Frequency Table:
  • Calculate running total cumulatively.
  • Verify with total count at end.
• Cumulative Frequency Graph:
  • Plot points accurately and connect with a smooth curve.
• Median and Quartiles:
  • Use cumulative frequency graph to estimate median and interquartile range.

3. Coordinate Geometry

• Length Calculation:
  • Use Pythagorean theorem for length between two points.
• Equation of a Line:
  • Find gradient and y-intercept to write line equation.
• Perpendicular Line:
  • Find slope of perpendicular line and write its equation.
• Intersection of Lines:
  • Set equations equal to find intersection point.

4. Probability

• Tree Diagrams:
  • Construct tree diagrams for events (e.g., drawing balls from bags).
• Calculating Probabilities:
  • Multiply probabilities along branches.
  • Use complementary probabilities where appropriate.
• Different Colors Problem:
  • Approach using total probability calculations.

5. Percentage Calculations

• Reverse Percentage Problems:
  • Set up equations to find original price based on given percentage.
• Loan Options:
  • Calculate total costs for different payment options, include interest calculations.

6. Transformations

• Translation:
  • Describe translations using vectors based on point movements.
• Reflections and Rotations:
  • Identify axes or points of reflection and the center of rotation.
• Stretch:
  • Describe stretch transformation, including scale factors and invariant lines.

7. Functions

• Function Evaluation:
  • Substitute values into functions correctly.
• Composite Functions:
  • Work from right to left; substitute step-by-step.
• Inverse Functions:
  • Swap x and y and solve for y to find inverse.

8. Sine and Cosine Rule / Bearings

• Right Angle Triangles:
  • Use basic trigonometry to solve for sides and angles.
• Cosine Rule:
  • Apply to find unknown angles in non-right triangles.
• Bearings:
  • Always measure clockwise from the north.

9. Proportionality / Variation

• Direct and Inverse Proportionality:
  • Set up proportionality statements and solve for constants.
• Variable Manipulations:
  • Substitute known values to find other unknowns.

10. Volume, Surface Area, and Similarity

• Volume of Shapes:
  • Use formulae for cones, cylinders, and frustums.
• Similarity in Shapes:
  • Establish scale factors and use them to find missing dimensions.
• Surface Areas:
  • Calculate curved and total surface areas based on shapes involved.

Conclusion

• Review of key topics provides a comprehensive overview for IGCSE 0607 Math preparation.
• Practice problems related to these topics for better understanding and proficiency.