Induction Workbook and Scheme of Lessons for Bridging the Gap Between GCSE and A-Level Mathematics

This resource is meticulously designed to support students transitioning from GCSE (9-1) to AS/A Level Mathematics. It serves as a comprehensive guide for students to use independently, featuring detailed examples, explanations, and practice questions on essential topics. Additionally, the workbook includes recommended readings to further prepare students for their A-Level studies.

Workbook Structure:

• Induction Workbook.docx: The main document that outlines the transition guide, providing a robust set of algebra questions and other key topics to reinforce foundational skills necessary for A-Level Mathematics.

• Lesson Folders: Each lesson folder contains specific topics and exercises aimed at bridging the gap from GCSE to A-Level Mathematics.

Lessons Breakdown:

1. Lesson 1:
   • Focus on reinforcing basic algebraic techniques and ensuring students are fluent in manipulating algebraic expressions and equations.
   • Includes exercises on simplifying expressions, solving equations, and understanding algebraic fractions.

2. Lesson 2:
   • Builds on algebraic skills with a focus on more complex algebraic fractions and quadratic expressions.
   • Exercises include factorisation, completing the square, and solving simultaneous equations involving quadratics.

3. Lesson 3:
   • Introduction to advanced algebraic techniques and functions.
   • Students practice manipulating and solving equations involving fractional and negative powers, as well as working with surds.

4. Lesson 4: Pythagoras and Trigonometry:
   • This lesson covers essential trigonometric concepts and equations.
   • Exercises focus on solving trigonometric equations, understanding the unit circle, and applying trigonometric identities.

5. Lesson 5: Equation of a Line:
   • A thorough exploration of linear equations and their graphs.
   • Students learn to convert between different forms of linear equations and practice sketching graphs to understand the relationship between algebraic equations and their graphical representations.

6. Lesson 6: Sketching Graphs:
   • Focuses on developing students’ skills in sketching and interpreting graphs of various functions.
   • Includes exercises on quadratic, cubic, and higher-degree polynomials, as well as hyperbolas and other important functions.