Service Description

It is a 1-3 small group course. Phase 1 Course Overview: Maths GCSE Advanced is a rigorous course designed for students aged 15-16 who are aiming for top grades (Grade 8-9 or A/A*) in their GCSE/IGCSE exams. Students are expected to have a understanding of the core maths topics, as the course will focus on advanced variations and applications of standard questions, fostering a deeper comprehension and broader application of mathematical concepts. Course Objectives: To solidify and deepen students' understanding of advanced mathematical concepts. To develop principled problem-solving skills applicable to a variety of high-level maths problems. To prepare students for achieving top grades in their GCSE/IGCSE exams. To stretch and challenge students, promoting critical thinking and application of maths in broader contexts. Lesson Plan: Lesson 1: Completing the Square Advanced techniques for completing the square. Applying this method to solve quadratic equations and sketch graphs. Lesson 2: Probability Equations Solving complex probability problems involving multiple events. Understanding and using probability equations in various contexts. Lesson 3: Proof Different types of mathematical proofs, including direct, contrapositive, and contradiction. Proving algebraic identities and geometric theorems. Lesson 4: Quadratic Simultaneous Equations Solving simultaneous equations where one or both are quadratic. Applications of these solutions in real-world problems. Lesson 5: Transforming Graphs Understanding transformations including translations, reflections, rotations, and dilations. Applying transformations to various functions and interpreting the results. Lesson 6: Vectors Advanced vector operations, including dot product and cross product. Applications of vectors in geometry and physics. Lesson 7: Velocity-Time Graphs Interpreting and analyzing velocity-time graphs. Calculating acceleration, displacement, and other related quantities. Lesson 8: Perpendicular Lines Understanding and proving the properties of perpendicular lines. Solving geometric problems involving perpendicularity. Lesson 9: Proof of Circle Theorems In-depth exploration of circle theorems. Proving key theorems and solving related problems. Lesson 10: Quadratic Inequalities Solving quadratic inequalities and representing solutions graphically. Applications in various mathematical contexts.