This course, offered by Imperial College London, is expertly designed to significantly develop skills needed for excelling in A-level maths exams. Through an in-depth exploration of essential mathematical concepts, the course enhances problem-solving capabilities and mathematical reasoning essential for A-level success.

  • Applying calculus to solve kinematics and motion problems in both one and two dimensions.
  • Utilizing both calculus and vector methods to solve complex projectile motion scenarios.
  • Applying the standard model of friction in practical contexts.
  • Understanding and calculating moments to solve statics problems involving rigid bodies.
  • Using Normal distribution for continuous data modeling and hypothesis testing.
  • Vector addition, subtraction, and scalar multiplication in mathematical problems.
  • Differentiation and integration techniques to solve various mathematical problems.
  • Solving differential equations and interpreting their solutions.

No specific prerequisites are required, making this course ideal for anyone with a general interest in mathematics and its applications in real-world scenarios.

  • Calculus applied to motion and kinematics.
  • Solving real-world problems using friction models.
  • Analyzing the equilibrium of rigid bodies.
  • Detailed techniques in vector mathematics.
  • Advanced methods in differentiation and integration.
  • Practical application of differential equations.

This course is geared towards students preparing for their A-level maths exams, educators seeking to enhance their teaching methodologies, or anyone interested in advanced mathematics and its applications.

Skills learned in this course are immensely beneficial in various fields including engineering, economics, physical sciences, and computer science. Understanding and applying these mathematical concepts can lead to better problem-solving skills, logical reasoning, and analytical abilities in professional and academic settings.

Module 1: Calculus in Kinematics and Projectile Motion

  • Detailed exploration of calculus for motion in both one and two dimensions.
  • Application of calculus in modeling projectile motion using vectors.

Module 2: Friction, Moments and Equilibrium

  • Study of friction models and their application in real-world scenarios.
  • Detailed analysis of moments and their applications in static contexts.

Module 3: The Normal Distribution

  • Comprehensive coverage of Normal distribution as a model for continuous data.
  • Techniques for conducting hypothesis tests using the Normal distribution.

Module 4: Vectors

  • Intensive study of vector operations and their applications in mathematics.

Module 5: Differentiation Methods

  • Advanced differentiation techniques such as the product rule, quotient rule, and chain rule.

Module 6: Integration Methods

  • Integration techniques including substitution, integration by parts, and usage of partial fractions.

Module 7: Differential Equations

  • Techniques for solving first order differential equations and interpreting their solutions.