Calculus

Summary and Exam Tips for Calculus

Calculus is a subtopic of Sequences, Functions, and Graphs, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. Calculus focuses on understanding the variable rate of change and involves key concepts like differentiation and stationary points. Differentiation is used to find the gradient of a curve at any point, which is the same as the gradient of the tangent at that point. This process is crucial for determining gradients, rates of change, stationary points, and turning points (maxima and minima). Differentiation can be applied to functions of the form $y = kx^n$, where $x$ is any real value, and $k$ is a constant. In practical applications, calculus is used in linear kinematics to solve problems involving motion. For instance, the gradient of a displacement-time graph gives velocity, while the gradient of a velocity-time graph gives acceleration. Understanding the nature of stationary points helps in identifying whether they are maxima or minima by analyzing the graph's shape. Calculus also aids in solving real-life problems, such as calculating the rate of change of volume in a vessel or the motion of a particle in a straight line.

Exam Tips

• Understand Differentiation: Practice differentiating various functions, especially power functions like $x^n$. Remember, the derivative of $x^n$ is $nx^{n-1}$.

• Stationary Points: Learn to identify stationary points where $f'(x) = 0$. Determine if these points are maxima or minima by analyzing the sign changes of the derivative.

• Graph Interpretation: Be comfortable with interpreting graphs. Know how to find the equation of a tangent line and understand the significance of gradients in motion problems.

• Practical Applications: Apply calculus concepts to solve real-world problems, such as calculating rates of change in kinematics or fluid dynamics.

• Practice Past Papers: Familiarize yourself with the types of questions asked in exams by solving past paper questions. This will help you manage time and understand the exam pattern better.