Study Notes
Calculus involves understanding how variables change and using differentiation to find gradients, rates of change, and stationary points on graphs. It applies to practical problems like linear kinematics.
- Variable Rate of Change — The rate at which a quantity changes over time. Example: The speed of a car increasing as it accelerates.
- Differentiation — The process of finding the derivative of a function. Example: Finding the derivative of x² gives 2x.
- Stationary Point — A point on a graph where the gradient is zero. Example: The top of a hill on a graph where the slope flattens out.
- Maximum and Minimum Points — Points where the function reaches its highest or lowest value. Example: The peak of a mountain (maximum) or the bottom of a valley (minimum) on a graph.
Exam Tips
Key Definitions to Remember
- Differentiation is finding the derivative of a function.
- A stationary point is where the gradient is zero.
- Maximum and minimum points are where the function reaches its highest or lowest value.
Common Confusions
- Confusing the gradient of a tangent with the gradient of the curve.
- Misidentifying maxima and minima without considering the graph's shape.
Typical Exam Questions
- What is the derivative of x²? The derivative is 2x.
- How do you find the gradient of a curve at a point? Use the gradient of the tangent at that point.
- What is a stationary point? A point where the gradient is zero.
What Examiners Usually Test
- Ability to differentiate functions correctly.
- Identifying and classifying stationary points.
- Applying calculus to solve practical problems.