Related Rates of Change What is meant by rates of change? A rate of change is a measure of how a quantity is changing with respect to another quantity Mathematically rates of change are derivatives...
Chain Rule What is the chain rule?How do I know when to use the chain rule? How do I use the chain rule? Are there any standard results for using chain rule? Exam Tip You should aim to be able to s...
Differentiating Trig Functions How do I differentiate sin, cos and tan?These last three results can be derived using the chain rule For calculus with trigonometric functions angles must be measured...
Modelling with Differentiation What can be modelled with differentiation? Recall that differentiation is about the rate of change of a function and provides a way of finding minimum and maximum val...
Increasing & Decreasing Functions What are increasing and decreasing functions? How do I find where functions are increasing, decreasing or stationary? To identify the intervals on which a func...
Introduction to Derivatives Before introducing a derivative, an understanding of a limit is helpful What is a limit? What might I be asked about limits?What is a derivative? How are limits and deri...
Transition Matrices What is a transition matrix? A transition matrix T shows the transition probabilities between the current state and the next state The columns represent the current states The r...
Markov Chains What is meant by a “state”? States refer to mutually exclusive events with the current event able to change over time Examples of states include: Daily weather conditions The states c...
Type I & Type II Errors What are Type I & Type II errors? There are four possible outcomes of a hypothesis test: H0 is false and H0 is rejected H0 is true and H0 is not rejected The test is...
