Sequences and series

Subtopics:

• Sequences and how to specify them
• Arithmetic sequences
• Geometric sequences
• Solving problems involving APs and GPs
• Adding up the terms of a sequence
• Summing an arithmetic series
• Summing a geometric series
• The limiting sum of a geometric series
• Recurring decimals and geometric series

Graphs and equations

Subtopics:

• The sign of a function
• Vertical and horizontal asymptotes
• A curve‐sketching menu
• Solving inequations
• Using graphs to solve equations and inequations
• Review of translations and refl ections
• Dilations
• Combinations of transformations
• Trigonometric graphs

Curve‐sketching using the derivative

• Increasing, decreasing and stationary at a point
• Stationary points and turning points
• Second and higher derivatives
• Concavity and points of infl ection
• Systematic curve sketching with the derivative
• Global maximum and minimum
• Applications of maximisation and minimisation
• Primitive functions

Integration

Subtopicss:

• Areas and the defi nite integral
• The fundamental theorem of calculus
• The defi nite integral and its properties
• Challenge – proving the fundamental theorem
• The indefi nite integral
• Finding areas by integration
• Areas of compound regions
• The trapezoidal rule
• The reverse chain rules

The exponential and logarithmic functions

Subtopics:

• Review of exponential functions base e
• Differentiation of exponential functions
• Applications of differentiation
• Integration of exponential functions
• Applications of integration
• Differentiation of logarithmic functions
• Applications of differentiation of log e x
• Integration of the reciprocal function
• Applications of integration of 1 / x
• Calculus with other bases

The trigonometric functions

Subtopics:

• The behaviour of sin x near the origin
• Differentiating the trigonometric functions
• Applications of differentiation
• Integrating the trigonometric functions
• Applications of integration

Motion and rates

• Average velocity and speed
• Velocity and acceleration as derivatives
• Integrating with respect to time
• Rates and differentiation
• Rates and integration
• Exponential growth and decay

Series and finance

• Applications of APs and GPs
• The use of logarithms with GPs
• Simple and compound interest
• Investing money by regular instalments
• Paying off a loan

Displaying and interpreting data

• Displaying data
• Grouped data and histograms
• Quartiles and interquartile range
• Bivariate data
• Formulae for correlation and regression
• Using technology with bivariate data

Working with time

• Units of time
• Timetables
• Latitude and longitude
• Time zones
• Time difference and local time

Continuous probability distributions

• Relative frequency
• Continuous distributions
• Mean and variance of a distribution
• The standard normal distribution
• General normal distributions
• Applications of the normal distribution
• Investigations using the normal distribution