Maths · AQA Paper 2
Functions, Sequences and Rates of Change
The further graph and algebra skills tested on AQA Paper 2: functions and inverse functions, geometric sequences, iteration, gradients and areas under graphs, and transformations of graphs.
Lessons
Ticks are remembered on this device only.
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1
Functions and Function Notation
Using f(x) notation, composite functions such as fg(x), and inverse functions.
9 terms -
2
Geometric and Special Sequences
Recognising geometric and Fibonacci-type sequences, and finding the common ratio from two terms.
9 terms -
3
Iteration
Using iterative formulae, rearranging equations, and finding roots by a change of sign and trial and improvement.
9 terms -
4
Rates of Change and Areas Under Graphs
Finding gradients of curves with tangents, average rates of change, and estimating areas under graphs with trapezia.
9 terms -
5
Transformations of Graphs
Sketching and describing translations and reflections of graphs, including trigonometric graphs.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- Function
- A rule that gives one output for each input.
- Function notation
- Writing a function as \(f(x)\).
- Input
- The value put into a function.
- Output
- The value that comes out of a function.
- Composite function
- One function applied after another.
- Inverse function
- A function that reverses another function.
- Subject
- The letter on its own on one side of an equation.
- Substitute
- Replace a letter by a number or expression.
- Domain
- The set of allowed input values.
- Geometric sequence
- A sequence with a common ratio between terms.
- Common ratio
- The number each term is multiplied by.
- Term-to-term rule
- A rule that gives each term from the one before it.
- Fibonacci-type sequence
- A sequence where each term is the sum of the two before.
- Triangular numbers
- The sequence 1, 3, 6, 10, 15, and so on.
- Square numbers
- The numbers 1, 4, 9, 16, and so on.
- Cube numbers
- The numbers 1, 8, 27, 64, and so on.
- Arithmetic sequence
- A sequence with a common difference between terms.
- Surd
- A root that cannot be written as a whole number or fraction.
- Iteration
- A process that is repeated, using each output as the next input.
- Iterative formula
- A formula that gives the next value from the current one.
- Limit
- The value that the terms of an iteration approach.
- Root
- A solution of an equation \(f(x) = 0\).
- Change of sign
- The function is negative at one value and positive at another.
- Continuous
- A graph with no breaks or gaps.
- Trial and improvement
- Testing values to find a solution to a given accuracy.
- Converge
- To get closer and closer to a value.
- Starting value
- The first input of an iteration.
- Tangent
- A straight line that touches a curve at one point.
- Chord
- A straight line joining two points on a curve.
- Gradient
- A measure of the steepness of a line.
- Rate of change
- How quickly one quantity changes compared with another.
- Average rate of change
- The gradient of the chord between two points.
- Trapezium
- A quadrilateral with one pair of parallel sides.
- Estimate
- An approximate answer.
- Overestimate
- An estimate that is larger than the true value.
- Underestimate
- An estimate that is smaller than the true value.
- Transformation
- A change to the position or shape of a graph.
- Translation
- A movement of a graph without turning or flipping it.
- Reflection
- A flip of a graph in a line, such as an axis.
- Turning point
- A point where a graph changes from rising to falling, or the reverse.
- Intercept
- A point where a graph crosses an axis.
- Function notation
- Writing a function as \(f(x)\).
- Vector
- A pair of numbers that gives a movement.
- Maximum
- The highest point of a graph.
- Minimum
- The lowest point of a graph.