What this topic covers
Topic 3: Sequences, Functions and Graphs has 3 subtopics:
- Sequences and Series
- Functions, Coordinates and Linear Graphs
- Quadratic and Other Graphs
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IGCSE Edexcel Higher Maths · Topic 6 of 12
Topic 3: Sequences, Functions and Graphs – IGCSE Edexcel Higher Maths revision notes
Choose a subtopic. IGCSE Mathematics A Topic 3: Sequences, Functions and Graphs. 20 lessons in 3 subtopics.
Revise Topic 3: Sequences, Functions and Graphs for IGCSE Edexcel Higher Maths, including Sequences and Series and Functions, Coordinates and Linear Graphs.
20
Lessons
3
Subtopics
Topic 3: Sequences, Functions and Graphs lessons by subtopic
20 lessons, grouped by subtopic.
Sequences and Series
- Generating Sequence Terms
- Triangular, Square and Cube Numbers and Arithmetic Progressions
- Finding the nth Term of Linear Sequences
Functions, Coordinates and Linear Graphs
- Interpreting Expressions as Functions
- Composite and Inverse Functions: Build and evaluate composite functions and identify inverse functions that undo each other.
- Function Notation, Domain and Range: Interpret function notation confidently and identify sensible domains and ranges from algebraic rules and graphs.
- Working with Coordinates in All Four Quadrants
- Plotting Straight-Line Graphs
- Gradients and Intercepts of Linear Functions
- Straight-Line Graph Skills and Gradients
- Transformations of Linear and Quadratic Graphs
Quadratic and Other Graphs
- Turning Points and Symmetry of Quadratics
- Quadratic Graphs - Roots and Intercepts
- Recognising and Sketching Linear and Quadratic Graphs
- Cubic Graphs: Recognise, sketch and interpret simple cubic graphs, including intercepts, turning behaviour and symmetry about the origin.
- Reciprocal and Trigonometric Graphs: Recognise and sketch simple reciprocal and trigonometric graphs, focusing on shape, key points and repeated patterns.
- Interpreting Real-World Graphs
- Interpreting Gradients and Areas Under Graphs
- Differentiating Integer Powers: Differentiate simple powers of x and interpret the derivative as the gradient function of the original graph.
- Gradients and Stationary Points by Differentiation: Use differentiation to find where a curve has zero gradient and classify those stationary points from the graph or the sign of the gradient.
More in this course
Go back to the full IGCSE Edexcel Higher Maths topic list, or practise this topic with past-paper questions.
Frequently asked questions
What is Topic 3: Sequences, Functions and Graphs?
IGCSE Mathematics A Topic 3: Sequences, Functions and Graphs. 20 lessons in 3 subtopics.
How do you use the trapezium rule?
The trapezium rule estimates the area under a curve using equal strips, where the first and last y-values appear once and the middle values are doubled. The Interpreting Gradients and Areas Under Graphs notes cover this in full.
What are triangular numbers?
Triangular numbers are the totals of stacked rows of dots, with one dot in the first row, then two, then three, and so on: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. The Triangular, Square and Cube Numbers and Arithmetic Progressions notes cover this in full.
What does the derivative tell you?
The derivative is the result of differentiation: a new function that gives the gradient of the original function at each point. The Differentiating Integer Powers notes cover this in full.
What is the difference between domain and range?
The domain is the set of input values a function is allowed to take. The Function Notation, Domain and Range notes cover this in full.
How do you find the range from a domain?
Use the allowed inputs to find the outputs they produce. The Function Notation, Domain and Range notes cover this in full.
What is differentiation?
Differentiation is finding a new function that gives the gradient of the original function. The Differentiating Integer Powers notes cover this in full.
How do you find the y-intercept?
The y-intercept is where the line crosses the y-axis, so read off the y-value when x = 0. The Gradients and Intercepts of Linear Functions notes cover this in full.
How do you find the inverse of a function?
Write the function as y = ..., then rearrange to make x the subject and replace y with x. The Composite and Inverse Functions notes cover this in full.