IGCSE Math RevisionEdexcel IGCSE Maths A (4MA1) · Foundation tier · Revision notes
IGCSE Maths 4MA1 Foundation Sequences and Graphs Notes
Revision notes for sequences, functions and graphs at Foundation tier (Papers 1F and 2F, grades 5 to 1). Each sub-topic has what you need to know, the key methods, a common mistake and a worked example. Cover the worked solution and try the example first.
- 2 sub-topics
- Papers 1F and 2F
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3.1 Sequences
What you need to know: term-to-term and position-to-term rules; the nth term of a linear sequence.
- A term-to-term rule says how to get from one term to the next, for example 'add 7'.
- A linear (arithmetic) sequence goes up or down by the same amount each time; that difference is the number in front of n.
- Find the nth term of a linear sequence: dn + (first term − d), where d is the difference.
- To check whether a number is in a sequence, set the nth term equal to it and see whether n is a whole number.
Watch out: For 4, 11, 18, … the nth term is 7n − 3, not n + 7.
Worked example (2 marks, grade 3):
Find an expression for the \(n\)th term of the sequence \(7, \ 10, \ 13, \ 16, \ \ldots\)
- The common difference is 3, so the nth term starts 3n.
- When n = 1, 3n = 3; the first term is 7, so add 4: 3n + 4.
Answer: \(3n + 4\)
Higher tier only: first term a and common difference d, and the sum of an arithmetic series.
Practise: Sequences questions with answers · Unit 3 practice (Foundation) · Higher level: Sequences questions
3.3 Graphs
What you need to know: coordinates and midpoints; reading real-life graphs, including distance–time and speed–time; conversion graphs; gradient and y = mx + c; plotting straight-line and quadratic graphs.
- The midpoint of two points is the mean of the x-coordinates and the mean of the y-coordinates.
- Gradient = change in y ÷ change in x; in y = mx + c, m is the gradient and the line crosses the y-axis at (0, c).
- Plot a graph from a table of values, then join the points: with a ruler for a straight line, with a smooth curve for a quadratic.
- On a distance–time graph the gradient is the speed; a horizontal section means the object has stopped.
Watch out: Rearrange to y = … before reading the gradient: 2y = 6x + 8 has gradient 3, not 6.
Worked example (2 marks, grade 3):
Find the gradient of the straight line through the points \((1, 2)\) and \((4, 11)\).
- Gradient = increase in y ÷ increase in x.
- (11 − 2) ÷ (4 − 1) = 9 ÷ 3 = 3.
Answer: \(3\)
Higher tier only: cubic, reciprocal and trigonometric graphs, transformations of graphs, gradients by tangents, parallel and perpendicular lines.
Practise: Graphs questions with answers · Unit 4 practice (Foundation) · Higher level: Straight Line Graphs questions · Quadratic and Cubic Graphs questions · Real-Life Graphs questions
Practise sequences and graphs
- Unit 3 practice, Unit 4 practice with the Foundation filter on: questions written for Foundation and 4MA1 questions at grades 4 and 5, each with a mark scheme (IGCSE plan, with a free preview)
- Edexcel IGCSE Maths 4MA1 past papers, to practise under exam conditions
- IGCSE Maths formula sheet and the 4MA1 Higher revision notes when you are ready to go further