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Edexcel IGCSE Maths A (4MA1) · Foundation tier · Questions

IGCSE Maths 4MA1 Foundation Sequences and Graphs Questions

6 original exam-style questions on sequences, functions and graphs for the Foundation tier, three for each sub-topic, from easier to harder. Try each one, then open the mark scheme and the worked solution. The marks are Edexcel style: M for method, A for accuracy, B for an independent result.

More sequences and graphs practice →Sequences and Graphs notes

3.1 Sequences questions

Revise it first: Sequences notes and worked example.

Question 1 · 2 marks · grade 1

Here are the first four terms of a sequence: \(4, \ 11, \ 18, \ 25, \ \ldots\)

(a) Write down the next two terms.

(b) Write down the term-to-term rule.

Show the answer, mark scheme and worked solution
  • B1 (a) 32, 39
  • B1 (b) add 7
  1. The terms go up by 7 each time: 25 + 7 = 32 and 32 + 7 = 39.

Answer: (a) \(32, 39\) (b) add 7

Question 2 · 2 marks · grade 4

The \(n\)th term of a sequence is \(3n - 1\).

Is 100 a term of the sequence? Give a reason for your answer.

Show the answer, mark scheme and worked solution
  • M1 for 3n − 1 = 100 or listing terms near 100 (98, 101)
  • A1 No, with a reason, e.g. n = 33.66… is not a whole number
  1. Solve 3n − 1 = 100: 3n = 101, n = 33.66…
  2. n must be a whole number, so 100 is not a term (the terms near it are 98 and 101).

Answer: No: \(3n - 1 = 100\) gives \(n = 33.66\ldots\), not a whole number

Question 3 · 3 marks · grade 5

Sequence A has \(n\)th term \(4n + 5\). Sequence B has \(n\)th term \(7n - 10\).

For which value of \(n\) are the \(n\)th terms of the two sequences equal, and what is that term?

Show the answer, mark scheme and worked solution
  • M1 for 4n + 5 = 7n − 10
  • A1 n = 5
  • A1 25
  1. Set the nth terms equal: 4n + 5 = 7n − 10.
  2. 15 = 3n, so n = 5.
  3. 4 × 5 + 5 = 25 (and 7 × 5 − 10 = 25).

Answer: \(n = 5\); both terms are \(25\)

3.3 Graphs questions

Revise it first: Graphs notes and worked example.

Question 4 · 1 mark · grade 1

Find the coordinates of the midpoint of the line segment from \((2, 3)\) to \((8, 7)\).

Show the answer, mark scheme and worked solution
  • B1 (5, 5)
  1. Add the x-coordinates and halve: (2 + 8) ÷ 2 = 5.
  2. Add the y-coordinates and halve: (3 + 7) ÷ 2 = 5.

Answer: \((5, 5)\)

Question 5 · 4 marks · grade 4

A line \(L\) has equation \(2y = 6x + 8\).

(a) Find the gradient of \(L\).

(b) Write down the coordinates of the point where \(L\) crosses the \(y\)-axis.

(c) Does the point \((3, 13)\) lie on \(L\)? Show how you decide.

Show the answer, mark scheme and worked solution
  • M1 for y = 3x + 4
  • A1 (a) 3
  • B1 (b) (0, 4)
  • B1 (c) Yes, 3 × 3 + 4 = 13
  1. Divide by 2 to get y = mx + c: y = 3x + 4.
  2. (a) The gradient is 3.
  3. (b) The y-intercept is (0, 4).
  4. (c) When x = 3, y = 9 + 4 = 13, so (3, 13) is on L.

Answer: (a) \(3\) (b) \((0, 4)\) (c) Yes, \(3 \times 3 + 4 = 13\)

Question 6 · 4 marks · grade 5

(a) Complete the table of values for \(y = x^2 - 2x - 3\) for \(x = -2, -1, 0, 1, 2, 3, 4\).

(b) Write down the values of \(x\) where the graph crosses the \(x\)-axis.

(c) Write down the equation of the line of symmetry of the graph.

Show the answer, mark scheme and worked solution
  • B2 (a) 5, 0, −3, −4, −3, 0, 5 (B1 for 5 or 6 correct)
  • B1 (b) −1 and 3
  • B1 (c) x = 1
  1. (a) For example x = −2: 4 + 4 − 3 = 5; x = 1: 1 − 2 − 3 = −4.
  2. (b) y = 0 at x = −1 and x = 3.
  3. (c) The graph is symmetrical about the line halfway between −1 and 3: x = 1.

Answer: (a) \(5, 0, -3, -4, -3, 0, 5\) (b) \(x = -1\) and \(x = 3\) (c) \(x = 1\)

Every question here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Topic list for Edexcel IGCSE Maths 4MA1 Foundation sequences and graphs: sequences, graphs
The 2 Foundation sub-topics of sequences and graphs.

Practise sequences and graphs