A-Level · Mathematics · AQA · Mark scheme decoded

AQA A-Level Mathematics: Sigma Notation for Sums of Series — mark scheme explained

Machine-verifiedchecked against the AQA A-Level Mathematics specificationlast verified 2 July 2026

The short answer

Sigma notation, represented by the Greek letter Σ (sigma), is a concise way to express the sum of a sequence of terms. It is particularly useful in mathematics and science for writing sums that would otherwise be cumbersome or lengthy.

The question

Evaluate Σ k=1 4 k 2 . [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

S1
Write down the expression: Σ k=1 4 k 2 .
S2
Substitute the values of k into the expression and add them up:
S3
(1) 2 + (2) 2 + (3) 2 + (4) 2
S4
= 1 + 4 + 9 + 16
S5
= 30

Model answer

Worked through, with each step tagged to the mark it earns.

S1
Write down the expression: Σ k=1 4 k 2 .
S2
Substitute the values of k into the expression and add them up:
S3
(1) 2 + (2) 2 + (3) 2 + (4) 2
S4
= 1 + 4 + 9 + 16
S5
= 30
Final answer: 30

Common mistakes

Forgetting to substitute the values of the index variable into the expression. — Always substitute the values of the index variable into the expression and add them up step-by-step.
Confusing the starting and ending values of the index. — Double-check the starting and ending values of the index variable before substituting them into the expression.
Forgetting to include all terms in the sum. — Ensure that you substitute every value of the index variable from the starting value to the ending value into the expression.
Incorrectly applying the function to the index variable. — Carefully apply the function to each value of the index variable and double-check your calculations.
Using the wrong range for the index variable. — Always verify the range of the index variable and ensure it matches the given problem.
Forgetting to add the terms together. — After substituting the values of the index variable into the expression, ensure you add all the terms together to get the final result.

Where the marks go

Full worked solution (all marking points)3 marks