AQA AS Level Mathematics Paper 1, June 2025: Question 1

1 mark · Easy difficulty · Short Answer

Identify the trigonometric expression equivalent to tan x from a multiple-choice list.

Practise this question

Question

Question 1 asks: 'Identify the expression that is equivalent to tan x. Circle your answer.' Below the text are four choices: sin^2 x + cos^2 x, sin^2 x - cos^2 x, cos x / sin x, and sin x / cos x. The question is worth 1 mark.
Question text

1 Identify the expression that is equivalent to tan x

Circle your answer.

[1 mark]

22 2 2 cos x sin x

sin x + cos x sin x – cos x

sin x cos x

Mark scheme

Show the mark scheme Mark scheme for Question 1 displays marking instructions: 'Circles fourth answer', AO 1.2, Mark B1, and typical solution 'sin x / cos x'. The total for Question 1 is 1 mark.

Q Marking instructions AO Marks Typical solution

1 Circles fourth answer 1.2 B1 sin x

cos x

Question 1 Total 1

How to answer it

Fundamental Trigonometric Identity for tan x

📋 What this question tests

This question assesses basic recall and recognition of core AS-level trigonometric definitions and identities (AO1.2), specifically the quotient identity relating the tangent, sine, and cosine functions.

Question 1

Multiple Choice: Identifying an Equivalent Expression [1 mark]

✅ Correct Answer

The correct option to circle is the fourth answer:

sin x cos x

Mark Scheme: B1 (AO1.2) awarded for clearly circling the fourth expression.

💡 Key Knowledge

  • Definition of tan x:
    tan x ≡ sin x cos x  (valid for all x where cos x ≠ 0).
  • Pythagorean Identity:
    sin²x + cos²x ≡ 1
  • Reciprocal Form:
    cos x sin x is the reciprocal, equivalent to 1 tan x (or cot x in A2).

📐 Breakdown of Options

  1. sin²x + cos²x: Evaluates to the constant 1 , not tan x.
  2. sin²x − cos²x: Equivalent to −cos(2x) , not tan x.
  3. cos x sin x : The inverted fraction ( 1 / tan x ).
  4. sin x cos x : Matches standard definition: Opposite / Adjacent = (Opp / Hyp) / (Adj / Hyp).

🧠 Exam Technique

  • Make selections unambiguous: Circle only one answer clearly. If you change your mind, fully cross out your first choice with an 'X' and circle the intended one.
  • Quick sanity check: If in doubt, substitute a simple angle into your calculator:
    tan(45°) = 1
    sin(45°) / cos(45°) = 1

❌ Common Errors

  • Inverting numerator and denominator: Circling cos x sin x due to rushed reading.
  • Confusing identities: Mistaking the quotient identity for the Pythagorean identity sin²x + cos²x = 1.
  • Double circling: Circling multiple options without clearly negating one, leading to an automatic loss of the mark.

Topics

Pure Mathematics · E: Trigonometry

Question and mark scheme from the AQA AS Level Mathematics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.