AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 25

1 mark · Easy difficulty · Short Answer

Identify the exact trigonometric value of sin 90° from four given options.

Practise this question

Question

Question 25 asks to 'Circle the value of sin 90°' for 1 mark. Four multiple choice options are presented horizontally: 0, 1/2, square root of 3 over 2, and 1.

Mark scheme

Show the mark scheme Mark scheme table for question 25 indicates that the correct answer is 1, awarded with mark B1.

How to answer it

Exact Trigonometric Values: sin 90°

📌 What this question tests

This question assesses the recall of exact trigonometric values without a calculator (AQA GCSE Specification 8300, Non-Calculator Paper).

  • Recalling standard trigonometric ratios for 0°, 30°, 45°, 60°, and 90°.
  • Understanding the sine curve and its key coordinates between 0° and 360°.
Question 25 • 1 Mark

Circle the value of sin 90°

0 ½ (√3)/2 1

✅ Correct Answer

1

B1: Standalone mark for circling or indicating 1 .

💡 Key Knowledge: Exact Sine Values

You are required to memorise the exact values of sine for standard angles:

Angle (θ) 0° 30° 45° 60° 90°
sin θ 0 ½ (√2)/2 (√3)/2 1

Notice the square-root pattern: √(0)/2, √(1)/2, √(2)/2, √(3)/2, √(4)/2.

📐 Visual Method: The Sine Wave

Sketching a quick sine wave is the most reliable way to avoid mixing up sine and cosine at boundaries:

  • Starts at origin: (0°, 0)
  • Reaches peak maximum at: (90°, 1)
  • Crosses horizontal axis at: (180°, 0)
  • Reaches lowest point at: (270°, -1)
  • Completes one cycle at: (360°, 0)

Since 90° is the first peak of the sine graph, sin 90° = 1.

❌ Common Misconceptions

  • Choosing 0: Confusing sin 90° with cos 90° = 0 or sin 0° = 0 .
  • Choosing ½: Confusing 90° with 30°, since sin 30° = ½ .
  • Choosing (√3)/2: Confusing 90° with 60°, since sin 60° = (√3)/2 .

🧠 Exam Technique & Examiner Insight

  • Quick 5-Second Check: Before answering, write down the pattern: sin goes UP from 0 to 1 as the angle goes from 0° to 90°, while cos goes DOWN from 1 to 0.
  • Examiner Report Insight: Multiple-choice questions on exact trigonometric values are often lost due to hasty guessing. Drawing a 5-second sine wave in the margin guarantees full marks.
  • Clear Circling: If you change your mind, cross out your old choice clearly and circle your new answer. Do not leave two options circled.

Topics

Geometry and measures · 3.4.2 Mensuration and calculation

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