Give a Reason & Justify
Justification Questions
"Give a reason" and "Justify" questions require you to support your answer with mathematical evidence. Simply stating the answer is never enough.
The Structure of a Good Justification
Claim → Evidence → Conclusion
- Claim: State what you believe to be true
- Evidence: Provide mathematical facts or calculations
- Conclusion: Link back to the original question
Geometry Reasoning
Geometry questions are the most common place for "give a reason" prompts.
Key Angle Facts to Quote:
| Situation | Correct Reason |
|---|---|
| Angles on a straight line | "Angles on a straight line sum to 180°" |
| Angles around a point | "Angles around a point sum to 360°" |
| Vertically opposite angles | "Vertically opposite angles are equal" |
| Angles in a triangle | "Angles in a triangle sum to 180°" |
| Angles in a quadrilateral | "Angles in a quadrilateral sum to 360°" |
| Corresponding angles | "Corresponding angles are equal" (parallel lines) |
| Alternate angles | "Alternate angles are equal" (parallel lines) |
| Co-interior angles | "Co-interior angles sum to 180°" (parallel lines) |
Circle Theorem Reasons:
| Theorem | How to Express It |
|---|---|
| Angle at centre | "The angle at the centre is twice the angle at the circumference" |
| Angle in semicircle | "The angle in a semicircle is 90°" |
| Same segment | "Angles in the same segment are equal" |
| Cyclic quadrilateral | "Opposite angles in a cyclic quadrilateral sum to 180°" |
| Tangent perpendicular | "A tangent is perpendicular to the radius at the point of contact" |
| Tangents from point | "Tangents from an external point are equal in length" |
Example: Full Marks vs Partial Marks
Question: Find angle x. Give a reason for your answer.
(Diagram shows two parallel lines cut by a transversal, with angle 72° marked and x as an alternate angle)
1 mark answer: $x = 72°$ because alternate angles.
Full marks answer: $x = 72°$ because alternate angles are equal when formed by parallel lines and a transversal.
"Justify" in Statistics
When asked to justify which average to use:
Use the mean when:
- Data has no outliers
- You need to use all the data values
- "Fair" representation is needed (e.g., sharing equally)
Use the median when:
- Data has outliers or extreme values
- Data is skewed
- "Typical" value is more important than total
Use the mode when:
- Data is categorical
- Most popular/common item is relevant
- "What occurs most often" is the question
Example Justification: "The median is the best average to use because the data contains the outlier value of £150,000, which would make the mean unrepresentative of the typical salary. The median is not affected by extreme values."
"Justify" in Problem Solving
When justifying a decision or interpretation:
- State your conclusion clearly
- Reference specific numbers from your calculation
- Explain why these numbers lead to your conclusion
Example: Amy has £500. Tickets cost £47 each. She wants to buy tickets for a group of 12. Justify whether she has enough money.
"Amy needs 12 × £47 = £564 for the tickets. Since £564 > £500, Amy does not have enough money. She is £64 short."