National 5 Exam Hall

Mark-savers

Every year Qualifications Scotland publishes a course report on where candidates lost marks. These are the ones that keep coming back.

1. 1

   Comparing two data sets with numbers, not words

   Write two sentences in the question’s context. The median or mean: “On average, the café’s waiting times were lower.” The IQR or standard deviation: “The restaurant’s waiting times were more consistent.” Never put “on average” in the consistency sentence.

   Course reports 2023, 2024, 2025, 2026

2. 2

   Using the semi-interquartile range or the range

   The interquartile range is Q3 − Q1. Order the data first, then find the quartiles.

   Course reports 2023, 2024, 2025, 2026

3. 3

   Starting the converse of Pythagoras with a² + b² = c²

   Work out the longest side squared, and the other two squared and added, separately. Only then say they are equal, so the triangle is right-angled. The conclusion must mention the right angle.

   Course reports 2023, 2026

4. 4

   Forgetting to reverse the inequality sign

   Keep the x-term positive by moving it to the side where it stays positive. If you divide or multiply by a negative, flip the sign.

   Course reports 2024, 2026

5. 5

   Giving one angle when a trig equation has two

   Between 0° and 360° there are usually two answers. Sketch the graph, or use the quadrant diagram, and find both. If you get cos x or sin x bigger than 1 or less than −1, your rearranging has gone wrong: go back and check it.

   Course reports 2023, 2025, 2026

6. 6

   Stopping one step short

   Read the question again before you move on. Solving the simultaneous equations is often not the last step, so check what was actually asked. And 5 cos 180° is not an answer: cos 180° = −1, so it is −5.

   Course reports 2025, 2026

7. 7

   Rounding too early, or to the wrong accuracy

   Keep the full number on your calculator until the end. Then round to what the question asks, such as 3 significant figures, and money to 2 decimal places.

   Course reports 2024, 2025, 2026

8. 8

   Working out angles away from the diagram

   Write every angle you find on the diagram, in the right place. Markers are unlikely to give marks for angles worked out elsewhere on the page.

   Course reports 2024, 2025, 2026

9. 9

   Half-describing the roots from the discriminant

   Use the full words: “two real and distinct roots”, “two equal real roots”, or “no real roots”. Show the calculation of b² − 4ac first.

   Course reports 2023, 2025

10. 10

    Taking a percentage of the new price

    For the original price, divide. If a price after an 8% rise is £540, the original is £540 ÷ 1.08 = £500. Taking 8% off £540 gives the wrong answer.

    Course reports 2023, 2024, 2025

11. 11

    Keeping both answers to a quadratic in context

    A length or a time can’t be negative. Say which root you reject, and why, then answer the question.

    Course reports 2023, 2025, 2026

12. 12

    Reading the gradient without rearranging

    Get y on its own first: 3y + 2x = 12 becomes y = −⅔x + 4, so the gradient is −⅔. For a line of best fit, write the final equation in the question’s letters, such as F and P.

    Course reports 2023, 2024, 2026

13. 13

    Proving a trig identity without a plan

    Start from the more complicated side. Factorise first if you can, then use sin²x + cos²x = 1 or tan x = sin x ÷ cos x. Write one step a line until you reach the other side.

    Course reports 2023, 2024, 2026

14. 14

    Not forming the quadratic equation in context

    Write the expression the question describes, set it equal to the number it gives you, then expand and rearrange until it matches the form asked for exactly. Then solve that equation in the next part.

    Course reports 2023, 2025, 2026

15. 15

    Leaving fractions in an equation

    Multiply every term on both sides by the lowest common denominator first, then solve as usual.

    Course reports 2023, 2025

16. 16

    Sketching a right-angled triangle without the right angle

    Mark the right angle with a small square, so the marker can see which angle it is.

    Course reports 2024, 2026

17. 17

    Lines of working that don’t follow on

    Each line must equal the line before. When you factorise, multiply your brackets back out to check before you move on.

    Course reports 2026

Mark-savers summarise the Qualifications Scotland National 5 Mathematics course reports 2023 to 2026. Qualifications Scotland does not endorse this material.