National 5 Mathematics: money, fractions, vectors and statistics

This set covers the part of National 5 Maths that looks least like algebra: money growing or shrinking year on year, fractions, vectors, and the handful of statistics a candidate is expected to calculate and interpret. This set covers appreciation and depreciation over several years, reversing a percentage increase, dividing mixed numbers, adding vectors and finding a magnitude, the interquartile range, what a larger standard deviation actually tells you, reading a prediction off a line of best fit, and working out the saving in a three-for-two offer.

The percentage questions are built around the mistake that costs most marks: treating repeated percentage change as a single multiplication, so that three years of 15 per cent depreciation becomes 45 per cent off. Both of those wrong answers are offered, along with the value after stopping a year early. The statistics questions separate the three numbers that get confused with each other — the range, the median and the interquartile range are all among the options, so only the right calculation picks the right one.

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  • Calculate appreciation and depreciation over several years by compounding, not by multiplying the rate
  • Reverse a percentage increase by dividing by the multiplier
  • Divide mixed numbers by converting to improper fractions and multiplying by the reciprocal
  • Add vectors by components and find a magnitude using Pythagoras
  • Find quartiles from an ordered list and calculate the interquartile range
  • Interpret what a larger standard deviation means when two means are equal
  • Predict a value from the equation of a line of best fit
  • Work out the percentage saved on a multi-buy offer

A car is worth 12 000 pounds and depreciates by 15 per cent each year. What is its value after 3 years? — $12\,000 \times 0.85^3 = 12\,000 \times 0.614125 = 7369.50$ pounds.

Sample question

The vector w = (6, −8) drawn as an arrow, with its horizontal component 6 and vertical component −8 (downwards) shown as dashed lines meeting at a right angle.

What is the magnitude of the vector $w = (6, -8)$?

See the answer

10

The magnitude is calculated using Pythagoras: $|w| = \sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10$. Adding the components (14) is a common mistake.

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National 5 and Higher qualifications are awarded by Qualifications Scotland, which took over the awarding functions of the Scottish Qualifications Authority (SQA) in February 2026. Zestly is not affiliated with or endorsed by Qualifications Scotland or the SQA. These materials are our own and reproduce no past-paper content.