SQA · National 5 · Free archive

Mathematics Free Topical Past Papers

SQA National 5 Mathematics past-paper questions grouped by official syllabus topic. Free archive, no signup. Want step-by-step worked solutions? See Mathematics Topical Solved.

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46 topics covered, mapped to the official SQA 2026 syllabus.

Topic 1

Numerical skills

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Topic 2

Working with surds

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Topic 3

Simplifying expressions using

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Topic 4

Rounding

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Topic 5

Working with reverse

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Topic 6

Working with

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Topic 7

Working with fractions

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Topic 8

Algebraic skills

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Topic 9

Working with algebraic

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Topic 10

Factorising an algebraic

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Topic 11

Completing the square in a

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Topic 12

Reducing an algebraic fraction

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Topic 13

Applying the four operations to

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Topic 14

Determining the equation of a

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Topic 15

Working with linear equations

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Topic 16

Working with simultaneous

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Topic 17

Changing the subject of a

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Topic 18

Recognise and determine the

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Topic 19

Sketching a quadratic function

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Topic 20

Identifying features of a

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Topic 21

Solving a quadratic equation

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Topic 22

Using the discriminant to

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Topic 23

Geometric skills

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Topic 24

Determining the gradient of a

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Topic 25

Circle geometry

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Topic 26

Calculating the volume of a

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Topic 27

Applying Pythagoras’ theorem

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Topic 28

Applying the properties of

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Topic 29

Using similarity

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Topic 30

Working with two-dimensional

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Topic 31

Working with three-

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Topic 32

Using vector components

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Topic 33

Calculating the magnitude of a

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Topic 34

Trigonometric skills

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Topic 35

Working with the graphs of

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Topic 36

Working with trigonometric

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Topic 37

Calculating the area of a

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Topic 38

Using the sine and cosine

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Topic 39

Using bearings with

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Topic 40

Statistical skills

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Topic 41

Comparing data sets using

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Topic 42

Forming a linear model from a

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Topic 43

Reasoning skills

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Topic 44

Interpreting a situation where

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Topic 45

Explaining a solution and

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Topic 46

Skills for learning, skills for life and skills for work

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