National 5Mathematics
Algebra
Algebraic fractions
Factorise before cancelling and retain restrictions on the denominator.
8 sittings · 8 linked pages
Repeated appearances grouped into this type.
2017–2026 · National 5 & Higher
More skills.
Less repetition.
524 distinct skill groups across 14 subjects. Find a question type, open an example in its original paper and check the published marking instructions. Repeated appearances are grouped, not duplicated.
Practise from the original PDFs, then return to record completion and optional self-marks. These are 524 rule-assisted skill groups, not teacher-approved worked answers. Each example links to its matched numbered questions in the same practice index. Automatic topic and marking matches remain distinct from wording-checked pairs. Older formats and scan gaps are listed below.
Find your next skill.
524 distinct types · showing 379–396
- National 5Mathematics
Algebra
Constructing algebraic expressions
Translate the given relationships into an algebraic expression or equation.
8 sittings · 29 linked pages
Practise this type 2026 example · PDF page 6 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Algebra
Expanding and factorising
Expand products or identify an appropriate factorisation.
8 sittings · 14 linked pages
Practise this type 2026 example · PDF page 3 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Algebra
Linear equations and inequations
Solve algebraically and reverse an inequality when multiplying by a negative.
5 sittings · 5 linked pages
Practise this type 2026 example · PDF page 5 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Algebra
Rearranging a formula
Apply inverse operations to isolate the requested variable.
8 sittings · 8 linked pages
Practise this type 2026 example · PDF page 8 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Algebra
Simultaneous equations
Form and solve linked equations, then interpret the solution.
5 sittings · 5 linked pages
Practise this type 2026 example · PDF page 6 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Algebra
Surds and rationalising denominators
Simplify exact roots and rationalise a denominator where required.
5 sittings · 5 linked pages
Practise this type 2026 example · PDF page 7 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Coordinate geometry
Circle equations and tangents
Connect the centre and radius with a circle equation or perpendicular tangent.
8 sittings · 20 linked pages
Practise this type 2026 example · PDF page 9 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Coordinate geometry
Coordinates and midpoints
Read or calculate coordinates and locate a midpoint in two or three dimensions.
7 sittings · 20 linked pages
Practise this type 2026 example · PDF page 10 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Coordinate geometry
Straight-line equations
Find the gradient and a suitable equation using the supplied coordinates.
8 sittings · 12 linked pages
Practise this type 2026 example · PDF page 6 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Functions
Evaluating functions
Substitute the input carefully, respecting brackets and angle units.
6 sittings · 8 linked pages
Practise this type 2026 example · PDF page 12 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Geometry
Angles in polygons and parallel lines
Use angle sums and parallel-line relationships, stating the property when a reason is required.
3 sittings · 3 linked pages
Practise this type 2026 example · PDF page 12 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Geometry
Circle geometry
Use the relevant circle property and justify relationships.
8 sittings · 18 linked pages
Practise this type 2026 example · PDF page 9 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Geometry
Pythagoras and its converse
Identify the hypotenuse and test or apply the squared-length relationship.
1 sitting · 1 linked page
Practise this type 2026 example · PDF page 10 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Geometry
Similarity and scale factors
Distinguish length, area and volume scale factors.
5 sittings · 5 linked pages
Practise this type 2026 example · PDF page 5 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Geometry
Surface area and volume
Select a suitable solid model, use consistent units and interpret the result.
8 sittings · 17 linked pages
Practise this type 2026 example · PDF page 5 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Numerical skills
Compound growth and depreciation
Apply a repeated multiplier, retaining precision until the final answer.
7 sittings · 7 linked pages
Practise this type 2026 example · PDF page 3 (opens original official paper in a new tab)
Repeated appearances grouped into this type. - National 5Mathematics
Numerical skills
Fractions and numerical operations
Work with exact fractions and show the order of operations.
8 sittings · 10 linked pages
Practise this type 2026 example · PDF page 5 (opens original official paper in a new tab)
Repeated appearances grouped into this type.
What is covered, and what still needs review?
Skill groups are derived from the same numbered-question index used in practice, with exact question IDs retained on every example page. One entry per subject, level and family; repeated appearances are grouped rather than additional types. Source pairs checked against wording and PDF digests are distinguished from automatic table and rule matches. Classification is provisional, not a claim of exhaustive syllabus coverage or independent subject-review sign-off. A historical appearance does not establish that the skill remains in the current syllabus. 3 scanned question papers need OCR. 2020 and 2021 exams were cancelled. Older questions can use different course or marking formats. Counts below are skill groups and linked question documents, not question counts or exam predictions. Counts awaiting classification now refer to numbered entries in the shared question index, not arbitrary text fragments.
- National 5 Applications of Mathematics22 types · 16 question PDFs checked · 6 numbered entries awaiting classification
- Higher Applications of Mathematics25 types · 5 question PDFs checked · 0 numbered entries awaiting classification
- National 5 Biology27 types · 19 question PDFs checked · 26 numbered entries awaiting classification
- Higher Biology29 types · 19 question PDFs checked · 19 numbered entries awaiting classification
- National 5 Business Management23 types · 8 question PDFs checked · 0 numbered entries awaiting classification
- Higher Business Management24 types · 6 question PDFs checked · 0 numbered entries awaiting classification
- National 5 Chemistry27 types · 19 question PDFs checked · 37 numbered entries awaiting classification
- Higher Chemistry29 types · 19 question PDFs checked · 5 numbered entries awaiting classification
- National 5 Computing Science26 types · 8 question PDFs checked · 6 numbered entries awaiting classification
- Higher Computing Science26 types · 8 question PDFs checked · 3 numbered entries awaiting classification
- National 5 English14 types · 16 question PDFs checked · 19 numbered entries awaiting classification
- Higher English15 types · 16 question PDFs checked · 11 numbered entries awaiting classification
- National 5 French7 types · 24 question PDFs checked · 0 numbered entries awaiting classification
- Higher French7 types · 24 question PDFs checked · 6 numbered entries awaiting classification
- National 5 Geography21 types · 8 question PDFs checked · 0 numbered entries awaiting classification
- Higher Geography20 types · 17 question PDFs checked · 0 numbered entries awaiting classification
- National 5 History6 types · 6 question PDFs checked · 0 numbered entries awaiting classification
- Higher History6 types · 14 question PDFs checked · 0 numbered entries awaiting classification
- Higher Human Biology24 types · 19 question PDFs checked · 18 numbered entries awaiting classification
- National 5 Mathematics26 types · 16 question PDFs checked · 52 numbered entries awaiting classification
- Higher Mathematics23 types · 16 question PDFs checked · 20 numbered entries awaiting classification
- National 5 Modern Studies14 types · 8 question PDFs checked · 0 numbered entries awaiting classification
- Higher Modern Studies13 types · 14 question PDFs checked · 0 numbered entries awaiting classification
- National 5 Physics24 types · 19 question PDFs checked · 9 numbered entries awaiting classification
- Higher Physics32 types · 19 question PDFs checked · 3 numbered entries awaiting classification
- National 5 Spanish7 types · 24 question PDFs checked · 0 numbered entries awaiting classification
- Higher Spanish7 types · 24 question PDFs checked · 6 numbered entries awaiting classification