📚 All Topics 🧪 Revision Quiz 📐 Formula Sheet 💡 Exam Tips 📅 Study Plan
🎓 SQA National 5 Mathematics

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Complete revision for every National 5 Maths topic — quizzes, formula guides, worked examples and a structured study plan. All in one place, completely free.

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Topics Covered
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Quiz Questions
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Core Units
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Curriculum

All National 5 Topics

Organised into the three SQA units. Click any topic for key skills, bullet points and formula hints.

📐
Unit 1 — Expressions & Formulae
Algebra, geometry of circles and volumes
📉
Unit 2 — Relationships
Equations, graphs and trigonometric functions
🌍
Unit 3 — Applications
Real-world maths, statistics and problem solving
Practice

Revision Quiz

Test your knowledge on any topic. Instant feedback with explanations for every question.

Question 1 of 5
QUESTION 1
Score: 0 / 0
Reference

Formula Sheet

Key formulae you need to know — and those provided in the SQA exam.

📐

Straight Line

General form\(y = mx + c\)
Gradient\(m = \dfrac{y_2-y_1}{x_2-x_1}\)
Point-gradient\(y - b = m(x - a)\)
Parallel lines\(m_1 = m_2\)
Perpendicular\(m_1 \times m_2 = -1\)
📏

Circle Geometry

Arc length\(\ell = \frac{\theta}{360} \times \pi d\)
Sector area\(A = \frac{\theta}{360} \times \pi r^2\)
Circumference\(C = \pi d = 2\pi r\)
Area\(A = \pi r^2\)
📦

Volume

Sphere\(V = \tfrac{4}{3}\pi r^3\)
Cone\(V = \tfrac{1}{3}\pi r^2 h\)
Cylinder\(V = \pi r^2 h\)
Prism\(V = Ah\)
Pyramid\(V = \tfrac{1}{3}Ah\)
📐

Trigonometry

SOH\(\sin\theta = \frac{O}{H}\)
CAH\(\cos\theta = \frac{A}{H}\)
TOA\(\tan\theta = \frac{O}{A}\)
Sine Rule\(\frac{a}{\sin A} = \frac{b}{\sin B}\)
Cosine Rule\(a^2 = b^2+c^2-2bc\cos A\)
Area of △\(A = \tfrac{1}{2}ab\sin C\)
📊

Statistics

Mean\(\bar{x} = \dfrac{\sum x}{n}\)
Std Dev (pop)\(s = \sqrt{\dfrac{\sum(x-\bar{x})^2}{n}}\)
Std Dev (sample)\(s = \sqrt{\dfrac{\sum(x-\bar{x})^2}{n-1}}\)
IQR\(Q_3 - Q_1\)
🔢

Quadratics & Algebra

Quadratic formula\(x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)
Discriminant\(b^2 - 4ac\)
Diff of squares\(a^2-b^2 = (a+b)(a-b)\)
Completing sq.\((x+p)^2 + q\)
Index laws\(a^m \times a^n = a^{m+n}\)
📐

Vectors

Magnitude 2D\(|\mathbf{u}| = \sqrt{x^2+y^2}\)
Magnitude 3D\(|\mathbf{u}| = \sqrt{x^2+y^2+z^2}\)
Scalar mult.\(k(x,y) = (kx,ky)\)
Addition\((a,c)+(b,d) = (a+b,\,c+d)\)
📈

Sequences & Finance

Arithmetic nth\(U_n = a + (n-1)d\)
Percentage change\(\times\left(1 \pm \tfrac{r}{100}\right)^n\)
Reverse %\(\div\left(1 \pm \tfrac{r}{100}\right)\)
Pythagoras\(a^2 + b^2 = c^2\)
Advice

Exam Tips & Strategies

Proven strategies from top-performing students to help you score maximum marks.

🖊️ Show Your Working

Even if your final answer is wrong, clear working earns partial marks. Never skip steps.

  • Write the formula first, then substitute
  • State what each variable represents
  • One line = one mathematical step
  • Box or underline your final answer

⏱️ Time Management

Paper 1 (non-calc) is 45 min; Paper 2 (calc) is 75 min. Budget roughly 1 min per mark.

  • Do easy questions first to build confidence
  • Mark hard questions and come back
  • Leave 5 min at the end to check answers
  • Never spend more than 3× the marks on a question

🔢 Calculator Paper Tips

Paper 2 allows a scientific calculator — use it strategically, not as a crutch.

  • Store intermediate answers in memory
  • Use Ans key to avoid re-entering values
  • Round only at the final step
  • Check calculator is in DEG mode for trig

📋 Common Mistakes to Avoid

These are the most frequent errors that cost students marks in N5 Maths.

  • Forgetting ± in the quadratic formula
  • Not squaring the radius (using diameter)
  • Rounding too early in multi-step problems
  • Using sine rule when cosine rule is needed

📖 Revision Techniques

Active revision beats passive reading every time. Struggle builds memory.

  • Practice past papers under exam conditions
  • Make a formula card to test yourself
  • Teach a topic to someone else
  • Focus on topics you got wrong last time

🏁 In the Exam

Calm, systematic thinking outperforms rushing. These habits help on the day.

  • Read every question twice before starting
  • Underline key information and units
  • Sketch a diagram for geometry questions
  • Check your answer makes sense in context
Schedule

6-Week Revision Plan

A suggested schedule to cover all topics methodically before your exam.

Week 1
Algebra Foundations
  • Surds & Indices
  • Expanding Brackets
  • Factorising
  • Algebraic Fractions
Week 2
Lines & Geometry
  • Gradient & Straight Line
  • Arcs & Sectors
  • Volume of Solids
  • Completing the Square
Week 3
Equations & Graphs
  • Solving Equations
  • Simultaneous Equations
  • Quadratic Equations
  • Functions & Graphs
Week 4
Trigonometry
  • SOH CAH TOA
  • Sine & Cosine Rules
  • Trig Graphs
  • Exact Values
Week 5
Applications
  • Statistics & Std Dev
  • Pythagoras
  • Similar Shapes
  • Vectors
Week 6
Past Papers
  • Full past paper × 3
  • Weak topic review
  • Formula memorisation
  • Exam technique focus