🏴󠁧󠁢󠁳󠁣󠁴󠁿 Nat 5 Maths Scotland

Your fun maths companion — now with 🎓 Higher Maths!
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Algebra Q1
🚫 No Calculator Level 1 — Easy
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Answer as many questions as you can before time runs out!

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🃏 Formula Flashcards

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📄 Worksheets

📋 Key Nat 5 Formulas

📐 Algebra

Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Difference of Squares
a²−b² = (a+b)(a−b)
Completing the Square
x²+bx = (x+b/2)² − (b/2)²
Discriminant
b²−4ac > 0: 2 roots | = 0: 1 root | < 0: no roots

📏 Trigonometry

SOH-CAH-TOA
sin=opp/hyp · cos=adj/hyp · tan=opp/adj
Sine Rule
a/sin A = b/sin B = c/sin C
Cosine Rule
a² = b²+c²−2bc·cos A
Area of Triangle
Area = ½ab·sin C
Trig Identity
sin²θ + cos²θ = 1
Standard Angles
sin30°=½ · cos60°=½ · tan45°=1 · sin90°=1

🔵 Geometry

Circle
Area = πr² · Circumference = 2πr = πd
Pythagoras
c² = a² + b²
Volumes
Cylinder: πr²h · Cone: ⅓πr²h · Sphere: ⁴⁄₃πr³
Arc & Sector
Arc = θ/360×2πr · Sector = θ/360×πr²

📊 Statistics

Averages
Mean=Σx/n · Median=middle · Mode=most common
Std Deviation
s = √(Σ(x−x̄)²/(n−1))
Probability
P(A)=fav/total · P(not A)=1−P(A)
IQR
IQR = Q3 − Q1

√ Surds & Indices

Index Laws
aᵐ×aⁿ=aᵐ⁺ⁿ · aᵐ÷aⁿ=aᵐ⁻ⁿ · (aᵐ)ⁿ=aᵐⁿ
Special Indices
a⁰=1 · a⁻ⁿ=1/aⁿ · a^(1/n)=ⁿ√a · a^(m/n)=(ⁿ√a)ᵐ
Surds
√(ab)=√a×√b · Rationalise: ×√b/√b

📈 Functions & Graphs

Straight Line
y = mx + c (m=gradient, c=y-intercept)
Gradient
m = (y₂−y₁)/(x₂−x₁)
Parabola
y=(x−a)²+b: turning point (a,b)

➡ Vectors

Magnitude
|a| = √(x²+y²+z²)
Dot Product
a·b=a₁b₁+a₂b₂+a₃b₃ · a·b=0 → perpendicular

🔢 Scientific Calculator

0
sin/cos/tan = degrees · sin⁻¹/cos⁻¹/tan⁻¹ = inverse · √ = square root · x² = square · xⁿ = any power · π · ln · log

📝 Notepad

Topic Progress

🏆 Timer High Scores

🔗 Helpful Links

🏛

SQA National 5 Maths

Official past papers & marking schemes

📺

BBC Bitesize — Nat 5 Maths

Videos, notes and quizzes for every topic

🎓

SCHOLAR (Heriot-Watt)

Detailed online course for Scottish Nat 5

📖

Maths Revision — Nat 5

Notes, worksheets and worked examples

🎬

Corbett Maths

Videos for every maths topic

📝 Exam Tips

Show ALL workingYou get method marks even if the final answer is wrong!
Paper 1 = No Calculator · Paper 2 = CalculatorKnow which paper you're on before you start.
Read questions carefullyKey words: "exact value", "round to 2dp", "simplify", "factorise".
Check your answerSubstitute it back in — does it work?
Draw triangles for trigLabel the sides first, then SOH-CAH-TOA / sine rule / cosine rule becomes much easier.
Never leave blanksAlways attempt every question — you can't get marks for nothing!

⚙️ Personalise

ℹ️ About

Covers all Nat 5 and Higher Maths Scotland topics with 3 difficulty levels. Questions auto-level up as you earn XP. Wrong answers get full worked explanations. Calculator topics are clearly marked. Progress saves automatically in your browser, and the whole app works offline.

📝 Mock Exams

Based on the official SQA curriculum. Papers just like the real exam.
Nat 5 Paper 1: Non-calculator · 40 marks · 1 hour
Nat 5 Paper 2: Calculator allowed · 50 marks · 1 hour 30 mins
🎓 Higher Paper: Non-calculator · 40 marks · 1 hour

📋 Exam Tips

✏️ Show ALL working — method marks are awarded even if the final answer is wrong
🕐 Watch the time — don't spend too long on one question
🔢 Paper 1 is non-calculator — use the on-screen calculator for Paper 2 only
✅ Check your answers — substitute back in where possible
📐 Draw diagrams — especially for trig and geometry questions

🛒 Recommended Resources

Everything your child needs to succeed in Nat 5 Maths. Links go to Amazon — we may earn a small commission at no extra cost to you.

As an Amazon Associate we earn from qualifying purchases.
📚 Revision Books
📗
Nat 5 Maths Revision Guide
Complete coverage of all SQA topics with worked examples
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Nat 5 Practice Papers
Past paper style questions with full marking schemes
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Hodder Nat 5 Maths
Popular textbook used in Scottish schools
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CGP Nat 5 Maths
Clear notes and exam practice — great for quick revision
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🔢 Scientific Calculators
🧮
Casio FX-85GTX
Most popular calculator for Scottish exams — SQA approved
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🔬
Casio FX-991EX
Advanced model — great for Higher Maths too
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✏️ Stationery & Study Supplies
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Geometry Set
Compass, protractor, ruler, set squares — everything needed
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Graph Paper Notebook
Essential for drawing graphs and geometry questions
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Blank Flashcards
Write your own formula cards for revision anywhere
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Highlighter & Pen Set
Colour-code your notes and make key formulas stand out
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💻 Laptops & Tablets for Study
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Student Laptops
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