Comprehensive National 5 Maths Revision Guide

Foundation Skills: Numbers, Fractions & Basic Algebra

Scientific notation is your friend for handling massive or tiny numbers - you'll multiply and divide these values and express regular numbers in this compact form. It's surprisingly straightforward once you get the hang of it.

Fractions and percentages form the backbone of many exam questions. You'll need to confidently add, subtract, multiply and divide fractions (including mixed numbers), plus tackle percentage calculations. Reverse percentages help you work backwards to find original values, whilst compound percentages deal with things like interest rates over time.

Expanding brackets might seem tedious, but it's essential for higher-level work. You'll expand everything from simple forms like a$bx + c$ + d$ex + f$ to more complex expressions like $ax + b$(cx² + dx + e). The key is systematic practice.

Top tip: Master these foundation skills first - they're the building blocks for everything else on this list!

Intermediate Algebra & Geometry

Factorising is essentially expanding in reverse - you'll use common factors, difference of two squares, and trinomials (both simple and complex forms). This skill is crucial for solving quadratic equations later.

Straight line equations pop up everywhere, so you'll need to find equations from coordinates, graphs, or real-world contexts. Surds require you to simplify expressions by breaking them down systematically.

Index laws govern how you handle powers and roots. The main rules (aⁿ × aᵐ = aⁿ⁺ᵐ, aⁿ ÷ aᵐ = aⁿ⁻ᵐ, and (aⁿ)ᵐ = aⁿᵐ) will become second nature with practice. Don't forget that a⁻ⁿ = 1/aⁿ.

Arcs, sectors and volume calculations involve specific formulas for cylinders, cones, spheres, hemispheres, and pyramids. Completing the square transforms quadratics from x² + bx + c into the more useful form $x + p$² + q.

Remember: Pythagoras' theorem works in 2D, 3D, and circle contexts - it's one of the most versatile tools in your mathematical arsenal!

Advanced Topics: Trigonometry & Quadratics

Trigonometry extends far beyond basic SOHCAHTOA. You'll use the sine and cosine rules for non-right-angled triangles, plus the area formula. Trigonometric graphs require understanding amplitude, frequency, and period changes.

Trigonometric equations need you to find all solutions within a given range, whilst trigonometric identities like tan$x$ = sin x/cos x and sin²x + cos²x = 1 help simplify complex expressions.

Angle properties cover everything from basic triangle rules to complex circle theorems. You'll identify isosceles triangles, work with triangles in semicircles, and handle tangents to circles. Polygons have their own angle rules for central and interior angles.

Algebraic fractions require the same four operations as numerical fractions, but with variables thrown in. You'll cancel terms, combine fractions, and simplify complex expressions. Simultaneous equations can be solved algebraically or interpreted from context.

Key insight: Quadratic graphs in different forms (y = k$x + a$² + b, y = ax² + bx + c, or y = ax + b$$cx + d) each reveal different information about turning points, roots, and intercepts.

Final Skills: Problem Solving & Precision

Quadratic equations can be solved through factorising or the quadratic formula - knowing when to use each method saves valuable exam time. The quadratic formula works for any quadratic, whilst factorising is quicker when possible.

Functions use special notation like f$x$ to represent mathematical relationships. You'll evaluate expressions using functional notation, which is essentially substituting values into given formulas.

Rounding might seem basic, but precision matters in exams. You'll round to specified decimal places or significant figures - make sure you understand the difference between these two methods.

Exam strategy: Practice changing the subject of a formula involving squares and square roots - these questions often appear and can boost your confidence early in the exam!