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27 Dec 2025

•

2 pages

💚 Revision Guide for Maths Topics

𝐌𝐈𝐊𝐀𝐘𝐋𝐀 💝🪽

@m1kaylax

Welcome to your quick guide to key maths concepts! We'll... Show more

Maths mods
index laws.
a+b (add powers)
y²+yb sya+b
a-b (subtract powers)
(ya)b = yaxb (multiply)
eg Simplify 2x (m²)³
(m4)3 = m12
m²
12x312

Essential Maths Skills

Ever wondered how to simplify complex expressions? Index laws are your best friends here! When dealing with the same base, remember: add powers when multiplying $y^a × y^b = y^(a+b)$ , subtract powers when dividing $y^a ÷ y^b = y^(a-b)$ , and multiply powers when raising to another power $(y^a)^b = y^(a×b)$ .

Surds are simply irrational numbers that come from roots (like √2). They can't be written as simple fractions or terminating decimals. When working with surds, remember that √a × √b = √(ab) and √a ÷ √b = √ $a/b$ . To rationalise a surd in the denominator, multiply both top and bottom by the same surd to eliminate it from the bottom.

Linear inequalities use symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Solve them just like equations, but remember to flip the inequality sign if you multiply or divide by a negative number.

Pro Tip: When working with sequences, identify the pattern first - is it arithmetic $add/subtract same number$ , geometric $multiply/divide by same number$ , or quadratic (second difference is constant)? This will determine which formula to use!

Understanding special graphs gives you powerful visual tools. Cubic graphs $y = x³$ have distinctive S-shapes, exponential graphs $y = a^x$ curve upward rapidly, reciprocal graphs $y = 1/x$ have asymptotes, and trigonometric graphs (sine, cosine, tangent) have regular wave patterns with key intercepts and turning points.

Trigonometry Essentials

Knowing the exact trigonometric values for common angles will save you tons of time in exams! For angles 0°, 30°, 45°, 60° and 90°, there are specific values for sine, cosine and tangent that you should memorise rather than calculate each time.

The fundamental trigonometric ratios relate the sides of a right-angled triangle: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent. These are the building blocks for solving any triangle problem you'll encounter.

A clever way to remember these values is using the "finger trick" - counting from your thumb (0°) to your pinky (90°). For sin, the values start at 0 and increase (0, 1/2, √2/2, √3/2, 1), while for cos, they decrease from 1 to 0 (1, √3/2, √2/2, 1/2, 0).

Remember This: Trig values appear everywhere in maths and physics! When you see sin60°, you should immediately know it equals √3/2 without needing a calculator.

When working with angles beyond 90°, you'll need to understand how these values repeat in patterns. Sine and cosine have a period of 360°, while tangent repeats every 180°. This knowledge is crucial for sketching graphs and solving equations involving trigonometric functions.

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Maths

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419

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27 Dec 2025

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2 pages

💚 Revision Guide for Maths Topics

𝐌𝐈𝐊𝐀𝐘𝐋𝐀 💝🪽

@m1kaylax

Welcome to your quick guide to key maths concepts! We'll explore index laws, surds, inequalities, sequences, and more. These fundamental ideas are crucial for solving complex problems and will appear in many of your exams.

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Essential Maths Skills

Pro Tip: When working with sequences, identify the pattern first - is it arithmetic $add/subtract same number$ , geometric $multiply/divide by same number$ , or quadratic (second difference is constant)? This will determine which formula to use!

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Trigonometry Essentials

Remember This: Trig values appear everywhere in maths and physics! When you see sin60°, you should immediately know it equals √3/2 without needing a calculator.