Essential Maths Concepts

Powers and indices are simply repeated multiplication - when you see 3², it means 3 × 3 = 9, whilst 3⁴ means 3 × 3 × 3 × 3 = 81. Think of the small number as telling you how many times to multiply the base number by itself.

When expanding brackets like x+3$$x+5, use FOIL - First, Outside, Inside, Last. Multiply the first terms $x × x = x²$, then outside terms $x × 5 = 5x$, inside terms $3 × x = 3x$, and finally last terms $3 × 5 = 15$. Add them together: x² + 5x + 3x + 15 = x² + 8x + 15.

Remember BODMAS for the order of operations: Brackets first, then Order (powers), Division, Multiplication, Addition, and Subtraction. This ensures you always get the correct answer when solving complex calculations.

Standard form helps you write very large or tiny numbers more easily. Move the decimal point so you have one digit before it (like 5.4), then multiply by 10 to the power of how many places you moved. For example, 0.0000054 becomes 5.4 × 10⁻⁶.

💡 Quick Tip: In standard form, negative powers mean very small numbers, whilst positive powers mean very large numbers.

HCF (Highest Common Factor) is the largest number that divides into two or more numbers, whilst LCM (Lowest Common Multiple) is the smallest number that both numbers divide into evenly.

The Pythagorean theorem $a² + b² = c²$ helps you find missing sides in right-angled triangles, where c is always the longest side (hypotenuse).

Polygon angles follow a pattern: triangles have 180°, quadrilaterals have 360°, pentagons have 540°, and each additional side adds another 180° to the total internal angles.