Edexcel AS Pure Maths, AS-Level Pure Maths, pure maths As level

Edexcel AS Pure Maths, AS-Level Pure Maths, pure maths As level a unit vector in the direction of a is - ANSWER-a/|a| .area of a trapezoid - ANSWER-A=a+b/2xh .Area of a Triangle - ANSWER-½ x ab x sin(C) .Area of a triangle with two sides and angle in between - ANSWER-area = ½absinC .Binomial expansion - ANSWER- .Binomial Expansion - ANSWER-(a + b)ⁿ = (ⁿCᵣ)(aⁿ⁻¹bʳ) (a + b)ⁿ = aⁿ + (ⁿC₁)(aⁿ⁻¹b) + (ⁿC₂)(aⁿ⁻²b²) + ... + (ⁿCᵣ)(aⁿ⁻ʳbʳ) + ... + bⁿ .Brackets - rules of indices - ANSWER-(a⁴)² = a⁸ multiply the powers .CAST Diagram - ANSWER- .Circle Theorems - ANSWER-• Tangent to a circle is perpendicular to the radius of the circle at the point of intersection. • Perpendicular bisector of a chord will go through the circle centre. • If triangle forms across the circle, its diameter is the hypotenuse of the right-angled triangle. • Equations of the perpendicular bisectors of two different chords will intersect at the circle centre. .completing the square - ANSWER-x² + bx = (x+b/2)² - (b/2)² ax² + bx + c = a(x + b/2a)² + (c - b²/4a²) .Cosine Graph - ANSWER- .Cosine Rule (a²) - ANSWER- .Cosine Rule (cos(A)) - ANSWER- .Derivative or gradient function equation - ANSWER-Where h represents a small change. .Differentiating a quadratic - ANSWER-If y = ax² + bx + c then dy/dx = 2ax + b .Differentiating eˣ - ANSWER-y = eᵏˣ → dy/dx = keᵏˣ .Differentiating x^n - ANSWER-If f(x) = xⁿ then f'(x) = nxⁿ⁻¹ If f(x) = axⁿ then f'(x) = anxⁿ⁻¹ .Differentiation Formula - ANSWER-dy/dx = anxⁿ⁻¹ .Discriminant - ANSWER-b² - 4ac 0 then two distinct real roots. b² - 4ac = 0 then one repeated real root. b² - 4ac 0 then a quadratic function has no real roots. .Distance between two points - ANSWER-√(x₁-x₂)² + (y₁-y₂)² .Distance between two points - ANSWER-d = √(x₁-x₂)² + (y₁-y₂)² .Distance Formula - ANSWER-√((x₂ - x₁)² + (y₂ - y₁)²) from (x₁, y₁) to (x₂, y₂) .Dividing - rules of indices - ANSWER-a⁶ ÷ a² = a⁴ minus the powers .Dividing surds - ANSWER-√a ÷ √b = √a/b .division law of logs - ANSWER-logax-logay=loga(x/y) .Domain - ANSWER-The set of possible inputs for a function. .equation for midpoint - ANSWER-(x₁+x₂/2 , y₁+y₂/2) .equation of a circle - ANSWER-(x-a)^2 + (y-b)^2 = r^2 .Equation of a circle - ANSWER-(x-a)² + (y-b)² = r² with centre (a,b) and radius r. .Equation of a Circle (fg) - ANSWER-x² + y² + 2fx + 2gy + c = 0 with centre (-f, -g) and radius √(f² + g² - c) .Equation of a Line - ANSWER-y - y₁ = m(x - x₁) with coords (x₁, y₁) .Equation of a line using two known points. - ANSWER-y - y₁ = m(x - x₁) where m = gradient and (x₁,y₁) are the coordinates used. .Equation of a straight line - ANSWER-y = mx + c