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
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
