Edexcel AS Pure Maths, AS Level Pure Maths, QUESTIONS WITH SOLVED ANSWERS

Edexcel AS Pure Maths, AS-
Level Pure Maths, QUESTIONS
WITH SOLVED ANSWERS.

a unit vector in the direction of a is - CORRECT ANSWER✅✅a/|a|

area of a trapezoid - CORRECT ANSWER✅✅A=a+b/2xh

Area of a Triangle - CORRECT ANSWER✅✅½ x ab x sin(C)

Area of a triangle with two sides and angle in between - CORRECT ANSWER✅✅area
= ½absinC

Binomial expansion - CORRECT ANSWER✅✅

Binomial Expansion - CORRECT 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 - CORRECT ANSWER✅✅(a⁴)² = a⁸
multiply the powers

CAST Diagram - CORRECT ANSWER✅✅

Circle Theorems - CORRECT 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 - CORRECT ANSWER✅✅x² + bx = (x+b/2)² - (b/2)²

ax² + bx + c = a(x + b/2a)² + (c - b²/4a²)

Cosine Graph - CORRECT ANSWER✅✅

Cosine Rule (a²) - CORRECT ANSWER✅✅

, Cosine Rule (cos(A)) - CORRECT ANSWER✅✅

Derivative or gradient function equation - CORRECT ANSWER✅✅Where h represents
a small change.

Differentiating a quadratic - CORRECT ANSWER✅✅If y = ax² + bx + c
then dy/dx = 2ax + b

Differentiating eˣ - CORRECT ANSWER✅✅y = eᵏˣ → dy/dx = keᵏˣ

Differentiating x^n - CORRECT ANSWER✅✅If f(x) = xⁿ then f'(x) = nxⁿ⁻¹

If f(x) = axⁿ then f'(x) = anxⁿ⁻¹

Differentiation Formula - CORRECT ANSWER✅✅dy/dx = anxⁿ⁻¹

Discriminant - CORRECT 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 - CORRECT ANSWER✅✅√(x₁-x₂)² + (y₁-y₂)²

Distance between two points - CORRECT ANSWER✅✅d = √(x₁-x₂)² + (y₁-y₂)²

Distance Formula - CORRECT ANSWER✅✅√((x₂ - x₁)² + (y₂ - y₁)²)

from (x₁, y₁) to (x₂, y₂)

Dividing - rules of indices - CORRECT ANSWER✅✅a⁶ ÷ a² = a⁴
minus the powers

Dividing surds - CORRECT ANSWER✅✅√a ÷ √b = √a/b

division law of logs - CORRECT ANSWER✅✅logax-logay=loga(x/y)

Domain - CORRECT ANSWER✅✅The set of possible inputs for a function.

equation for midpoint - CORRECT ANSWER✅✅(x₁+x₂/2 , y₁+y₂/2)

equation of a circle - CORRECT ANSWER✅✅(x-a)^2 + (y-b)^2 = r^2