Edexcel A-Level Pure Maths Exam 2026/2027 Questions With Completed Solutions.

Edexcel A-Level Pure Maths

area of sector (where θ is in radians)

½r²θ


angles in 3D vectors
cosθₓ =x/|a|

cosθᵧ =y/|a|

cosθ₂ =z/|a|

this is where vector a makes an angle θ with the x/y/z axis (because x/y/z would be the adjacent
and a the hypotenuse)




Expanding (a + bx)ⁿ
(a + bx)ⁿ = aⁿ(1 + (b/a)x)ⁿ


cosine rule
a² = b² +c² -2bc cosA


rule for parametric integration
∫y dx = ∫(y dx/dt)dt

as (dx/dt) x dt would cancel out to give you ∫y dx


unit vector (â)
a / |a|

vector / magnitude of vector


rule for implicit differentiation of terms with xy
d/dx (xy) = x dy/dx + y

, (basically use the product rule then times the x-term by dy/dx)

e.g. d/dx (3xy) = 3x x 1(dy/dx) + 3y
= 3x(dy/dx) + 3y


arc length
rθ (where θ is in radians)


cosθ in terms of sin
cosθ = sin(90° - θ)


sinθ in terms of cos
sinθ = cos(90° - θ)


rules for domain and range of parametrics
the domain of f(x) (i.e. the Cartesian equation) is the range of the x values, given the range of t
values
the range of f(x) (i.e. the Cartesian equation) is the range of the y values, given the range of t
values


quartic graphs


set notation
x < a or x > b = { x : x < a } ∪ { x : x > b }
c<x<d={x:c<x}∩{x:x<d}


formula for nth term of arithmetic sequence
u = a + (n-1)d




formula for nth term of geometric sequence
u = arⁿ⁻¹




symbol for 'is a subset of'