Pure Mathematics 1 (P1) Past Papers

Pure Maths 1 covers: Algebra and Functions, Coordinate Geometry (including circles), Sequences and Series (including binomial expansion), Differentiation, and Integration.

Differentiation from first principles uses the limit: f'(x) = lim(h→0) [f(x+h) - f(x)]/h. You substitute f(x+h), simplify, and take the limit as h approaches 0.

For arithmetic sequences: nth term = a + (n-1)d, sum of n terms = n/2[2a + (n-1)d] or n/2(a + l), where a is first term, d is common difference, l is last term.

To find stationary points: 1) Differentiate to get dy/dx, 2) Set dy/dx = 0 and solve, 3) Find corresponding y-values, 4) Use second derivative to determine if max, min, or point of inflection.

(a+b)ⁿ = Σ(r=0 to n) ⁿCᵣ × aⁿ⁻ʳ × bʳ. For (1+x)ⁿ, the general term is ⁿCᵣ × xʳ. Remember ⁿCᵣ = n!/(r!(n-r)!).