EDEXCEL A LEVEL MATHS|2023 LATEST UPDATE|GUARANTEED SUCCESS

1 + tan2θ = sec2θ cot2θ + 1 = cosec2θ = cosec2θ Sin2θ 2sinθcosθ Cos2θ cos²θ-sin²θ 2cos²θ-1 1-2sin²θ Tan2θ 2tanθ / (1 - tan²θ) How do you write a rational number in a proof? a/b What does y=|f(x)| do? Reflects values below the x-axis in the x-axis What does y=f(|x|) do? Reflects values of x≥0 in the y-axis Arithmetic sequence formula a₁+(n-1)d Geometric sequence formula uₙ = arⁿ⁻¹ Convergent geometric series Convergent if |r|<1 where r is the common ratio Periodic sequences Sequence is periodic if terms repeat in a cycle Vectors and angles If the vector a = xi + yj + zk makes an angle θₓ with the positive x-axis, then cos(θₓ) = x/(|a|) and similarly for the angles θᵧ and θz. Radian to degree conversion 1 radian = 180°= π Arc length l=rθ Area of a circle sector a=1/2 x r²θ Arcsin(x) Graph Arccos(x) Graph Arctan(x) Graph Differentiating y = eᵏˣ dy/dx = keᵏˣ Differentiating y = ln(x) dy/dx = 1/x Differentiating y = aᵏˣ dy/dx = (aᵏˣ)kln(a) The Chain Rule dy/dx = dy/du x du/dx The Product Rule The Quotient Rule Differentiating parametric equations Implicit differentiation Concave function f(x) concave if f''(x) ≤ 0 for all values of x in that interval Convex function f(x) concave if f''(x) ≥ 0 for all values of x in that interval Point of inflection Point at which f''(x) changes sign ∫ eˣ dx eˣ + c ∫ 1/x dx ln(x) + c