Edexcel A Level Maths 100%

integrate sinx -cosx + c integrate cosx sinx + c integrate sec^2 x tanx + c integrate cosecxcotx -cosecx + c integrate cosec^2x -cotx + c integrate secx tanx secx + c cosec^2 x = cot^2 x + 1 sec^2 x = tan^2 x + 1 sin^2 x 1 - cos^2 x sin^2 x (1-cos2x)/2 cos^2 x (1+cos2x)/2 Integral of 1/x ln IxI + C Differentiate sin x cos x Differentiate tan x sec² x Differentiate cot x - cosec² x Differentiate sec x sec x tan x Differentiate cos x - sin x Differentiate cosec x - cosec x cot x Differentiate sin 2x 2 cos 2x Differentiate cot 3x - 3 cosec² 3x Differentiate sin² x 2 sin x cos x Differentiate cos 0.5x - 0.5 sin 0.5x Differentiate sin x cos x cos 2x Differentiate 2cos0.5x -sin0.5x Sin2θ 2sinθcosθ Cos2θ cos²θ-sin²θ =2cos²θ-1 =1-2sin²θ Tan2θ 2tanθ / (1 - tan²θ) When using tan addition formula, watch out for.. Signs: top and bottom should have opposite signs with the top being the same as the same as the one in the tan(a+-b). 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 State the domain of y = arcsinx -1 ≤ x ≤ 1 State the range of y = arcsinx -π/2 ≤ y ≤ π/2 Arccos(x) Graph State the domain of y = arccosx -1 ≤ x ≤ 1 State the range of y = arccosx 0 ≤ y ≤ π Arctan(x) Graph State the domain of y = arctanx -∞ < x < ∞ State the range of y = arctanx -π/2 < y < π/2 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 ∫ sin(x) dx -cos(x) + c ∫ cos(x) dx sin(x) + c Integration by parts uv - ∫ v(du/dx) dx tan² θ sec² θ - 1 1 sec² θ - tan² θ cot² θ csc² θ - 1 sin²θ+cos²θ=? 1 sec²x-1 tan²x sec²x-tan²x 1 sin²x 1-cos²x cos²x 1-sin²x cot²x+1 csc²x csc²x-cot²x 1 linear regression - do not extrapolate data - should not use the linear regression line to find a value of x for a given y experiment - repeatable process - rise to number of outcomes event A collection of one or more outcomes of an experiment