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Victorian Certificate of Education Year MATHEMATICAL METHODS Written examinations 1 and 2 FORMULA SHEET Instructions This formula sheet is provided for your reference. Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room. © VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2016 Version 2 – April 2016 MATHMETH EXAMS 1 & 2 (SAMPLE) 2 Version 2 – April 2016 Mathematical Methods formulas Mensuration area of a trapezium 1 a+b h ( ) 2 volume of a pyramid 1 Ah 3 curved surface area of a cylinder 2π rh volume of a sphere 4 3 πr 3 volume of a cylinder π r 2h area of a triangle 1 bc sin ( A ) 2 volume of a cone 1 2 πr h 3 Calculus d n x = nx n − 1 dx ∫ x dx = n + 1 x n +1 d n −1 (ax + b) n = an ( ax + b ) dx ∫ 1 (ax + b) n + 1 + c, n ≠ − 1 a (n + 1) d ax e = ae ax dx ∫e ( ) ( 1 n ) ( ) (ax + b) n dx = ax dx = + c, n ≠ −1 1 ax e +c a ∫ 1 dx = log e ( x) + c, x > 0 x d ( sin (ax) ) = a cos (ax) dx ∫ 1 sin (ax)dx = − cos (ax) + c a d ( cos (ax) ) = − a sin (ax) dx ∫ cos (ax)dx = a sin (ax) + c d 1 ( log e ( x) ) = x dx 1 d a = a sec 2 (ax) ( tan (ax) ) = 2 dx cos (ax) product rule d dv du ( uv ) = u + v dx dx dx chain rule dy dy du = dx du dx quotient rule du dv −u v d u dx dx = dx v v2 Version 2 – April 2016 3 MATHMETH EXAMS 1 & 2 (SAMPLE) Probability Pr(A ∪ B) = Pr(A) + Pr(B) – Pr(A ∩ B) Pr(A) = 1 – Pr(A′) Pr(A|B) = Pr ( A ∩ B ) Pr ( B ) µ = E(X) mean var(X) = σ 2 = E((X – µ)2) = E(X 2) – µ2 variance Probability distribution discrete Pr(X = x) = p(x) continuous Pr(a < X < b) = Mean Variance σ 2 = ∑ (x – µ)2 p(x) µ = ∑ x p(x) ∫ b a f ( x)dx µ= ∫ ∞ −∞ x f ( x)dx σ2 = ∫ ∞ ( x − µ ) 2 f ( x)dx −∞ Sample proportions P̂ = X n standard deviation sd ( Pˆ ) = p (1 − p ) n mean E(P̂ ) = p approximate confidence interval pˆ (1 − pˆ ) pˆ (1 − pˆ ) pˆ − z , pˆ + z n n END OF FORMULA SHEET