Aquinas College. Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET

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1 Aquinas College Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET

2 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

3 1 AS Mathematics Pure Mathematics 1 Mensuration Surface area of sphere = 4πr Area of curved surface of cone = πr slant height Binomial series (a + b) n = a n + 1 an 1 b + an b r an r b r b n (n ) where r = n C r = n! r!( n r)! Logarithms and exponentials log a x = log log e x ln a = a x b b x a Differentiation First Principles f + f f ( ) = lim ( x h x ) ( x ) h 0 h Statistics Probability P( A ) = 1 P( A) Standard deviation Standard deviation = (Variance) Interquartile range = IQR = Q 3 Q 1 For a set of n values x 1, x,... x i,... x n S xx = Σ(x i x) = Σx i (Σ x i ) n Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017 3

4 Standard deviation = S xx n or n x x Statistical tables The following statistical tables are required for A Level Mathematics: Binomial Cumulative Distribution Function (see page 9) Random Numbers (see page 38) Mechanics Kinematics For motion in a straight line with constant acceleration: v = u + at s = ut + 1 at s = vt 1 at v = u + as s = 1 (u + v)t 4 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

5 A Level Mathematics Pure Mathematics Mensuration Surface area of sphere = 4πr Area of curved surface of cone = πr slant height Arithmetic series S n = 1 n(a + l) = 1 n[a + (n 1)d] Binomial series (a + b) n = a n + 1 an 1 b + an b r an r b r b n (n ) where r = n C r = n! r!( n r)! (1 + x) n = 1 + nx + nn ( 1 ) 1 x nn ( 1)...( n r + 1) x r +... (½ x ½ < 1, n ) 1... r Logarithms and exponentials log a x = log log e x ln a = a x b b x a Geometric series S n = a r n ( 1 ) 1 r S = a 1 r for ½ r ½ < 1 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017 5

6 Trigonometric identities sin(a ± B) = sin A cosb ± cosa sinb cos(a ± B) = cosa cosb sin A sinb tan(a ± B) = tan A ± tan B (A ± B (k tan Atan B )π) sin A + sinb = sin A + B cos A B sin A sinb = cos A + B sin A B cosa + cosb = cos A + B cos A B cosa cosb = sin A + B sin A B Small angle approximations sin θ θ cos θ 1 tan θ θ θ where θ is measured in radians Differentiation First Principles f + f f ( ) = lim ( x h x ) ( x ) h 0 h f(x) tan kx sec kx cot kx cosec kx f ( x) g( x) f (x) k sec kx k sec kx tan kx k cosec kx k cosec kx cot kx f ( x) g( x) f( x) g ( x) (g ( x)) 6 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

7 Integration (+ constant) f(x) f(x) dx sec kx tan kx cot kx 1 k tan kx 1 ln½sec kx½ k 1 ln½sin kx½ k cosec kx 1 k ln½cosec kx + cot kx½, 1 k ln½tan ( 1 kx)½ sec kx u d v dx dx = uv v d u dx dx 1 k ln½sec kx + tan kx½, 1 k ln½tan ( 1 kx + 1 π)½ 4 Numerical Methods The trapezium rule: b y dx 1 h{( y + y ) + (y + y y b a )}, where h = a 0 n 1 n 1 n The Newton-Raphson iteration for solving f(x) = 0 : x n+1 = x n f ( xn ) f ( x ) Statistics n Probability P( A ) = 1 P( A) P(A B) = P(A) + P(B) P(A B) P(A B) = P(A)P(B ½ A) P( B A) P( A) P(A ½ B) = P( B A) P( A) + P( B A ) P( A ) For independent events A and B, P(B ½ A) = P(B) P(A ½ B) = P(A) P(A B) = P(A) P(B) Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017 7

8 Standard deviation Standard deviation = (Variance) Interquartile range = IQR = Q 3 Q 1 For a set of n values x 1, x,... x i,... x n S xx = Σ(x i x) = Σx i (Σ x i ) n Standard deviation = S xx n or n x x Discrete distributions Distribution of X P(X = x) Mean Variance Binomial B(n, p) x px (1 p) n x np np(1 p) Sampling distributions For a random sample of n observations from N(μ, σ ) X σ / μ n ~ N(0, 1) Statistical tables The following statistical tables are required for A Level Mathematics: Binomial Cumulative Distribution Function (see page 9) Percentage Points of The Normal Distribution (see page 34) Critical Values for Correlation Coefficients: Product Moment Coefficient (see page 37) Random Numbers (see page 38) Mechanics Kinematics For motion in a straight line with constant acceleration: v = u + at s = ut + 1 at s = vt 1 at v = u + as s = 1 (u + v)t 8 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

9 5 Statistical Tables Binomial Cumulative Distribution Function The tabulated value is P(X x), where X has a binomial distribution with index n and parameter p. p = n = 5, x = n = 6, x = n = 7, x = n = 8, x = n = 9, x = n = 10, x = Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017 9

10 p = n = 1, x = n = 15, x = n = 0, x = Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

11 p = n = 5, x = n = 30, x = Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited

12 p = n = 40, x = Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

13 p = n = 50, x = Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited

14 Percentage Points of The Normal Distribution The values z in the table are those which a random variable Z N(0, 1) exceeds with probability p; that is, P(Z > z) = 1 Φ(z) = p. p z p z Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

15 Critical Values for Correlation Coefficients These tables concern tests of the hypothesis that a population correlation coefficient ρ is 0. The values in the tables are the minimum values which need to be reached by a sample correlation coefficient in order to be significant at the level shown, on a one tailed test. Product Moment Coefficient Spearman s Coefficient Level Sample size, n Level Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited

16 Random Numbers Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 017 Pearson Education Limited 017

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