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Definitions and Formulas for Advanced Mathematics LOGIC ALGEBRA a → b a implies b i = -1 imaginary unit a ↔ b a if and only if b z complex conjugate of z a ∧ b a and b A-1 inverse of matrix A a ∨ b a or b ~a not a A ∪ B A union B A ∩ B A intersect B A complement of A U universal set { } empty set v vector v SERIES ∞ n=0 arn = a 1 - r for ⏐r⏐ < 1

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Advanced Higher Mathematics: Formulae Green (G): Formulae you must memorise in order to pass Advanced Higher maths as they are not on the formula sheet. Amber (A): These formulae are given on the formula sheet. But it will still be useful for you to memorise them.

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Equation of a plane A point r (x, y, z)is on a plane if either (a) r bd= jdj, where d is the normal from the origin to the plane, or (b) x X + y Y + z Z = 1 where X,Y, Z are the intercepts on the axes. Vector product A B = n jAjjBjsin , where is the angle between the vectors and n is a unit vector normal to the plane containing A and B in the direction for which A, B, n form a right-handed set.

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Page two FORMULAE LIST Circle: The equation x2 2+ y + 2gx + 2fy + c = 0 represents a circle centre (-g, -f) and radius gf22+− c. The equation (x - 2a) 2+ (y - b)2 = r represents a circle centre (a, b) and radius r.Scalar Product: a.b = |a||b| cos q, where q is the angle between a and b a.b = a 1 b 1 + aor 2 b 2 + a 3 b 3 where a =. Trigonometric formulae: sin (A ± B) = sin A cos B.

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FORMULAE LIST Standard derivatives f ( x ) f ′( x ) sin−1 x 1 1 − x 2 cos−1 x − 1 1 − x 2 tan−1 x 1 2 + x 1 tan x sec2 x cot x − cosec2

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n = 1 n ( a + l ) = 1 n {2 a + ( n − 2 2 1) d } For a geometric series: un = ar n − 1 , a (1 − rn ) S n = ( r ≠ 1) , ∞ = − r r − 1 ( r < 1 ) Binomial series: n − 1 n n a = n ) b + a ( n − a b + a 2 2 + b a n − 3 b 3 + K + b n , where n is a positive integer 1 2 3 n n

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8 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 uly 2017 Pearson Education Limited 2017 Standard deviation Standard deviation =√ (Variance) Interquartile range = IQR = Q 3 - Q 1 For a set of n values x 1, x 2, . . . x i, . . . x n S xx.

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ad = ! bc Properties of Exponents xnxm = xn+m (xn)m xnm = (xy)n = xnyn n n 1 m x m

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Title: Mathematics Advanced, Extension 1 and Extension 2 Reference Sheet Author: NSW Education Standards Authority Created Date: 11/12/2018 2:16:34 PM

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New Advanced Higher Mathematics: Formulae Green (G): Formulae you must memorise in order to pass Advanced Higher maths as they are not on the formula sheet. Amber (A): These formulae are given on the formula sheet. But it will still be useful for you to memorise them.

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Title: Mathematics Advanced, Extension 1 and Extension 2 Reference Sheet Author: NSW Education Standards Authority Created Date: 11/7/2019 1:47:30 PM

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Last updated on Jul 11, 2023 Download as PDF Overview Test Series Mathematics is the universal language of logic, patterns, and relationships. It is a discipline that explores the properties and structure of numbers, quantities, shapes, and patterns.

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Then, the distance is calculated using the formula: d 6 L :3 64 ; L9 E16 L25 We get d 625, so d √25 L𝟓 If we define two points generally as (x1, y1) and (x2, y2), then the 2-dimensional distance formula would be: distance L ¥ :x 6x 5 ; 6 E :y 6y 5 ; 6. Midpoint - To obtain the value of the midpoint in two or more dimensions, add the

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The 2014 GED® Mathematical Reasoning test contains a formula sheet, which displays formulas relating to geometric measurement and certain algebra concepts. Formulas are provided to test-takers so that. they may focus on application, Mathematics rather Formula than the Sheet memorization, of formulas. Area of a: square. A = s2.

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0345 279 1000 Centre Enquiries 0303 333 0330 Find SQA Advanced Higher Mathematics past papers, specimen question papers and course specification and important subject updates here.