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n = 1 n ( a + l ) = 1 n {2 a + ( n โ 2 2 1) d } For a geometric series: un = ar n โ 1 , a (1 โ rn ) S n = ( r โ 1) , โ = โ r r โ 1 ( r < 1 ) Binomial series: n โ 1 n n a = n ) b + a ( n โ a b + a 2 2 + b a n โ 3 b 3 + K + b n , where n is a positive integer 1 2 3 n n
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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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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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Definitions and Formulas for Advanced Mathematics LOGIC ALGEBRA a โ b a implies b i = -1 imaginary unit a โ b a if and only if b z complex conjugate of z a โง b a and b A-1 inverse of matrix A a โจ b a or b ~a not a A โช B A union B A โฉ B A intersect B A complement of A U universal set { } empty set v vector v SERIES โ n=0 arn = a 1 - r for โrโ < 1
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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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FORMULAE LIST Standard derivatives f ( x ) f โฒ( x ) sinโ1 x 1 1 โ x 2 cosโ1 x โ 1 1 โ x 2 tanโ1 x 1 2 + x 1 tan x sec2 x cot x โ cosec2
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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+โ 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 ยฑ B) = sin A cos B.
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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 โ25 L๐ If we define two points generally as (x1, y1) and (x2, y2), then the 2-dimensional distance formula would be: distance L ยฅ :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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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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Advanced Higher Maths: Formulae Green (G): Formulae you absolutely must memorise in order to pass Advanced Higher maths. Remember you get no formula sheet at all in the exam! Amber (A): You don't have to memorise these formulae, as it is possible to deri ve them from scratch in the exam.
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Advanced Algebra Lessons Arithmetic Series Formula Arithmetic Series Formula Practice Problems Change-of-Base Formula for Logarithms Complex Fractions: Simplifying Complex Numbers: Division Complex Numbers: Multiplication Composition of Functions Cramer's Rule in 2ร2 Cramer's Rule in 3ร3 Determinants: 2ร2 Matrix Determinants: 3ร3 Matrix Distance between Point and Line Exponential.
Annotated Datasheet for Advanced/Extension 1/Extension 2 MathsFaculty
Title: Mathematics Advanced, Extension 1 and Extension 2 Reference Sheet Author: NSW Education Standards Authority Created Date: 11/7/2019 1:47:30 PM
Mathematics Advanced Extension 1 and Extension 2 Reference Sheet PDF PDF Educational
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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1.4. Compound interest. kn. FV = PV ร 1 + r , where FV is the future value, 100 k PV is the present value, n is the number of years, k is the number of compounding periods per year, r% is the nominal annual rate of interest. SL. 1.5. Exponents and logarithms. x = b โ x = log.