Advanced Higher Maths Newbattle Community High School D Watkins 2011 Unit 2.4: Sequences and Series 1 1 2 (1) (1) (2(1)) 1 1 1 1 n n n n n n uand uar ar Snand S r r a S r r - ¥ = + - = - = + - = „ - = < - Arithmetic Series Geometric Series In particular, you are supposed to know that as a consequence of the last formula (A):
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. Red (R): Don’t worry about memorising these, but they might be useful to save time in classwork and homework ...
Advanced Higher Formula List Note: no formulae given in exam – remember everything ! Unit 1 Binomial Theorem Factorial n n! def = n × (n − 1) × (n − 2) × … × 3 × 2 × 1 Binomial Coefficient n r C ≡ n r def = !! ( )! n r n r− Symmetry Identity n r = n n r
Pupils studying Advanced Higher Maths will develop the following skills: select and apply complex mathematical techniques in a variety of mathematical situations, both practical and abstract; extend and apply skills in problem solving and logical thinking; extending skills in interpreting, analysing, communicating and managing
Numerical Formulae 19 Vector Formulae 23 Mechanics 25 Algebraic Structures 27 Statistical Distributions 29 F-Distribution 29 Normal Distribution 31 t-Distribution 32 ´2 (Chi-squared)- Distribution 33 Physical and Astronomical constants 34 2
Higher Maths Formula List Exponential & Logarithmic Functions Ô + Ô = Ô( ) Ô − Ô = Ô( ) Ô = Ô Ô =1 Ô1=0 Trigonometry Trigonometric exact values for common angles in degrees. Angle 0 30° 45° 60° 90° 0 𝜋 6 𝜋
FORMULAE LIST (continued) De Moivre’s theorem []r(cos sin) cos sinθ+= +i θn rnn( ) θ in θ Vector product × sin ˆ 2 3 13 12 123 2 3 13 12 123 aa aa aa θ aaa bb bb bb bbb = = = −+ ijk ab ab n i j k Matrix transformation Anti-clockwise rotation through an angle, θ about the origin, cos sin sin cos ⎡⎤ − ⎢⎥ ⎣⎦ θθ θθ
CfE Advanced Higher Mathematics Formulae List Standard derivatives Standard integrals Arithmetic series S n a n d n 1 21 2 Geometric series n n ar S r 1 1 Summations ( ) ( ),, n n n r r r n n n nn n n r r r 22 23 1 1 1 111 2 1 2 6 4 Binomial theorem n nn r r r n a b a b 0 r where ! r!( )! C r r n r
11. AH Maths Course Outline, Formulae Sheets & Check List. 12. AH Maths Practice Unit Assessments – Solutions Included. 13. AH Maths Video Links. 14. AH Maths X-Mas Special. 15. AH Maths Recommended Text Book. 16. Online Study Pack – Students looking for a ‘good’ Pass. Advanced Higher Maths Resources. 1. AH Maths Exam Focused Online ...
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.
Formula Sheet: a colour coded list of formulae relevant to the course; ... Advanced Higher Maths Revision Notes (cost: £45 for schools/colleges/tutors, £10 for individual learners, parents or carers. Bulk discount available if purchasing more than one level.) Free Solver Spreadsheets (easy ways for teachers to check answers to questions):
This website is designed to aid revision for SQA Advanced Higher Pure Mathematics by collating sources into one simple site and is divided into 2 sections: ... It also had a list of topics and subtopics for each question. The formulae list can easily be accessed at the top of every question.
Formulae Sheet for Advanced Higher Maths Summations (Arithmetic series) S n a n d n ª º ¬¼ 1 21 2 (Geometric series) n n ar S r 1 1 ( ) ( ) ,, n n n
Study with Quizlet and memorise flashcards containing terms like Differentiate sinax, Differentiate cosax, Integrate sinax and others.
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. Red (R): Don’t worry about memorising these, but they might be useful to save time in classwork and homework ...
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 derive them from scratch in the exam. But… it will save you a lot of time if you do choose
Advanced Higher Mathematics Formal Homework Assignment Sequences and Series 1. The sum of the first n terms of an arithmetic series is n(n+5). Find the first 3 terms of the series. 2. (a) In an arithmetic series of 9 terms, the first term is 5 and the last is 23. Find the sum of the 9 terms.
