Further maths cheat sheet
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Further maths cheat sheet. π‘π‘β. To geometrically represent complex numbers, we use an Argand diagram which Ch. Matrices III Cheat Sheet (A-Level Only) AQA A Level Further Maths: Core Solving Systems of Three Triangular Simultaneous Equations Three simultaneous equations containing three A set of unknowns can be rewritten and solved using matrices. Circular Motion I Cheat Sheet AQA A Level Further Maths: Mechanics Circular Motion with a Constant Speed Velocity is a vector quantity so has magnitude and direction. 0=π2−3π+2=Ὠπ−1ὩὨπ−2Ὡ⇒π 1=1, π2=2 Write complementary function πΆπΉ. For past papers visit the Maths Past Paper page. our first term is y − = w. Find the magnitude of the impulse exerted on the wall by the ball. 1 2. Core Pure 1 Mechanics 1. To find the length Ch. For example, the Differential Equations V Cheat Sheet (A Level Only) AQA A Level Further Maths: Core Using Hooke’s Law to Formulate Differential Equations for Simple Harmonic Motion The process of observing a system and modelling it using a differential equation requires some knowledge of the forces acting in the system. e. Vectors Cheat Sheet Edexcel Core Pure 1 5 −’ %) % 6 & & = 7 ’ ’ in cartesian form. The ball strikes a smooth plane which is inclined at an angle π’π’ to the horizontal, where tan π’π’= 1 2. Immediately before striking the plane the ball has speed 5 ms−1. We would write that: Further Vectors II Cheat Sheet AQA A Level Further Maths: Core ; Begin by calculating the vectors of two sides of this triangle. As a result, it is very useful to be able to solve these equations. On this page you can find formula sheets, cheat sheets and questions by topic for Further Additional Pure for Edexcel, AQA and OCR (A). eigenvalue. A matrix is an array of numbers, or elements, arranged in rows and columns. ππsuch that the output is a scalar multiple of . Many real-life situations can be modelled using differential equations. + + = L + + = M +β U+π= N The above equations can be rewritten as: π΄= Free online university thermodynamics cheat sheet with key equations needed to solve thermodynamic processes. Common quantities are mass, time, and length (or distance). The order of a matrix is the number of rows and columns in the matrix. This series in particular is an arithmetic series which is introduced in Pure Year 2. 6 Hyperbolic Functions Cheat Sheet - Edexcel Further Maths A-level - CP2 Author: PMT Education Created Date: 9/21/2021 9:43:21 PM Proof by induction Cheat Sheet Edexcel Core Pure 1 Example 1: +Prove by induction that, for ∈β€ ΰ·( vπ3− uπ2+π)= 3( + s) π π=1 Start by making a note of what you want to prove in the inductive step. Videos and Worksheets for Level 2 Further Maths. Since one of the Complex Numbers II Cheat Sheet AQA A Level Further Maths: Core Geometric Representation of Complex Numbers Argand Diagrams All real numbers exist on a straight, infinite number line; all complex numbers exist beyond the real number line in the complex plane. Matrices Cheat Sheet Edexcel Core Pure 1 : det ππππ ππππ = ππππ ππππ = ad − bc ππππππ π π ππ ππ ππππππ, ππππππ π π ππππ ππππππ , ππππππ π π ππππ Example 2: Find the general solution to the differential equation You might at first find it difficult to spot the use of the product rule. Polar Coordinates Cheat Sheet AQA A Level Further Maths: Core The familiar and axes of the 2D plane are just one set of coordinates which can be used to describe each point in the plane. πΆπΉ= Complex Numbers Cheat Sheet Edexcel Core 1 KWWSV ELW O\ SPW HGX KWWSV ELW O\ SPW FF KWWSV ELW O\ SPW FF. A trick is to look at the term involving ππππ Ch. Eigenvectors are Further Algebra and Functions I Cheat Sheet AQA A Level Further Maths: Core Relationship Between the Roots and Coefficients of a Polynomial The roots of a polynomial are the points at which the curve crosses the -axis. 4 2 = [ ] 4 9 13. work done= π Ch. Below are some examples of matrices: 4 7 2. 5The coefficient of restitution Further Algebra and Functions V Cheat Sheet AQA A Level Further Maths: Core Graphs of the Parabola, Ellipse and Hyperbola Graphs of the parabola, ellipse and hyperbola are called conic sections because they are all found to be the intersection of a plane and a cone. derivatives using Leibnitz’s theorem, evaluating certain indeterminate limits using L’Hospital’s rule, and finding definite and indefinite integrals using the Weierstrass Complex Numbers I Cheat Sheet AQA A Level Further Maths Core Complex Numbers and Complex Algebra Complex numbers are a superset of the real numbers. Since being introduced to the modern number system, they have proved useful in many fields - including quantum mechanics and electronics. These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. ΰ· ( v π3− u2 + )=( π s)3 t π+1 π=1 We start with the basis step; we show the πΏπ» = π» : 3 Continuous Random Variables I Cheat Sheet AQA A Level Further Maths: Statistics a) i) Integrate pdf and set equal to 1 and solve for π. =’+>" ’=$ 4 −1 & vector ", subtract the position vectors. Of course, these relationships also need to be proved true. There will be one zip file per paper, you can find the individual files to download in the ‘By Paper’ cabinets. Further Calculus VI Cheat Sheet AQA A Level Further Maths: Core Mean Value of a Function Integration can be used to find the mean value of a function between two points. wall with speed We begin by drawing a diagram: Put the loci equation into the form |#−#!|=&. Solving Trigonometric Equations 2 Video Practice Questions Answers. Writing ππ∈ππ shows that the element ππ is a member of the set ππ. Ch. of matrix ππ, with ππ its corresponding . The numbers in a matrix are called the elements of the matrix. Find a vector equation of the straight line which passes through the points 1 and 2, with position vectors 44 +56−8 and 64+36+28 respectively. Back to Subjects | Back to Maths. 0= 2+2 +1=( +1)2 ⇒ = −1 Substitute into the general solution for released from rest and moves down the slope. % passes through both 1 and 2 so we can use !. By integrating, all the values that the function takes within the given interval are Notes and questions on A-Level Further maths. 4 Roots of Polynomials Cheat Sheet - Edexcel Further Maths A-level - CP1 Author: PMT Education Created Date: 20190916221821Z Differential Equations I Cheat Sheet (A Level Only) AQA A Level Further Maths: Core Classifying Differential Equations Differential equations are incredibly useful and can be used to model various phenomena since they describe the rate of change of a quantity with respect to another quantity. The geometric distribution . A) Find its initial acceleration. 1 Roots of Polynomials for the Edexcel A Level Further Maths: Core Pure syllabus, written by the Further Maths experts at Save My Exams. In the 15th century, French Methods in Calculus Cheat Sheet Edexcel A Level Further Maths: FP1 . Numerical Methods Cheat Sheet (A Level Only) AQA A Level Further Maths: Core The Mid-Ordinate Rule The mid-ordinate rule is a way of approximating the area under a curve by using vertical strips of equal width. Eigenvectors and Eigenvalues . Another set which could be used are called polar coordinates where each point is described by its 2radial distance from the origin and an angle. For use during the course and in the examinations . First examinations 2014 . then . They have a range of applications in mathematics and physics such as Ch. eigenvector. If you are carrying out a fixed number of independent trials each with a constant probability of success, ππ, then you can model the number of trials needed to achieve one success using a geometric distribution. Core Pure 2 Mechanics 2. our last term will be y −( t4) = −1 ∑ This is the value of r where our series starts, i. The aim of this chapter is to be able to quantify the reliability of a hypothesis test. Solving Trigonometric Equations 1 Video Practice Questions Answers. Consider a particle moving in a horizontal circular path in the -plane, as seen in Oct 5, 2010 Β· CIE Further Maths (9231) Cheat Sheet is a reference document that contains important formulas, derivatives, and integrals for the CIE Further Maths (9231) exam. In other words, how the change Work, Energy and Power I Cheat Sheet AQA A Level Further Maths: Mechanics Definition of Work Force Acting Along the Line of Motion The definition of work done is given by the product of force ( ) and the distance moved in the direction of force (π). 1. For a matrix #, the determinant can be denoted by t ( #), t #, | #| or β. ] = [ = [7 4 ] 1 5 10 6 3. The ball rebounds with speed 2. # × Matrices For a matrix #=[ ], | #|= − Polar Coordinates Cheat Sheet ππ2= π₯π₯2 π¦π¦2 tanππ= ππ ππ ⇒ Edexcel Pure Year 2 π΄π΄ππππ= 1 2 ππ2 ππ ππ Edexcel Pure Year 2 KWWSV ELW O\ SPW HGX KWWSV ELW O\ SPW FF KWWSV ELW O\ SPW FF Proof Cheat Sheet AQA A Level Further Maths: Core Proof by Induction Proof by induction is a robust and diverse method of mathematical proof used when the result or final expression is already known. is called an . Instead of using the endpoints of each vertical strip, the -value of the curve at each midpoint is used to fit a rectangle. It is a useful tool for students to quickly review and memorize key concepts. |#−(6−3*)|=4 Thus, the loci of # is a circle of radius 4, centred at (6,−3) Argand diagrams look similar to Cartesian diagrams Quality of Tests Cheat Sheet Hypothesis tests are not perfect. Circular Motion II Cheat Sheet (A Level Only) AQA A Level Further Maths: Mechanics Kinetic Quantities as Vectors in Circular Motion A particle moving in a horizontal circular orbit can have its displacement, velocity and acceleration described by vectors. HΕ½ ÓW©Ã úºcfo7± ¾Ø®t¶ávçÎÝÎ=¢³_½ Üd6"+T3â7¼àF˜§Ã0B #¾ë w ¸ Ÿî_p [ Ûk«Äj»½Ø –‰’ XI*! éf&# ©¨;xÍ %¢ss¬ „ýZ}v it»÷Ú Q^WçU°b✠œΕΎV¢ AŸZ:ƒ ɹà•À•X0E /ˆ `®¤ ¸@32 Ø æ8Èq8Ç t‰U9*§ Â"°,µ¶ oµî~·ÿgãÅÊ„’%b Ö FU©Ôáújk½ñYRseC©x"M 9€…‚Œ!–ù Dimensional Analysis Cheat Sheet AQA A Level Further Maths: Mechanics Dimensional Analysis Dimensions of Quantities The dimension of a quantity is used to describe what sort of quantity is being measured. The direction of velocity of a particle as it moves in a circle is constantly changing. Using contingency tables Another type of question you can be asked is one where you are given a contingency table (sometimes called a two-way table) and you need Elastic Collisions in Two Dimensions Cheat Sheet Edexcel FM1 Example 1: A small smooth ball is failing vertically. v, ππππ= ππππ, E. Edited in 2015 (version 2) Diploma Programme Solving Trigonometric Equations: Introduction Video. They are a great revision tool for students to use alongside their studies. The division algorithm Recalling set theory from GCSE Maths, a set is a collection of distinct objects. Mathematics HL and further mathematics HL formula booklet . Practice papers for AS and A level Further Mathematics by topic. This point could be at either end of the interval, or somewhere in the middle. They can lead to incorrect conclusions which can have 1serious consequences, depending on the context of the hypothesis test. Matrix Arithmetic and Multiplying a Matrix by a Scalar. Core Pure 1. • A binary operation on a set is a calculation that combines two elements of the set to output another element of the same set. Differential Equations II Cheat Sheet (A Level Only) AQA A Level Further Maths: Core a) Write auxiliary equation. This cheat sheet explores three useful ideas in calculus: evaluating ππ. 6 4 8. ∫ ππ₯2 3 1 π₯=1⇒ Reducible Differential Equations Cheat Sheet Edexcel A Level Further Maths: FP1 . Consider a differentiable curve = ( ), given in cartesian coordinates. 4 Inequalities Cheat Sheet - Edexcel Further Maths A-level - FP1 Author: PMT Education Created Date: 9/22/2021 11:36:48 AM Momentum and impulse Cheat Sheet Edexcel FM1 Example 1: A ball of mass 0. Elastic energy. In springs, when they Geometric and Negative Binomial Distributions Cheat Sheet Edexcel FS1 . If you run out of questions by topic for your own exam board you should move onto another exam board’s tab. They serve as Matrices IV Cheat Sheet AQA A Level Further Maths: Core 3 Eigenvalues show the scale factor Factorisation of Determinants Using Row and Column Operations Eigenvalues and Eigenvectors (A Level Only) 2 A triangular matrix is a matrix which has non-zero entries only on the leading diagonal (top left to bottom Revision notes on 3. 7 Linear Transformations Cheat Sheet - Edexcel Further Maths A-level - CP1 Author: PMT Education Created Date: 20190916222029Z Core Pure Formula Sheet - Edexcel Further Maths A-level Author: PMT Education Created Date: 9/7/2022 4:07:05 PM Matrices Cheat Sheet II AQA A Level Further Maths: Core Determinant of a Matrix The determinant of a matrix is a scalar value which can be calculated from a square matrix. B) Without any further calculation, state how your answer to part awould chang e if the coefficient of friction between the particle and the plane was greater than . Number theory is used in cryptography. Revision notes, summary sheets with key points, checklists, worksheets, topic questions and papers with model solutions for AQA, Edexcel, OCR, MEI Maths A-level On this page you can find formula sheets, cheat sheets and questions by topic for Further Statistics for Edexcel, AQA and OCR (A). On this page you can find formula sheets, cheat sheets and questions by topic for Further Core Pure for Edexcel, AQA and OCR (A). v. First-order differential equations Series Cheat Sheet Edexcel Core Pure 1 This tells us the last value of r for our sequence, i. In AQA A-Level Further Mathematics, it is involved only in proving sums of series, divisibility, and powers of matrices. Matrices are Centres of Mass and Moments II Cheat Sheet AQA A Level Further Maths: Mechanics (A Level Only) Centres of Mass of Composite Bodies Composite bodies are comprised of different shapes, and so to find their centre of mass, the centres of mass of all the component parts are taken, and a weighted average is calculated. Differential Equations III Cheat Sheet (A Level Only) AQA A Level Further Maths: Core Find the roots of the auxiliary equation to the associated homogeneous differential equation d 2 d 2 −3d d +2 =0. Further Vectors I Cheat Sheet AQA A Level Further Maths: Core Equation of a plane (A Level Only) A plane can also be described using a vector equation: !=#+%&+’( As before, # is a vector to the plane, & and ( are two non-parallel vectors along the plane, % and ’ parameters which have a unique value for each point on the plane. Numerous methods can be employed to solve differential equations of different forms. 2 αΊhits a fixed vertical wall at right angles with speed 3. If a matrix ππ transforms a non-zero vector . 2 Conic Sections 1 Cheat Sheet - Edexcel Further Maths A-level - FP1 Author: PMT Education Created Date: 9/8/2022 12:03:54 PM Further Vectors I Cheat Sheet AQA A Level Further Maths: Core Equation of a plane (A Level Only) A plane can also be described using a vector equation: !=#+%&+’( As before, # is a vector to the plane, & and ( are two non-parallel vectors along the plane, % and ’ parameters which have a unique value for each point on the plane. 5 −1. Title: Ch. Further Maths Matrix Summary 1 Further Maths Matrix Summary A matrix is a rectangular array of numbers arranged in rows and columns. 6 Integration Techniques Cheat Sheet - Edexcel Further Maths A-level - FP2 Author: PMT Education Created Date: 9/8/2022 6:22:35 PM Further Calculus I Cheat Sheet AQA A Level Further Maths: Core Improper Integrals (A Level Only) Integrals With Undefined Points When integrating a function over an interval, it is possible that it will be undefined at one or more points within it. Example 1 [is a ] 3 by 2 or matrix as it has 3 rows and 2 columns. Independent of Further Calculus V Cheat Sheet (A Level Only) AQA A Level Further Maths: Core Arc Length of a Curve Arc Length of a Curve Expressed in Cartesian Coordinates Integration is used to find the arc length of a curve between two end points. 1 Complex Numbers Cheat Sheet - Edexcel Further Number theory is a branch of mathematics that is concerned with the study of the propertie s of numbers, and the interesting and unexpected relationships between different sorts of numbers. Let β»this function βΊπ₯= 0+ 1π₯+ 2π₯2+ 3π₯3+β― Chi-Squared Tests Cheat Sheet Edexcel FS1 c) Stating your hypotheses clearly, use a 10% level of significance to test the motorway supervisor’s belief. 2 Work, Energy and Power Cheat Sheet - Edexcel Further Maths A-level - FM1 Author: PMT Education Subject Keywords Created Date: Further Algebra and Functions II Cheat Sheet AQA A Level Further Maths: Core Maclaurin Series of a Function and the General Term (A-Level Only) The Maclaurin series is a method of approximating a function by expressing the function as an infinite series polynomial. These are comprised of a mixture of legacy past paper questions, new shadow exam questions and some new questions. Matrix Algebra Cheat Sheet Edexcel FP2 . jhjoj jgnlmfx uettlzj eowke cerjj nnpke cmljs vzy nvwmyx rtem