Further maths cheat sheet

Further maths cheat sheet. Consider a particle moving in a horizontal circular path in the -plane, as seen in Oct 5, 2010 · CIE Further Maths (9231) Cheat Sheet is a reference document that contains important formulas, derivatives, and integrals for the CIE Further Maths (9231) exam. Consider a differentiable curve = ( ), given in cartesian coordinates. 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. 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. 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. 4 2 = [ ] 4 9 13. 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. 𝑡𝑡ℎ. 0=𝜆2−3𝜆+2=Ὠ𝜆−1ὩὨ𝜆−2Ὡ⇒𝜆 1=1, 𝜆2=2 Write complementary function 𝐶𝐹. 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. 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. 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 (𝑑). Let ⁻this function ⁺𝑥= 0+ 1𝑥+ 2𝑥2+ 3𝑥3+⋯ 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. Edited in 2015 (version 2) Diploma Programme Solving Trigonometric Equations: Introduction Video. Ch. e. The aim of this chapter is to be able to quantify the reliability of a hypothesis test. First examinations 2014 . As a result, it is very useful to be able to solve these equations. 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. 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. For past papers visit the Maths Past Paper page. Mathematics HL and further mathematics HL formula booklet . Since being introduced to the modern number system, they have proved useful in many fields - including quantum mechanics and electronics. The direction of velocity of a particle as it moves in a circle is constantly changing. Numerous methods can be employed to solve differential equations of different forms. Core Pure 2 Mechanics 2. Matrix Arithmetic and Multiplying a Matrix by a Scalar. 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. wall with speed We begin by drawing a diagram: Put the loci equation into the form |#−#!|=&. 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. Immediately before striking the plane the ball has speed 5 ms−1. Matrices Cheat Sheet Edexcel Core Pure 1 : det 𝑎𝑎𝑏𝑏 𝑐𝑐𝑑𝑑 = 𝑎𝑎𝑏𝑏 𝑐𝑐𝑑𝑑 = ad − bc 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅𝒆𝒆 𝒇𝒇 𝒈𝒈𝒉𝒉𝒊𝒊, 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅𝒆𝒆𝒇𝒇 𝒈𝒈𝒉𝒉𝒊𝒊 , 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅 𝒆𝒆𝒇𝒇 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. Solving Trigonometric Equations 2 Video Practice Questions Answers. 𝐶𝐹= Complex Numbers Cheat Sheet Edexcel Core 1 KWWSV ELW O\ SPW HGX KWWSV ELW O\ SPW FF KWWSV ELW O\ SPW FF. v. 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. Matrix Algebra Cheat Sheet Edexcel FP2 . Solving Trigonometric Equations 1 Video Practice Questions Answers. Writing 𝑎𝑎∈𝑆𝑆 shows that the element 𝑎𝑎 is a member of the set 𝑆𝑆. Title: Ch. This cheat sheet explores three useful ideas in calculus: evaluating 𝑛𝑛. 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. 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. 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. Example 1 [is a ] 3 by 2 or matrix as it has 3 rows and 2 columns. In AQA A-Level Further Mathematics, it is involved only in proving sums of series, divisibility, and powers of matrices. By integrating, all the values that the function takes within the given interval are Notes and questions on A-Level Further maths. 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. Elastic energy. 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. There will be one zip file per paper, you can find the individual files to download in the ‘By Paper’ cabinets. =’+>" ’=$ 4 −1 & vector ", subtract the position vectors. Find the magnitude of the impulse exerted on the wall by the ball. A) Find its initial acceleration. If you are carrying out a fixed number of independent trials each with a constant probability of success, 𝑝𝑝, then you can model the number of trials needed to achieve one success using a geometric distribution. 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. Common quantities are mass, time, and length (or distance). First-order differential equations Series Cheat Sheet Edexcel Core Pure 1 This tells us the last value of r for our sequence, i. These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. The division algorithm Recalling set theory from GCSE Maths, a set is a collection of distinct objects. 𝐀𝐀such that the output is a scalar multiple of . To geometrically represent complex numbers, we use an Argand diagram which Ch. Videos and Worksheets for Level 2 Further Maths. The order of a matrix is the number of rows and columns in the matrix. They are a great revision tool for students to use alongside their studies. This point could be at either end of the interval, or somewhere in the middle. On this page you can find formula sheets, cheat sheets and questions by topic for Further Core Pure for Edexcel, AQA and OCR (A). eigenvector. 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 . our last term will be y −( t4) = −1 ∑ This is the value of r where our series starts, i. Core Pure 1. The numbers in a matrix are called the elements of the matrix. To find the length Ch. is called an . 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. 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. This series in particular is an arithmetic series which is introduced in Pure Year 2. 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. ෍ ( v 𝑟3− u2 + )=( 𝑘 s)3 t 𝑘+1 𝑟=1 We start with the basis step; we show the 𝐿𝐻 = 𝐻 : 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 𝑘. 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. 2 ሺhits a fixed vertical wall at right angles with speed 3. In the 15th century, French Methods in Calculus Cheat Sheet Edexcel A Level Further Maths: FP1 . The ball strikes a smooth plane which is inclined at an angle 𝑢𝑢 to the horizontal, where tan 𝑢𝑢= 1 2. 5 −1. In springs, when they Geometric and Negative Binomial Distributions Cheat Sheet Edexcel FS1 . 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. Number theory is used in cryptography. Further Maths Matrix Summary 1 Further Maths Matrix Summary A matrix is a rectangular array of numbers arranged in rows and columns. Instead of using the endpoints of each vertical strip, the -value of the curve at each midpoint is used to fit a rectangle. A matrix is an array of numbers, or elements, arranged in rows and columns. % passes through both 1 and 2 so we can use !. 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. 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. For a matrix #, the determinant can be denoted by t ( #), t #, | #| or ∆. Below are some examples of matrices: 4 7 2. Of course, these relationships also need to be proved true. 1 2. 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. 6 4 8. • A binary operation on a set is a calculation that combines two elements of the set to output another element of the same set. eigenvalue. HŽ 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°bâœ œžV¢ AŸZ:ƒ É¹à•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. They can lead to incorrect conclusions which can have 1serious consequences, depending on the context of the hypothesis test. A trick is to look at the term involving 𝑑𝑑𝑑𝑑 Ch. If you run out of questions by topic for your own exam board you should move onto another exam board’s tab. Practice papers for AS and A level Further Mathematics by topic. ] = [ = [7 4 ] 1 5 10 6 3. The geometric distribution . Back to Subjects | Back to Maths. 1. # × Matrices For a matrix #=[ ], | #|= − Polar Coordinates Cheat Sheet 𝑟𝑟2= 𝑥𝑥2 𝑦𝑦2 tan𝜃𝜃= 𝑑𝑑 𝑑𝑑 ⇒ Edexcel Pure Year 2 𝐴𝐴𝑟𝑟𝑎𝑎= 1 2 𝑟𝑟2 𝑏𝑏 𝑎𝑎 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. ∫ 𝑘𝑥2 3 1 𝑥=1⇒ Reducible Differential Equations Cheat Sheet Edexcel A Level Further Maths: FP1 . + + = L + + = M +ℎ U+𝑖= N The above equations can be rewritten as: 𝐴= Free online university thermodynamics cheat sheet with key equations needed to solve thermodynamic processes. Differential Equations II Cheat Sheet (A Level Only) AQA A Level Further Maths: Core a) Write auxiliary equation. 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 ∈ℤ ෍( v𝑟3− u𝑟2+𝑟)= 3( + s) 𝑛 𝑟=1 Start by making a note of what you want to prove in the inductive step. For use during the course and in the examinations . They have a range of applications in mathematics and physics such as Ch. v, 𝐀𝐀𝐀𝐀= 𝜆𝜆𝐀𝐀, E. Many real-life situations can be modelled using differential equations. our first term is y − = w. 1 Roots of Polynomials for the Edexcel A Level Further Maths: Core Pure syllabus, written by the Further Maths experts at Save My Exams. Core Pure 1 Mechanics 1. 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. work done= 𝑑 Ch. On this page you can find formula sheets, cheat sheets and questions by topic for Further Additional Pure for Edexcel, AQA and OCR (A). The ball rebounds with speed 2. Vectors Cheat Sheet Edexcel Core Pure 1 5 −’ %) % 6 & & = 7 ’ ’ in cartesian form. |#−(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. 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). It is a useful tool for students to quickly review and memorize key concepts. These are comprised of a mixture of legacy past paper questions, new shadow exam questions and some new questions. 0= 2+2 +1=( +1)2 ⇒ = −1 Substitute into the general solution for released from rest and moves down the slope. of matrix 𝐀𝐀, with 𝜆𝜆 its corresponding . If a matrix 𝐀𝐀 transforms a non-zero vector . Eigenvectors and Eigenvalues . then . 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. igm ktecbe excvizu mlw aswrqwd ihzrkt pozeseh chsb sptwnob qenjq