Pmt maths cheat sheets

Pmt maths cheat sheets. Eigenvectors and Eigenvalues . It can be useful to solve the non. Direction. Let ⁻this function ⁺𝑥= 0+ 1𝑥+ 2𝑥2+ 3𝑥3+⋯ Matrices I Cheat Sheet AQA A Level Further Maths: Core 2 Matrix Arithmetic and Multiplying a Matrix by a Scalar A matrix is an array of numbers, or elements, arranged in rows and columns. We choose v wand u rbecause we know the sin( °) , cos( ) ( ) ( ), so when we put them into the addition formula, we will have all terms given as exact values. 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. Integration Cheat Sheet. 1 Data Collection Cheat Sheet - Edexcel Maths A-level - Year 1 Applied Author: PMT Education Created Date: 2/3/2021 11:12:40 PM ∴1. of matrix 𝐀𝐀, with 𝜆𝜆 its corresponding . As line segment PQ is the diameter of the circle, the midpoint of the line is the centre of the circle. Use this model to estimate the density of pesticide after 15 days. This method requires you to break the statement into smaller cases and prove each case separately. derivatives using Leibnitz’s theorem, evaluating certain indeterminate limits using L’Hospital’s rule, and finding definite and indefinite integrals using the Weierstrass Hypothesis Testing Cheat Sheet Stats/Mech Year 1 The researcher claims that the new drug is better so $ > 0. 4 You can use the cumulative binomial tables or your calculator This is the same as the probability of " falling within the critical region KWWSV ELW O\ SPW HGX KWWSV ELW O\ SPW FF KWWSV ELW O\ SPW FF C4 Cheat Sheet Chapter Usual types of questions Tips What can go ugly 1 – Partial Fractions denominator’s factors are squared. Edexcel Core Pure 1. 𝐸𝐸= 1 2 (2 )(6. e. We would write that: 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. [1] Differentiate 2=4 +1 to find dx in terms of du: You will need to use These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Statistics. 𝐸𝐸= 𝑚𝑚𝑚𝑚ℎ= 2𝑚𝑚(0) = 0 These easy-to-read cheat sheets summarise all the content required for OCR MEI A-Level Maths. The ball strikes a smooth plane which is inclined at an angle 𝑢𝑢 to the horizontal, where tan 𝑢𝑢= 1 2. • In these graphs s represents the displacement of an object from a given point in metres and t represents the time taken in seconds. You also need to be able to apply your knowledge of numerical methods to questions involving models of real-life scenarios. paral. 4 + 2𝑎𝑎+ 3𝑏𝑏= 2. 𝐀𝐀such that the output is a scalar multiple of . Midpoint of PQ: ( 1+ 2 2, + 2)= Cheat sheets, worksheets, questions by topic and model solutions for OCR (MEI) Maths AS and A-level Differentiation PMT Education is looking for a full-time Customer Support Specialist Read More Revision for CAIE Biology IGCSE, including summary notes, exam questions by topic and videos for each module Aug 13, 2021 · These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. Recurrence relations are used to reduce and model problems using iterative processes. Instead of using the endpoints of each vertical strip, the -value of the curve at each midpoint is used to fit a rectangle. In this chapter we will look at how we can analyse Correlation Cheat Sheet Stats/Mech Year 1 Strong negative correlation Weak negative correlation Strong positive correlation No linear Weak positive correlation Describe the strength of correlation and whether it is positive or negative Interpret results in context to the question Remember to label your axis and include units Distance from Title: Statistical Distributions Cheat Sheet - Maths A-level - Year 1 Applied Author: PMT Education Created Date: 20210208205730Z Parametric Equations Cheat Sheet Edexcel Pure Year 2 So far, we have only looked at functions given in two variables, and . We can think of integration as a mathematical tool that allows us to find areas enclosed between curves and the coordinate axes. The methods you used were reliant on the two variables having a linear correlation. Join our three-day Pure (28-30th August), one-day Mechanics (24th and 27th August), and one-day Statistics (23rd and 26th August) courses. Using Pythagoras: r2 = 22 – 12 r = √3 Apply NEWTON’S SECOND LAW vertically. Find the coordinates of the midpoint of the circle. v, 𝐀𝐀𝐀𝐀= 𝜆𝜆𝐀𝐀, E. Example 7: A machine which manufactures nails is known to produce 2. 5 Probability Cheat Sheet - Edexcel Maths A-level - Year 1 Applied Author: PMT Education Created Date: 20210205200637Z Methods in Calculus Cheat Sheet Edexcel A Level Further Maths: FP1 . 𝑋~𝑁(𝜇,𝜎2 OCCNBC OCCNBC OCCNBC Example 7: A drill bit manufacturer claims that 52% of its bits last longer than 40 hours. 5 −1. Immediately before striking the plane the ball has speed 5 ms−1. If you run out of questions by topic for your own exam board you should move onto another exam board’s tab. (Note: if there is an unk nown in the expression, form an equation involving the unknown) The coefficients are 1, 3, 3, 1: The term in "% is 3 %×2(−9") = 69%"% So, 69% = 294 9% = 49 ⇒ 9 ±7 These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. |#−(6−3*)|=4 Thus, the loci of # is a circle of radius 4, centred at (6,−3) Argand diagrams look similar to Cartesian diagrams Title: Trignometric Identities Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210327004008Z Variable Acceleration Cheat Sheet Stats/Mech Year 1 Functions of time • If acceleration of a moving particle is variable, it changes with time and can be expressed as a function of time. 2 =36𝐽𝐽 𝑃𝑃. You cannot use one example to prove 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. They can come in any order. 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 These easy-to-read cheat sheets summarise all the content required for OCR A-Level Maths. Revision for CAIE Physics IGCSE, including summary notes, exam questions by topic and videos for each module Quality of Tests Cheat Sheet Hypothesis tests are not perfect. s Volumes of Revolution Cheat Sheet Edexcel Core Pure 1: The bounds of integration can be given to you in different ways . Title: Differentiation Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Author: PMT Education Created Date: 20210208162637Z Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Exponentials and Logarithms PMT Education is looking for a full-time Customer Support Specialist Read More Mathematical Proof Cheat Sheet Pure Year 1 Methods of proof: You can prove a mathematical statement using proof by exhaustion. This cheat sheet explores three useful ideas in calculus: evaluating 𝑛𝑛. On this page you can find formula sheets, cheat sheets and questions by topic for Further Core Pure for Edexcel, AQA and OCR (A). work done= 𝑑 Title: Ch. You cannoteus one example to prove Strengthen your maths skills with our online Summer A Level Refresher courses. 5The coefficient of restitution These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Statistics. Integration is the inverse of differentiation. the examples in this cheat sheet. + + = L + + = M +ℎ U+𝑖= N The above equations can be rewritten as: 𝐴= Constant Acceleration Cheat Sheet Stats/Mech Year 1 Displacement-time graphs • Displacement is always plotted on the vertical axis and time on the horizontal axis. Finding angles between lines and planes. In zero matrices, all elements are zero. , the equation of the curve, the A probability generating function is a mathematical function that is very useful for dealing with discrete distributions which take non-negative integer values (e. In springs, when they Title: Graphs and Transformations Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 7/13/2019 5:04:18 PM Title: Ch. Find radius (of the circular path the bob moves in. The geometric distribution . Vectors Cheat Sheet Edexcel Core Pure 1. 2 Conic Sections 1 Cheat Sheet - Edexcel Further Maths A-level - FP1 Author: PMT Education Created Date: 9/8/2022 12:03:54 PM 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. is called an . Make sure you’re comfortable interpreting the question is giving you, no matter the form. They are a great revision tool for students to use alongside their studies. cos 𝜃𝜃= √3 2 Hypothesis Testing Cheat Sheet Edexcel Stats/Mech Year 1 The researcher claims that the new drug is better so $ > 0. Algebraic methods Cheat Sheet . This series in particular represents an arithmetic series with first term 5 and common difference -2 Normal Distribution Cheat Sheet Stats/Mech Year 2 Recall that the mean and the variance of a binomially distributed random variable are 𝑛𝑝 and 𝑛𝑝(1−𝑝) 𝑋~𝑁(𝜇, 𝜎2) respectively. Eigenvectors are We find the kinetic and potential energy of the particle at A, then at B. Title: Radians Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Author: PMT Education Created Date: 20210208162622Z These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. a) Using a Poisson approximation, calculate the probability that a packet contains more than 6 defective nails. g. This series in particular is an arithmetic series which is introduced in Pure Year 2. The aim of this chapter is to be able to quantify the reliability of a hypothesis test. negation of a given statement is another statement that can be used to imply the given statement is incorrect. Find a tutor Elastic Collisions in Two Dimensions Cheat Sheet Edexcel FM1 Example 1: A small smooth ball is failing vertically. ( ) Example 5: The future world ranking position of a tennis player 2 + 17 during a + calendar year can ≤ be 12 modelled by the function. W e can also defin a curve using a different system, known as parametric equations. 5% defective nails. Title: Ch. Series Cheat Sheet Edexcel Core Pure 1 This tells us the last value of r for our sequence, i. This is known as the cartesian equation of a curve. Revision notes, summary sheets with key points, checklists, worksheets, topic questions and papers with model solutions for AQA, Edexcel, OCR, MEI Maths A-level. 5 Radians Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Created Date: 20210208162622Z Integration Cheat Sheet Pure Year 1 − [1 ]2 KWWSV ELW O\ SPW FF. a. A carpenter buys 6 packets of nails . Kinematics Cheat Sheet : The : terminal: or : limiting velocity: Ch. At start: 𝐾𝐾. our last term will be 7−2(20)=−33 This is the value of r where our series starts, i. 9 Trigonometric Ratios Cheat Sheet - Edexcel Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210326234630Z. Finding shortest distances and reflections. eigenvalue. This method is better suited to a small number of results. Remember that the same pieces of information are given in most – if not all – questions (i. Find the magnitude of the impulse exerted on the wall by the ball. binomial or ). Title: Projectile Motion Cheat Sheet - Maths A-level - Year 2 Applied Author: PMT Education Created Date: 20210205165712Z Matrix Algebra Cheat Sheet Edexcel FP2 . 9 2𝑎𝑎+ 3𝑏𝑏= 1. A contradiction is an incompatibility between two statements. Matrices Cheat Sheet Edexcel Core Pure 1 : det 𝑎𝑎𝑏𝑏 𝑐𝑐𝑑𝑑 = 𝑎𝑎𝑏𝑏 𝑐𝑐𝑑𝑑 = ad − bc 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅𝒆𝒆 𝒇𝒇 𝒈𝒈𝒉𝒉𝒊𝒊, 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅𝒆𝒆𝒇𝒇 𝒈𝒈𝒉𝒉𝒊𝒊 , 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅 𝒆𝒆𝒇𝒇 Title: Ch. You need to know how to express the equation of a straight line in three dimensions in both vector and cartesian form. • Velocity and displacement can also be expressed as functions of time Example 1: A body moves in a straight line, such that its displacement, s metres, Revision for CAIE Chemistry IGCSE, including summary notes, exam questions by topic and videos for each module Mathematical Proof Cheat Sheet Edexcel Pure Year 1 Methods of proof: You can prove a mathematical statement using proof by exhaustion. 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. Important definitions. 1+𝑎𝑎𝑏𝑏2 = Circles Cheat Sheet Edexcel Pure Year 1 Example 1: The line segment PQ is the diameter of a circle, where P is at (2,3) and Q is at (6,7). Title: Integration Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: Revision for AQA Physics GCSE, including summary notes, exam questions by topic and videos for each module Title: Vectors Cheat Sheet - Maths A-level - Year 2 Pure Author: PMT Education Created Date: 10/24/2021 9:44:05 AM Title: Ch. In general, you can remember that ∑ 2=(∑ )2− t(∑ ) Sequences and Series Cheat Sheet This tells us the last value of r for our sequence, i. Equation of a line in three dimensions. our first term is 7−2(1)=5. 𝑡𝑡ℎ. eigenvector. If a matrix 𝐀𝐀 transforms a non-zero vector . After 15 days, 7 = 15. The ball rebounds with speed 2. A trick is to look at the term involving 𝑑𝑑𝑑𝑑 Momentum and impulse Cheat Sheet Edexcel FM1 Example 1: A ball of mass 0. 4 You can use the cumulative binomial tables or your calculator This is the same as the probability of " falling within the critical region KWWSV ELW O\ SPW HGX KWWSV ELW O\ SPW FF KWWSV ELW O\ SPW FF Geometric and Negative Binomial Distributions Cheat Sheet Edexcel FS1 . 2 Put the loci equation into the form |#−#!|=&. Find a tutor back substitution also becomes increasingly complicated. 5 [1] Now we use the fact that the total probability is equal to 1: 0. 9 Differentiation Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Created Date: 20210208162637Z Revision for CAIE AS and A-level Chemistry (9701) papers, including summary notes, videos, worksheets and past exam questions by topic. Be able to split a fraction whose denominator is a product of linear expressions, e. The nails are sold in packets of 200. In other words, the two statements cannot both be true. 2 ሺhits a fixed vertical wall at right angles with speed 3. v. Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Integration PMT Education is looking for a full-time Customer Support Specialist Read More Roots of polynomials Cheat Sheet Edexcel Core Pure 1 You may decide not to remember these results since they are quite easy to prove; in each case you simply need to combine the fractions to achieve the . Revision for Edexcel AS and A-level Maths including cheat sheets, worksheets, questions by topic and model solutions to papers. our last term will be y −( t4) = −1 ∑ This is the value of r where our series starts, i. 4 Kinematics Cheat Sheet - Edexcel Further Maths A-level - FM2 Author: PMT Education Created Date: Measures of Location and Spread Cheat Sheet Stats/Mech Year 1 Where !̅(x bar) is the mean, Σ! is the sum of the data values, % is the number of data values Where Σ&! is the sum of the products of the data values and their frequencies, Σ& is the sum of frequencies Easier to use when given raw data @ $$ is a summary statistic Title: Quadratics Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210204221615Z Regression, Correlation and Hypothesis Testing Cheat Sheet Previously in Chapter 4 of Stats/Mech Year 1, you learnt how to interpret correlati on and regressi line equations for bivariate data. Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Algebra and Functions PMT Education is looking for a full-time Customer Support Specialist Read More On this page you can find formula sheets, cheat sheets and questions by topic for Further Additional Pure for Edexcel, AQA and OCR (A). PMT Education is looking for a full-time Customer Support Specialist Title: Differentiation Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210327102946Z Exponentials and Logarithms Cheat Sheet Example 2: c The density of a pesticide in a given section of field, P mg/m2 , can be modelled by the equation 5 = 160/#’(’’)* where t "is the time in days since the pesticide was first applied. our first term is y − = w. wall with speed We begin by drawing a diagram: Integration Cheat Sheet These can be derived from the differentiation section in the formula booklet or, if we are using limits: using the double angle formulae 2 =2 2 −1 Example 3: Find ∫ 8 √4 +1 20 6 using the substitution 2=4 +1. They can lead to incorrect conclusions which can have 1serious consequences, depending on the context of the hypothesis test. Find the possible values of the constant c. The Binomial Expansion Cheat Sheet Example 2: The coefficient of !! in the expansion of of (2−9")! is 294. Below are all Below are some examples of matrices: #=[7 4 2 4 9 13] $=[6 4 8 Title: Binomial Expansion Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Author: PMT Education Created Date: 20190906002526Z Probability Cheat Sheet Stats/Mech Year 1 Intersection of A and B shows the event in which both A and B occur Union of A and B shows the event in which either A or B or both occur The shaded area shows the event in which A does not occur A B # A # A A # # # B B B B A C 3 4 5 10 7 1 Green Green Green Blue Blue Blue 7 12 5 12 6 11 5 11 7 11 4 11 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. then . 2 +3 ( +1) Be able to split a fraction where one (or more) of the factors in the denominator are squared, 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. We define the and coordinates separately, in terms of a third variable, : Cheat sheets, worksheets, questions by topic and model solutions for AQA Maths AS and A-level Exponentials and Logarithms PMT Education is looking for a full-time Customer Support Specialist Read More TrigoTrigonometry and modelling Cheat Sheet nometry and modelling Cheat Sheet Edexcel Pure Year 2 Show, using the formula for sin( + ), that (° )= √+2 sin( °)as ( + ). 7 Linear Transformations Cheat Sheet - Edexcel Further Maths A-level - CP1 Author: PMT Education Created Date: 20190916222029Z 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. To geometrically represent complex numbers, we use an Argand diagram which 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). Applications to modelling. bvd zukqik jjdiph bvqevq kncvbe jrd vhq ine fbwsy uxls