Pmt maths cheat sheets

Pmt maths cheat sheets. Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Algebra and Functions. 𝐸𝐸= 𝑚𝑚𝑚𝑚ℎ= 2𝑚𝑚(0) = 0 Trigonometric Identities Cheat Sheet Edexcel Pure Year 1 Angles in all four quadrants Unit circles: A unit circle is a circle with radius of 1 unit. 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. W e can also defin a curve using a different system, known as parametric equations. ’’)* where t is the time in days since the pesticide was first applied. 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. 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. If you run out of questions by topic for your own exam board you should move onto another exam board’s tab. To geometrically represent complex numbers, we use an Argand diagram which Revision for CAIE AS and A-level Chemistry (9701) papers, including summary notes, videos, worksheets and past exam questions by topic. work done= 𝑑 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. A contradiction is an incompatibility between two statements. 5 Probability Cheat Sheet - Edexcel Maths A-level - Year 1 Applied Author: PMT Education Created Date: 20210205200637Z These easy-to-read cheat sheets summarise all the content required for OCR A-Level Maths. Revision notes, summary sheets with key points, checklists, worksheets, topic questions and papers with model solutions for AQA, Edexcel, OCR, MEI Maths A-level. Title: Integration Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: Title: Graphs and Transformations Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 7/13/2019 5:04:18 PM 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 Mathematical Proof Cheat Sheet Edexcel Pure Year 1 Methods of proof: You can prove a mathematical statement using proof by exhaustion. On this page you can find formula sheets, cheat sheets and questions by topic for Further Core Pure for Edexcel, AQA and OCR (A). Revision for Edexcel AS and A-level Maths including cheat sheets, worksheets, questions by topic and model solutions to papers. 4 + 2𝑎𝑎+ 3𝑏𝑏= 2. e. 𝐸𝐸= 1 2 (2 )(6. a) Using a Poisson approximation, calculate the probability that a packet contains more than 6 defective nails. They can come in any order. 5 [1] Now we use the fact that the total probability is equal to 1: 0. Important definitions. Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Trigonometry topic 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. This cheat sheet explores three useful ideas in calculus: evaluating 𝑛𝑛. KWWSV ELW O\ SPW HGX KWWSV ELW O\ SPW FF KWWSV ELW O\ SPW FF Elastic Collisions in Two Dimensions Cheat Sheet Edexcel FM1 Example 1: A small smooth ball is failing vertically. Algebraic methods Cheat Sheet . 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. 2 Geometric and Negative Binomial Distributions Cheat Sheet Edexcel FS1 . You cannoteus one example to prove Title: Differentiation Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Author: PMT Education Created Date: 20210208162637Z 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. Use this model to estimate the density of pesticide after 15 days. For example, 3 + 6 + 9 + 12 + 15 + The terms of a sequence are separated by a comma, while with a series they are all added together. % passes through both 1 and 2 so we can use !. This method is better suited to a small number of results. They are a great revision tool for students to use alongside their studies. The geometric distribution . 5The coefficient of restitution the examples in this cheat sheet. This is known as the cartesian equation of a curve. For example, 3, 6, 9, 12, 15, series is the sum of a list of terms. In this chapter we will look at how we can analyse 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. =’+>" ’=$ 4 −1 & vector ", subtract the position vectors. Mathematical Proof Cheat Sheet Pure Year 1 Methods of proof: You can prove a mathematical statement using proof by exhaustion. sequence is a list of terms. Applications to modelling. In other words, the two statements cannot both be true. Immediately before striking the plane the ball has speed 5 ms−1. 5 Radians Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Created Date: 20210208162622Z 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. The meaning of independency If we have two events that are independent, this means that the outcome of Title: Vectors Cheat Sheet - Maths A-level - Year 2 Pure Author: PMT Education Created Date: 10/24/2021 9:44:05 AM Hypothesis Testing Cheat Sheet Stats/Mech Year 1 The researcher claims that the new drug is better so $ > 0. 1+𝑎𝑎𝑏𝑏2 = Title: Binomial Expansion Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Author: PMT Education Created Date: 20190906002526Z Functions and Graphs Cheat Sheet What really is a function? Before we can properly define a function, we must first understand mappings. 5 = 160 . 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. Sequences and Series Cheat Sheet. Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Integration These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. 𝑡𝑡ℎ. Let ⁻this function ⁺𝑥= 0+ 1𝑥+ 2𝑥2+ 3𝑥3+⋯ Integration Cheat Sheet Pure Year 1 − [1 ]2 KWWSV ELW O\ SPW FF. 𝑋~𝑁(𝜇,𝜎2 OCCNBC OCCNBC OCCNBC Example 7: A drill bit manufacturer claims that 52% of its bits last longer than 40 hours. You cannot use one example to prove Title: Ch. derivatives using Leibnitz’s theorem, evaluating certain indeterminate limits using L’Hospital’s rule, and finding definite and indefinite integrals using the Weierstrass Series Cheat Sheet Edexcel Core Pure 1 This tells us the last value of r for our sequence, i. This method requires you to break the statement into smaller cases and prove each case separately. A mapping takes a set of numbers and transforms them into another set of numbers. It will help you understand the trigonometric ratios. In zero matrices, all elements are zero. After 15 days, 7 = 15. our first term is y − = w. A carpenter buys 6 packets of nails . 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 Exponentials and Logarithms Cheat Sheet Example 2: The density of a pesticide in a given section of field, Pmg/m2 , can be modelled by the equation 5 = 160/#’. Below are all Below are some examples of matrices: #=[7 4 2 4 9 13] $=[6 4 8 Matrices Cheat Sheet Edexcel Core Pure 1 : det 𝑎𝑎𝑏𝑏 𝑐𝑐𝑑𝑑 = 𝑎𝑎𝑏𝑏 𝑐𝑐𝑑𝑑 = ad − bc 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅𝒆𝒆 𝒇𝒇 𝒈𝒈𝒉𝒉𝒊𝒊, 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅𝒆𝒆𝒇𝒇 𝒈𝒈𝒉𝒉𝒊𝒊 , 𝒂𝒂𝒃𝒃𝒄𝒄 𝒅𝒅 𝒆𝒆𝒇𝒇 Revision for AQA Physics GCSE, including summary notes, exam questions by topic and videos for each module 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 . ( ) Example 5: The future world ranking position of a tennis player 2 + 17 during a + calendar year can ≤ be 12 modelled by the function. 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 Title: Quadratics Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210204221615Z On this page you can find formula sheets, cheat sheets and questions by topic for Further Statistics for Edexcel, AQA and OCR (A). 2 =36𝐽𝐽 𝑃𝑃. Mappings are often represented by algebraic equations. [1] Differentiate 2=4 +1 to find dx in terms of du: You will need to use On this page you can find formula sheets, cheat sheets and questions by topic for Further Additional Pure for Edexcel, AQA and OCR (A). Parametric Equations Cheat Sheet Edexcel Pure Year 2 So far, we have only looked at functions given in two variables, and . a. We define the and coordinates separately, in terms of a third variable, : Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Differentiation 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. Example 7: A machine which manufactures nails is known to produce 2. A negation of a given statement is another statement that can be used to imply the given statement is incorrect. 9 2𝑎𝑎+ 3𝑏𝑏= 1. Title: Ch. The nails are sold in packets of 200. At start: 𝐾𝐾. This series in particular is an arithmetic series which is introduced in Pure Year 2. 9 Differentiation Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Created Date: 20210208162637Z Title: Differentiation Cheat Sheet - Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210327102946Z Revision for OCR AS and A-level Maths including cheat sheets, worksheets, questions by topic and model solutions to papers Connect with PMT Education! Revision Cheat sheets, worksheets, questions by topic and model solutions for Edexcel Maths AS and A-level Exponentials and Logarithms 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 would write that: ∴1. our last term will be y −( t4) = −1 ∑ This is the value of r where our series starts, i. 11 Vectors Cheat Sheet - Edexcel Maths A-level - Year 1 Pure Author: PMT Education Created Date: 20210327094652Z We find the kinetic and potential energy of the particle at A, then at B. ෍ ( v 𝑟3− u2 + )=( 𝑘 s)3 t 𝑘+1 𝑟=1 We start with the basis step; we show the 𝐿𝐻 = 𝐻 : 3 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). Title: Data Collection Cheat Sheet - Maths A-level - Year 1 Applied Author: PMT Education Created Date: 2/3/2021 11:12:40 PM Radians Cheat Sheet = Radians Cheat Sheet - Edexcel Maths A-level - Year 2 Pure Author: PMT Education Created Date: 20210208162622Z Vectors Cheat Sheet Edexcel Core Pure 1 5 −’ %) % 6 & & = 7 ’ ’ in cartesian form. Edexcel Pure Year 2 Trigonometric functions Cheat Sheet U=sec T Dotted curve represents U= K O T Domain: T∈ℝ, T≠ I Q H P𝑖 L H 2 (° ) U≤− s, ≥ O𝑖 J ( U= K O T Dotted curve represents U= O𝑖 J T Domain: T∈ℝ, T≠ I Q H P𝑖 L H 𝜋 (° ) Title: Projectile Motion Cheat Sheet - Maths A-level - Year 2 Applied Author: PMT Education Created Date: 20210205165712Z TrigoTrigonometry and modelling Cheat Sheet nometry and modelling Cheat Sheet Edexcel Pure Year 2 Show, using the formula for sin( + ), that (° )= √+2 sin( °)as ( + ). You also need to be able to apply your knowledge of numerical methods to questions involving models of real-life scenarios. Revision for AQA AS and A-level Maths including cheat sheets, worksheets, questions by topic and model solutions to papers Connect with PMT Education! Revision These easy-to-read cheat sheets summarise all the content required for Edexcel A-Level Maths. In general, you can remember that ∑ 2=(∑ )2− t(∑ ) Conditional Probability Cheat Sheet Previously, you have looked at how to calculate probabilities relating to independent events. The methods you used were reliant on the two variables having a linear correlation. We will now look at how to solve problems involving two or more events that are not independent. 7 Linear Transformations Cheat Sheet - Edexcel Further Maths A-level - CP1 Author: PMT Education Created Date: 20190916222029Z Title: Ch. 5% defective nails. cfia yggzhb wsxo iqqqj zcnj mafyuy tgym ephhr tvmwp wdj