Binomial expansion - Study guides, Class notes & Summaries

1 Find the coefficient of the x term in the binomial expansion of (3 þ x)4 Circle your answer. [1 mark] outside the box 12 27 54 108 2 Given that dy 1 d x ¼ x find d2y d x2 Circle your answer. [1 mark] 2 1 1 2 — x2 — x2 x2 x2 1 3 The graph of the equation y ¼ x is translated by the vector " 3 # outside the box 3 (a) Write down the equation of the transformed graph. [1 ...

Pure Mathematics Edexcel A-Level Year 1 and 2 revision notes, written by a straight A* student. Includes diagrams and explanations for concepts. Well organised and in order. Includes collated information from class, textbooks and online. Topics include: Quadratics, Graphs and transformations, Functions and graphs, Circles, Algebraic methods, The binomial expansion, Trigonomic ratios, Trigonomic identities and equations, Trigonometric functions, Trigonometry and modelling, Vectors, Differentiat...

1 Simplify 5a2c 3 #2a4c 5 ^ h - . [2] 2 Find the equation of the line joining the points (-1, 9) and (2, -3), giving your answer in the form y = mx + c. State the coordinates of the points where this line intersects the axes. [5] 3 Find the value of (i) 2 2 4 1 - a k , [2] (ii) 8000 3 2 ^ h . [2] 4 For the following equation, express x in terms of y. y x y x 3 2 2 1 = + + [4] 5 Find the coordinates of the point of intersection of the lines y = 4x + 3 and 3x + 2y = 9. [4] 6 Fi...

AQA AS MATHEMATICS 7356/1 Paper 1 Version: 1.0 Final PB/KL/Jun23/E4 7356/1 AS MATHEMATICS Paper 1 Time allowed: 1 hour 30 minutes Materials l You must have the AQA Formulae for A‑level Mathematics booklet. l You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions l Use black ink or black ball-point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l You...

Natural Numbers --------------------------------------------------------------------------11 Factors -------------------------------------------------------------------------------------18 Divisibility test ----------------------------------------------------------------------------23 G.C.D ---------------------------------------------------------------------------------------26 L.C.M ---------------------------------------------------------------------------------------29 Integers---------...

AS MATHEMATICS Paper 1 Thursday 18 May 2023 Afternoon Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae for A‑level Mathematics booklet.  You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  You must answer each question in the...

A level Maths Verified Solutions If two lines are perpendicular, what must their gradients equal to when multiplied together? ️-1 What is the equation to calculate the gradient of a line? ️y₂-y₁/x₂-x₁ What is the equation to calculate the length of a line? ️√(y₂−y₁)^2 + (x₂-x₁)^2 What is the equation to calculate the midpoint of a line? ️(x₂+x₁) over 2 , (y₂+y₁) over 2 What is the equation of a circle? ️x²+y²=r² How do you find the midpoint of...

Random Variables correct answers It is a set of possible values from a random experiment. Discrete Random Variable correct answers Variable where the number of outcomes can be counted. For example, the number of white balls in a sample of size three is a discrete random variable which may take one of the values 0, 1, 2, 3 Continuous Random Variable correct answers is one that can take any value in an interval of the real number line, and is usually (but not always) generated by measuring...

A-Level Mathematics Predicted Paper 2023 Edexcel Paper 3 – Statistics and Mechanics with correct marking schemes. Name ……………………………………………… Date ……………………………………………… 2 hours allowed Calculator Paper Maximum Mark: 100 Grade boundaries These are VERY rough guesses! Getting an A on this paper does not guarantee you the same mark in the exam. • A* 75% • A 55% • B 45% • C 35% • D 25% • E 15% ...

Differentiate tan(kx) ksec^2(kx) Differentiate cos(kx) -ksin(kx) Differentiate sin(kx) kcos(kx) Arithmetic sequence Un = a + (n - 1)d Arithmetic series Sn = n/2 (a + d) Geometric sequences Un = ar^n - 1 Geometric series Sn = a(r^n - 1) / r - 1 Sum to infinity a/1 - r Convergent series Sn closer to 0 Divergent series Sn further away from 0 Sigma notation Recurrence relationship Defines each term as function of...