Factorising - Study guides, Class notes & Summaries

1 a) Give n tha t f(x ) = x 3 – 4x 2 – 3x + 7, find f '(x ). (2) b) Hence find the values of x for which f(x) is a decreasing function, giving your answer in the form {x : x > a} {x : x < b} where a and b are real numbers to be found. (3) 2 A helicopter flies between 3 locations, A, B and C, which are positioned such that AB = 9 km, AC = 5 km and angle ABC = 24°. Find the possible values of angle ACB to 1 decimal place. ...

Quadratic equation Written as ax²+bx+c=0 where a, b, c and constants. Has 0-2 solutions Roots - The solutions to an equation - The values of x for which f(x)=0 - Find by factorising x Completing the square x²+bx = (x+b÷2)²-(b÷2)² Completing the square when a≠1 - Factorise as much as possible - Otherwise keep a outside the brackets Completing the square when a≠1 - method 2x²-12x = 2(x²-6x) = 2((x-3)²-3²) Complete the square = 2((x-3)²-9) Simpl...

Simplifying algebraic fractions - Factorise the numerator and denominator - Collect like terms Binomial An algebraic expression of the sum or the difference of two terms. E.g. x²-y³ Polynomial A finite expression with more than 2 terms. E.g. 6x²+24x+48 Dividend The base number that is being divided Divisor The number that is dividing into the dividend Quotient The whole number that results after dividing Remainder The number that is left over ...

Edexcel A-Level Mathematics Practice Set 1 Paper 1: Pure Mathematics 1 Time allowed: 2 hours Centre name Surname Centre number Other names Candidate number Candidate signature In addition to this paper you should have: • An Edexcel mathematical formula booklet • A calculator For examiner’s use Q Mark Q Mark 1 9 2 10 3 11 4 12 5 13 6 14 7 15 8 16 Total ...

This document contains detailed in-depth notes about complex numbers (algebra) for grade 12 mathematics. The following topics are dealt with: 1.1 Important Definitions and Notes for Complex Numbers 1.2 Multiplication, Addition and Subtraction 1.3 Division 1.4 Quadratic Formula 1.5 Determining the original quadratic equation from its roots 1.6 Solving Simultaneous Equations 1.7 Factorising 1.8 Solving Equations with Polynomials 1.9 Graphical Representation Alongside each of the topics...

MATHS A-LEVEL QUESTIONS AND ANSWERS RATED A How do you find the gradient of a line on a graph? Increase in y --------------- Increase in x How do you find the perpendicular gradient? How do you find the gradient of a line using two coordinates? y2-y1 ------ x2-x1 How do you find the equation of a straight line? y-y1 = m( x- x1) How do you find the points of intersection? By treating the two equations as simultaneous equations in order to work out the x and y coordinates. What are the three...

Edexcel A Level Maths – Pure A+ Graded 100% Verified Natural Numbers ANS: The set of numbers 1, 2, 3, 4, ... Also called counting numbers. Integers ANS: The set of whole numbers and their opposites Z⁺ Z⁺₀ Rational Number ANS: set of all numbers that can be written as a fraction of two integers Q irrational numbers ANS: Numbers that can't be written as a fraction... examples √2 and π Universal Set ANS: A set that includes all the objects being discussed. - Ex...

4 attempt. 4 1 5 ∫10 - 2x dx =- 10 - 2x Correctly states 10 A1 1 5 1 5 211 -  2 + 10 - 2a = States 10 10 10 M1 ft Makes an attempt to solve this equation. 1 10 - 2a 5 =243 5 For example, 10 10 or 10 - 2a =243 is seen. M1 ft a =7 Solves to find 2 A1 ft TOTAL: 5 marks NOTES: Student does not need to state ‘+C’ in an answer unless it is the final answer to an indefinite integral. Award ft marks for a correct answe...

Answer ALL the questions. Write your answers in the spaces provided. Leave blank 1 a) Give n tha t f(x ) = x 3 – 4x 2 – 3x + 7, find f '(x ). (2) b) Hence find the values of x for which f(x) is a decreasing function, giving your answer in the form {x : x > a}  {x : x < b} where a and b are real numbers to be found. (3) 2 A helicopter flies between 3 locations, A, B and C, which are positioned such that AB = 9 km, AC = 5 km and angle ABC = ...

1 a) Give n tha t f(x ) = x 3 – 4x 2 – 3x + 7, find f '(x ). (2) b) Hence find the values of x for which f(x) is a decreasing function, giving your answer in the form {x : x > a} {x : x < b} where a and b are real numbers to be found. (3) 2 A helicopter flies between 3 locations, A, B and C, which are positioned such that AB = 9 km, AC = 5 km and angle ABC = 24°. Find the possible values of angle ACB to 1 decimal place. (3) A-lev el Edexcel Maths / Set 1 / Paper 1 © CGP 201...