Factorise - Study guides, Study notes & Summaries

If two lines are perpendicular, what must their gradients equal to when multiplied together? Correct answer -1 What is the equation to calculate the gradient of a line? Correct answer y₂-y₁/x₂-x₁ What is the equation to calculate the length of a line? Correct answer √(y₂−y₁)^2 + (x₂-x₁)^2 What is the equation to calculate the midpoint of a line? Correct answer (x₂+x₁) over 2 , (y₂+y₁) over 2 What is the equation of a circle? Correct answer x²+y²=r² H...

What is the first way of factories? - correct answer Taking out the highest common factor second way of factorising? - correct answer Grouping third way of factorising? - correct answer Difference of 2 squares Fourth type of factorising? - correct answer Quadratics What are the steps of "taking out the HCF" method of factorising? - correct answer 1. find the HCF and write it outside the brackets 2. divide each term by the factor and write the results inside the bracket 3. Check ...

GCSE Mathematics Edexcel Predicted Paper 2023 Higher Paper 3 with correct marking scheme Name ……………………………………………… Date ……………………………………………… 1 hour 30 minutes allowed Calculator Paper Maximum Mark: 80 Grade boundaries These are VERY rough guesses! Getting a 7 on this paper does not guarantee you the same mark in the exam. • 9 70 • 8 60 • 7 50 • 6 40 • 5 30 • 4 20 ...

A LEVEL MATHS: Proof What does the following notation mean? {x:_______} The set of values for x such that ... What does the symbol → mean? x __ implies ____ or if...then.... What does the symbol ← mean? x____is implies by ____ What does the symbol ↔ mean? p implies q and q implies p or p ____ if and only if (iff) Even number notation 2n odd number notation 2n+1 consecutive even numbers notation 2n, 2n + 2 consecutive odd numbers notation 2n+1, 2n+3 rational number notation a= p/q ...

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...

Midpoint ([x₁+x₂]÷2 , [y₁+y₂]÷2) Perpendicular bisector The line that passes through the midpoint of another line at 90° Finding perpendicular bisectors 1. Find the midpoint of AB 2. Find the gradient of AB 3. Find the negative reciprocal of that 4. Sub the midpoint and the new gradient into y-y₁=m(x-x₁) Equation of a circle (x-a)²+(y-b)²=r² Finding the centre of a circle 1. Find the equation of the circle 2. Collect the x and y terms next ...

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 ...

GCSE Mathematics Edexcel Predicted Paper 2023 Higher Paper 3 with correct marking scheme Name ……………………………………………… Date ……………………………………………… 1 hour 30 minutes allowed Calculator Paper Maximum Mark: 80 Grade boundaries These are VERY rough guesses! Getting a 7 on this paper does not guarantee you the same mark in the exam. • 9 70 • 8 60 • 7 50 • 6 40 • 5 30 • 4 20 ...

1 From a constructivist perspective, it is important to create learning environments and learning activities that enable learners’ construction of knowledge rather than just absorb it. Write a 1000-word essay in which you critically respond to this statement with a lens on the teaching of numbers, patterns, and relationships in any grade in the Intermediate Phase. You should include examples, either from your learning experience at school, general reading, or observation as a learner...

A level Maths Questions and Answers 100% Pass 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 a circle...