EDEXCEL PUPRE MATHS EXAM PACK|GUARANTEED SUCCESS

Equation of a straight line y - y₁ = m(x - x₁) Distance between two points d = √(x₂ - x₁)² + (y₂ - y₁)² Integration by substitution ∫f(x) = ∫f(x) × (dx÷du) Integration by parts ∫u (dv÷dx) = uv - ∫v (du÷dx) Trapezium Rule A = ½h (y₀ + 2(...

What are the turning point co-ordinates in f(x)=a(x+p)^2 +q (-p,q) How many roots are there if the discriminent > 0? Two distinct roots How many roots are there if the discriminent = 0? One/repeated root How many roots are there if the discriminent < 0? no real roots ...

fg(x) apply g first then f Functions f(x) and f^-1(x) reflections of each other in the line y = x Domain of f(x) Range of f^-1(x) Range of f(x) Domain of f^-1(x) y = |f(x)| reflection of y = f(x) for x>0 in the x-axis y = f(|x|) reflection of y = f(x) for ...

Base The number that is going to be raised to a power. Exponent The number that is used as a reference for the power Add the powers Multiplying numbers with powers - rule Subtract the powers Dividing numbers with powers - rule Multiply the powers Multiplying numbers ...

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 - Fa...

Natural Numbers The set of numbers 1, 2, 3, 4, ... Also called counting numbers. Integers The set of whole numbers and their opposites Z⁺ Z⁺₀ Rational Number set of all numbers that can be written as a fraction of two integers Q irrational numbers Numbers that can'...

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 an...

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 ...

Contradiction A contradiction is a disagreement between two statements, which means that both cannot be true. Proof by contradiction is a powerful technique. Proof by contradiction To prove a statement by contradiction you start by assuming it is not true. You then use logical steps to show...

Cubic A graph where the highest exponent is 3 Cubic function f(x) = ax³+bx²+cx+d Repeated root A function where at least 2 of the roots are equal. The turning point of the graph is on the x-axis E.g. y=(x-3)(x-2)² Point of inflection A function where all the roots are e...

Study AS-level Edexcel Pure Maths - Module 5: Straight line graphs Share In-class activity Classic Live Checkpoint Self-study activity Flashcards Learn Test Match Profile Picture Created by Badman892 Teacher Terms in this set (13) Original

Gradient of a line (y₂-y₁) ÷ (x₂-x₁) Distance between 2 points Use pythagoras' theorem √[(∆x)²+(∆y)² Parallel lines - Gradient is equal - Y-intercept is different Perpendicular lines - Gradients multiply to make -1 - Gradients are a negative reciprocal t...

Pascal's triangle A triangle where the the two numbers above to make the number below. - The numbers are the coefficients of the expansion of (a+b)ⁿ - The (n+1)th row gives the coefficients of (a+b)ⁿ Binomial The sum or difference of two terms Expanding brackets Multiply ever...

How to calculate the gradient of a line joining 2 points y2-y1 / x2-x1 What are two ways of writing the equations of lines? -y=mx+c, where m is the gradient and c is the y intercept -ax+by+c, where a b and c are integers How can you define a straight line? By giving: one point on t...