A level Maths Questions and Answers 100% Pass

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 ...

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 from the equation? ✔✔(x-a)²+(y-b)²=r² If a factor of a line equation is (x-2)², or the line equation is just y=(x-2)², how many solutions does (x-2)² give and what does this look like on a graph. ✔✔This gives just one solution, that x=2. This means that the line just touches the x axis at (2,0). What does a x⁴ and a -x⁴ graph look like? ✔✔An x⁴ looks like a W A -x⁴ looks like an upside down W What does an x³ and a -x³ graph look like? ✔✔An x³ graph appears to travel from bottom left to top right with two curves A -x³ graph appears to travel from bottom right to top left with also two curves How do you find the min/max point of a quadratic? ✔✔Complete the square; the x in the bracket will be the x coordinate and the number out the bracket will be the y coordinate How do you establish that (x-3) for example, is a factor of an equation? ✔✔Sub in 3 for example. If it is a factor, there will be no remainder and it will equal 0. If no factors of an equation are given and you are asked to factorise, what should you do? ✔✔Try small integers using substitution How do you quickly find a remainder of an equation given a factor? ✔✔Substitute in the factor, and this will equal the remainder What change does the a in f(x) + a cause to a graph? ✔✔It causes the graph to move in the direction of the y axis What change does the a in f(x+a) cause to a graph? ✔✔It causes the graph to move in the direction of the x axis How do you change the factors of a graph that has been translated by f(x+a)? ✔✔If it was translated by moving to the right by 3, you would add 3 to each factor bracket. e.g (x+3) would change to (x+6) What can pascals triangle be used for during binomial expansion? ✔✔Pascals triangle shows the coefficients of the expansion. It also shows a pattern of the a²,a³ b²,b³ etc. What is the pattern of the a² etc and b² etc? ✔✔The a's decrease as you go across the triangle. The b's increase as you go across the triangle How else can you find a coefficient of an expansion? ✔✔Using ⁿCr What does the n and r stand for in nCr? ✔✔n is the number it is to the power of. r is the number of term which you want to find What does r start at? ✔✔It starts from 0 and then progresses What is nC0 always equal to no matter what n is? ✔✔1 For example, what does 5! mean? ✔✔5x4x3x2x1 How do you plot a quadratic inequality on a graph? ✔✔Factorise the quadratic to find x values. Plot a graph and determining on 0> or <0, solve. How do you simplify a surd in a fraction? ✔✔Multiply the denominator by DOTS of the surd clever number 1 What is the rule of x² × x⁷? ✔✔Add 2 and 7 to get x⁹ What is x⁻⁸? ✔✔1/x⁸ How would you write x to the power of ¾? ✔✔(4th root of x)³ What are natural numbers? ✔✔Postitive integers including 0 What does Z mean? ✔✔All the positive and negative integers What does Q mean? ✔✔Integers that can be written as fractions What does R mean? ✔✔Rational and irrational numbers (all numbers) What does the symbol → mean? ✔✔Leads to or implies How else can you also write → as? ✔✔∴ (three dots) What does the symbol ← mean? ✔✔Follows from or implied by When can you write the ↔ symbol and what does it mean? ✔✔You can write this when both←→ are true. This means they are equivalent What is the equation to calculate the area of a triangle? ✔✔A = ½abSinA What is the cosine equation? ✔✔CosA = b²+c²−a² / 2bc How do calculate the stationary points of a line? ✔✔dy/dx of the equation. Make this equal to 0 and find the values of x How do you decide whether the stationary points are minimum points, maximum points or points of inflexion? ✔✔By differentiating the differential by d²y/dx² and subbing in the values of x of the stationary points into this. When is the point a minimum point in terms of d²y/dx²? ✔✔When d²y/dx² equals a positive number When is the point a maximum point in terms of d²y/dx²? ✔✔When d²y/dx² equals a negative number When is the point a point of inflexion in terms of d²y/dx²? ✔✔When d²y/dx² equals 0 How do you tell if the point of inflexion is positive or negative? ✔✔By subbing in numbers to the dy/dx that are around the same value to see how the gradient changes around the stationary point When is the gradient positive? ✔✔When dy/dx is greater than 0 When is the gradient negative? ✔✔When dy/dx is less than 0 How do you work out the points of which the equation has a negative gradient? ✔✔Work out dy/dx of the equation and put it to zero using < if you're trying to find out when it's negative in gradient How do you work out the points of which the equation has a positive gradient? ✔✔Work out dy/dx of the equation and put it to zero using > if you're trying to find out when it's negative in gradient