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AQA A level Maths Formulas with
Answers.
- How do you find the midpoint of a circle from the equation? - Answer: ✔✔(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. - Answer: ✔✔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? - Answer: ✔✔An x⁴ looks like a W A -x⁴ looks like an upside down W
- What does an x³ and a -x³ graph look like? - Answer: ✔✔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? - Answer: ✔✔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? - Answer: ✔✔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? - Answer: ✔✔Try small integers using substitution
- How do you quickly find a remainder of an equation given a
factor? - Answer: ✔✔Substitute in the factor, and this will equal the remainder
- What change does the a in f(x) + a cause to a graph? - Answer:
✔✔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? -
Answer: ✔✔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)? - Answer: ✔✔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? - Answer: ✔✔Pascals triangle shows the coefficients of the expansion.
- How do you simplify a surd in a fraction? - Answer:
✔✔Multiply the denominator by DOTS of the surd clever number 1
- What is the rule of x² × x⁷? - Answer: ✔✔Add 2 and 7 to get x⁹
- What is x⁻⁸? - Answer: ✔✔1/x⁸
- How would you write x to the power of ¾? - Answer:
✔✔(4th root of x)³
- What are natural numbers? - Answer: ✔✔Postitive integers including 0
- What does Z mean? - Answer: ✔✔All the positive and negative integers
- What does Q mean? - Answer: ✔✔Integers that can be written as fractions
- What does R mean? - Answer: ✔✔Rational and irrational numbers (all numbers)
- What does the symbol → mean? - Answer: ✔✔Leads to or implies
- How else can you also write → as? - Answer: ✔✔∴ (three dots)
- What does the symbol ← mean? - Answer: ✔✔Follows from or implied by
- When can you write the ↔ symbol and what does it
mean? - Answer: ✔✔You can write this when both←→ are true. This means they are equivalent
- What is the equation to calculate the area of a triangle? -
Answer: ✔✔A = ½abSinA
- What is the cosine equation? - Answer: ✔✔CosA = b²+c²−a² / 2bc
- How do calculate the stationary points of a line? -
Answer: ✔✔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? - Answer: ✔✔By differentiating the differential by d²y/dx² and subbing in the values of x of the stationary points into this.
- How do you work out the points of which the equation
has a positive gradient? - Answer: ✔✔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
- if two lines are perpendicular, what must their gradients
equal to when multiplied together? - Answer: ✔✔-
- What is the equation to calculate the gradient of a line? -
Answer: ✔✔y₂-y₁/x₂-x₁
- What is the equation to calculate the length of a line? -
Answer: ✔✔√(y₂−y₁)^2 + (x₂-x₁)^
- What is the equation to calculate the midpoint of a line? -
Answer: ✔✔(x₂+x₁) over 2 , (y₂+y₁) over 2
- What is the equation of a circle? - Answer: ✔✔x²+y²=r²
