how to Flashcards
how do you complete the square
• half the coefficient -> in fraction
• subtract (term) squared
• simplify
how to complete the square for a negative coefficient
• take out as common factor
• complete square on bracket - introduce square bracket
• multiply through the square bracket by negative
• simplify
how to complete the square for coefficients of x squared
- remove coefficient of x squared as a common factor
- complete the square of resulting bracket
- multiply out square brackets
- collect like terms
how to do domain and range
- set denominator to not equal zero
- solve to find x
- write domain
how to use double angle formula
- use the formula sheet to write down formula
- substitute ( when yk all three sides )
- calculate
how to use the addition formula
- use formula sheet to write down chosen formula
- find missing sides
- substitute into formula
- calculate
how to find the wave function min + max values
- use addition formulae to expand
- find ksina and kcosa
- find k and a using usual process
- sub k and a back into formula
- find min and max values
how to use the wave function to solve an equation
- change to the form
- make cosx or sinx the subject of the formula
- calculate FQA
- calculate alternative solution (CAST)
- make the correction observing limits
how to use the wave function to solve an equations
- change form to kcos or ksin formula
- make cosx or sinx the subject
- calculate FQA
- calculate alternative solutions using cast diagram
- make corrections observing limits
- consider multiple waves
how to find POI
- set the equations equal to one another
- set equal to zero
- factor use and solve for x
- sub x in to find y(f(x))
how to use the discriminant
- double check the question to determine what t is asking you
- write down the discriminant formula
- plug in needed values
- determine nature of the roots
how to find quadratic inequalities
- find the roots of the quadratic by factorising
- sketch the parabola
- determine whether the parabola is above or below the x axis depending on symbol
- state range if values
how to inverse function
- change function to y
- change subject to x
- change notation
x -> h-1(x)
y -> x
how to do graph transformations
- identify transformations being applied
- apply each transformation in turn -> sketch intermediate graph write each new coordinate
- complete sketch and annotate with new coordinates
how to tell if pints are collinear
- show segments are parallel
- ensure there’s a common point and state it
how to do quadratic trig equations
- factorise the quadratic trig equation
- set each factor equal to zero
- find the solution for each factor
how to do further trig equations
- replace any double angles using formulae list
- remove any brackets
- factories
- split and solve using cast diagram
how do you calculate the derivative
- multiply by the power
- reduce the power by one
how to use the derivative
find the derivative
substitute and evaluate
how to do equation of tangents
- differentiate the function
- substitute x into f/(x) to find gradient
- substitue f(x) yo find the corresponding y
- use straight line equation to find equation of a tangent
how to do increasing and decreasing functions
- find the derivative
- if f/(x) < 0 the function is decreasing
- if f/(x) > the function is increasing
how to find stationary points
- find derivative
- set derivative equal to zero
- solve for x
- solve for y if necessary
- determine the value of the deriving just before and after sp using a nature table
how to du d the greatest and least values within a closed interval
-set the derivative equals to zero
- find sps
- evaluate f(x) or y fir the sps
- only consider sps in the interval
- evaluate the end point
- state the greatest and least values
how to do the differentiation chain rule
- prepare if necessary
- multiply by the power and reduce by 1
- multiply by the derivative of the bracket
