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higher maths > how to > Flashcards

how to Flashcards

1
Q

how do you complete the square

A

• half the coefficient -> in fraction
• subtract (term) squared
• simplify

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2
Q

how to complete the square for a negative coefficient

A

• take out as common factor
• complete square on bracket - introduce square bracket
• multiply through the square bracket by negative
• simplify

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3
Q

how to complete the square for coefficients of x squared

A
  • remove coefficient of x squared as a common factor
  • complete the square of resulting bracket
  • multiply out square brackets
  • collect like terms
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4
Q

how to do domain and range

A
  • set denominator to not equal zero
  • solve to find x
  • write domain
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5
Q

how to use double angle formula

A
  • use the formula sheet to write down formula
  • substitute ( when yk all three sides )
  • calculate
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6
Q

how to use the addition formula

A
  • use formula sheet to write down chosen formula
  • find missing sides
  • substitute into formula
  • calculate
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7
Q

how to find the wave function min + max values

A
  • 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
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8
Q

how to use the wave function to solve an equation

A
  • change to the form
  • make cosx or sinx the subject of the formula
  • calculate FQA
  • calculate alternative solution (CAST)
  • make the correction observing limits
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9
Q

how to use the wave function to solve an equations

A
  • 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
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10
Q

how to find POI

A
  • 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))
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11
Q

how to use the discriminant

A
  • 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
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12
Q

how to find quadratic inequalities

A
  • 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
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13
Q

how to inverse function

A
  • change function to y
  • change subject to x
  • change notation
    x -> h-1(x)
    y -> x
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14
Q

how to do graph transformations

A
  • identify transformations being applied
  • apply each transformation in turn -> sketch intermediate graph write each new coordinate
  • complete sketch and annotate with new coordinates
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15
Q

how to tell if pints are collinear

A
  • show segments are parallel
  • ensure there’s a common point and state it
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16
Q

how to do quadratic trig equations

A
  • factorise the quadratic trig equation
  • set each factor equal to zero
  • find the solution for each factor
17
Q

how to do further trig equations

A
  • replace any double angles using formulae list
  • remove any brackets
  • factories
  • split and solve using cast diagram
18
Q

how do you calculate the derivative

A
  • multiply by the power
  • reduce the power by one
19
Q

how to use the derivative

A

find the derivative
substitute and evaluate

20
Q

how to do equation of tangents

A
  • 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
21
Q

how to do increasing and decreasing functions

A
  • find the derivative
  • if f/(x) < 0 the function is decreasing
  • if f/(x) > the function is increasing
22
Q

how to find stationary points

A
  • 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
23
Q

how to du d the greatest and least values within a closed interval

A

-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

24
Q

how to do the differentiation chain rule

A
  • prepare if necessary
  • multiply by the power and reduce by 1
  • multiply by the derivative of the bracket

higher maths (2 decks)

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