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Maths > Further Maths > Flashcards

Further Maths Flashcards

1
Q

What are the exact trig values?

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2
Q

Draw the tan graph

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3
Q

Draw the sin graph

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4
Q

Draw the cosine graph

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5
Q

What is the sin Rule

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6
Q

What is the cosine rule?

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7
Q

How do you use cast diagrams?

A

🟢check which relm it is in to see if it is positive or negative
🟢then check which angle is nearest to the x axis, to use for calculating angle

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8
Q

What is the gradient of the line of a perpendicular line?

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The negative reciprocal

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9
Q

What is symmetry of the graph?

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10
Q

How do you differenciate?

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11
Q

How do you convert an equation involving 2 variables into a ratio ?

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12
Q

Draw Pascal’s triangle

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13
Q

Expand

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14
Q

Domain and range

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15
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16
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17
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18
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19
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20
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21
Q

How do you multiply two different matrices?

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22
Q

What are singular and non singular matrices?

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If singular , the determinant =0
If non - singular , the determinant !=0

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23
Q

What is an identity matricx?

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24
Q

Scalar multiplication of matrices

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25
Q

Adding and subtracting matrices

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26
Q

Figure out the determinants of the 2X2 matrices

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27
Q

What are the two equations of the circle?

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28
Q

What are the two equations of the circle?

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29
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30
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31
Q

What is an identity matrix?

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32
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33
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34
Q

Determine the equation of a circle with :
🟢 centre (0,0) , radius =3
🟢centre (4,-7) , radius =5
🟢centre (0,5) , radius = 1

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35
Q

determine the centre and the radius

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36
Q

What is the discriminant?

A

If less than 0 doesn’t touch the x axis and so no solutions

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37
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38
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39
Q

How do you find the midpoint of two points?

A

You find the average of the x and y values separately

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40
Q

A circle passes through the points A (0,0) and B (4,2). The centre of the circle has an x value of -1. Determine the equation of the circle:

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41
Q

The circle C has radius 5 and touches the y axis at (0,9). It’s centre is (-5, 9) and it’s radius is 5. A line through point P (8,-7) is a tangent to the circle at the
Point T. Find the length of PT

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42
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43
Q

Differentiate :

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44
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45
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46
Q

How do you find the gradient of a tangent to a curve ?

A
  1. Differentiate the equation to give the ‘gradient function’
  2. Then substitute the ❎ value into the function to give m
47
Q

How do you find the equation of a tangent to a curve ?

A
  1. Differentiate the equation to give the ‘gradient function’
  2. Then substitute the ❎ value into the function to give m
  3. Now that you have found m , substitute into y=mx +c
48
Q

How do you find the equation of a normal to a curve ?

A

*a normal is a straight line that crosses the tangent at 90° (perpendicular)

  1. Differentiate the equation to give the ‘gradient function’
  2. Then substitute the ❎ value into the function to give m
  3. Now that you have found m , you can find m of the or all by doing negative reciprocal
  4. Substitute this m into y=mx + c
49
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59
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60
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61
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62
Q

What is the determinant of a matrix ?

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63
Q

What is the inverse of a matrix

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64
Q

What is the inverse of a matrix ✖️matrix ?

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65
Q

How would you solve simultaneous equations using matrices

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66
Q

Convert this simultaneous equation into matrix form
And solve

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67
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68
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69
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70
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71
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72
Q

How can you recognise /guess some matrix transformations?

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73
Q

What are some cheeky tricks to Identify some linear transformation matrices?

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74
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75
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76
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77
Q

How do you find stationary points of a function?

A

Find dy/dx
Then make this gradient function =0
As at the stationary points the gradients are 0.

78
Q

How do you know whether the stationary points are maximum or minimum points ?

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79
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80
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81
Q

What is the circle geometry rule of chords

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The perpendicular from the centre to a chord , bisects a chord

82
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83
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84
Q

What is the transformation matrix for the reflection in the line y=x

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85
Q

What is the transformation matrix for a reflection in the x axis

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86
Q

What is the transformation for the reflection in the y axis

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87
Q

What is the transformation matrix for a 90° clockwise rotation?

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88
Q

What is the transformation matrix for a 90° anti clockwise rotation?

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89
Q

What is the transformation matrix for a 180° clockwise and anti clockwise rotation?

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90
Q

What is the transformation matrix for a 270°clockwise rotation?

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91
Q

What is the transformation matrix for a 270° anti clockwise rotation?

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92
Q

How would you find the limiting value ?

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93
Q

What does it mean when it says that x is an obtuse angle for cos(x) or sin (x)?

A

It must mean that it is cos(x)= - …..
Eg : obtuse angle for cos (x)=-0.8

94
Q

What does it mean when it says integer form?

A

Write out the possible numbers not an inequality

95
Q

What does it mean when it says integer form?

A

Write out the possible numbers not an inequality

96
Q

What are some general tips for myself in the exam ?

A
  • remembering +- before square roots
  • remembering that there are marks for marking and not answers. So write out each small sum made , SUBSTITUTIONS WITH BRACKETS , don’t get lazy
  • be extra careful with positive and negative signs
97
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98
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99
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100
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101
Q

How do you remember the reflection transformation matrices?

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102
Q

How do you remember the rotation matrices ?

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103
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104
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105
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106
Q

Giving a range of values

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Maths (6 decks)

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