Maths Flashcards

1
Q

What’s the rule for angles on a straight line?

A

They add up to 180*

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2
Q

What’s the rule for angles around a point?

A

They add up to 360*

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3
Q

What’s the rule for vertically opposite angles?

A

They’re equal

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4
Q

What’s the rule for angles in a triangle

A

They add up to 180*

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5
Q

What does an isosceles triangle have?

A

Two equal sides/lengths and two equal base angles

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6
Q

What’s a quadrilateral?

A

Shape with 4 sides

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7
Q

What’s the rule for angles on a quadrilateral?

A

They add up to 360*

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8
Q

What’s the rule for alternative angles and how do you recognise them?

A

Alternative angles are equal

They’re an s or z shape with parallel arms

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9
Q

What’s the rule for corresponding angles and how do you recognise them?

A

Corresponding angles are equal

F shape with parallel arms.

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10
Q

What’s the rule for co-interior angles and how do you recognise them?

A

They add up to 180*

Look for c shape with parallel arms

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11
Q

When’s a shape regular?

A

When all sides are the same shape and all angles are the same size

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12
Q

What’s equation for sum of interior angles in any polygon?

A

(n-2)x180*

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13
Q

An interior angle + an exterior angle =?

A

180*

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14
Q

What’s the rule for Exterior angles of a polygon?

A

They add up to 360*

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15
Q

What’s a polygon?

A

Shape with at least 3 sides and angles

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16
Q

What’s a tangent?

A

Line that touches the edge of a curve at one point

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17
Q

What’s the rule for circle theorem for tangent and radius?

A

A tangent and radius meet to make a 90* angle

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18
Q

What’s the circle theorem for two tangents?

A

Tangents from the same extended point to the circumference of the circle are equal in length

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19
Q

What’s the circle theorem for angle at circumference and angle at centre? What do you look for to apply this?

A

Angle at the centre is twice the size of the angle at the circumference

One angle must be at centre and other three must be touching circumference

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20
Q

What’s the circle theorem for angles in the same segment? What do you look for to apply this?

A

Angles in the same segment are equal

Look for a ‘bowtie’ shape. All points will be touching the circumference

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21
Q

What’s the circle theorem for angle in a semicircle? What do you look for to apply this?

A

Angle in a semicircle is 90*. One length of triangle must go through centre of circle, all vertices touching circumference

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22
Q

What’s the circle theorem for a cyclic quadrilateral? What do you look for to apply this?

A

Opposite angles (diagonally opposite) in a cyclic quadrilateral add up to 180*. All points of quadrilateral must be touching circumference

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23
Q

What are the two rules for bearings?

A

Always measured clockwise from north, must always have 3 digits

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24
Q

How do you work out HCF from a Venn diagram?

A

Multiply together numbers in middle

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25
Q

How do you work out LCF from a Venn diagram?

A

Multiply all numbers in diagram together

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26
Q

X^4 x X^3 =?

A

= X^7

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27
Q

P^8 / p^2 = ?

A

P^6

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28
Q

(X^4)^3 =?

A

X^12

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29
Q

X^4/X^4 = ?

A

X^0 = 1

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30
Q

9 ^ 1/2 = ?

A

(Little 2) (Square Root of 9)

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31
Q

16 ^ 3/2 = ?

A

(Little 2) (Square Root of 16^3 ) = 4^3 = 64

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32
Q

4^-2 = ?

A

1/(4^2) = 1/16

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33
Q

When asked to evaluate, what does it want you to do?

A

Work out

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34
Q

When using bus stop method, which number needs to be an integer?

A

The number inside the bus stop

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35
Q

How do you multiply two numbers that are both in standard form?

A

Time the first integers, add the indices. Write answer in standard form

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36
Q

When do you factorise into double brackets?

A

When expanding quadratics

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37
Q

When do you use smiley face method to factorise?

A

When the quadratic has an integer before it

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38
Q

What’s the rule of difference of two squares?

A

a^2-b^2= (a-b)(a+b)

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39
Q

What’s a surd?

A

A square root of an integer that doesn’t give you an integer answer

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40
Q

What’s the surd law?

A

(Square Root of a b) = (Square Root of a) (Square Root of b)

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41
Q

What does it mean to rationalise the denominator?

A

Getting rid of the surd on the denominator

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42
Q

What’s the first signification figure of a number?

A

The first non zero digit of a number when reading from the left

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43
Q

How do you estimate.

A

Round each number to 1sf, then work out the calculation

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44
Q

How do you convert from a percentage to a decimal?

A

Divide by 100

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45
Q

How do you convert from a percentage to a fraction?

A

Write it over 100

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46
Q

How do you convert from decimal to percentage.

A

Times by 100

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47
Q

How do you convert from decimal to fraction

A

Multiply by 100 and write over 100

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48
Q

How do you convert from fraction into decimal

A

Try writing it over 100, or divide numerator by denominator

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49
Q

How do you convert from fraction to percentage?

A

Write it over 100

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50
Q

Speed equation?

A

Speed = distance / time

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51
Q

Density equation?

A

Density (g/cm^3) = mass / volume

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52
Q

Pressure equation?

A

Pressure = force / area

Pressure is measured in N/m^2

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53
Q

1m^2 = ?^2 cm^2 = ? Cm?

A

1m^2 = 100^2 cm^2 = 10000cm^2

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54
Q

What does an expression have?

A

No equal sign

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55
Q

How do you solve fractional equations?

A

Make a common denominator (put numerator into foil brackets) Expand brackets. Solve.

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56
Q

What’s the basic equation of a line? And what do the parts mean

A

Y = mx +/- c
m is gradient
Y and x are coordinates
+/- c is the y intercept (where line crosses y axis)

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57
Q

What’s the rule for gradient of lines that are parallel?

A

They have the same gradient

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58
Q

What’s the rule for gradient of lines that are perpendicular?

A

Lines a and b are perpendicular

Gradient of line b will be the negative reciprocal of line a

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59
Q

Equation of gradient of a line between two points?

A

Difference in ys / difference in xs

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60
Q

How do you work out midpoint of two coordinates

A

( (x1 + x2)/2 , (y1+y2)/2 )

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61
Q

What’s Pythagoras theorem?

A

a^2 + b^2 = c^2

Only works on right angle triangles. C = hypotenuse, the line opposite the right angle

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62
Q

In trigonometry, what are the opposite and adjacent, what is theta.

A
Opposite = the length opposite theta
Adjacent = the side adjacent to theta, but not the hypotenuse 
Theta = an angle that’s not the right angle
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63
Q

Sin theta = ?

A

Sin theta = opposite / hypotenuse

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64
Q

Cos theta = ?

A

Cos theta = adjacent / hypotenuse

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65
Q

Tan theta = ?

A

Tan theta = opposite / hypotenuse

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66
Q

If you end up with 10 x sin 60 = x, what do you enter into your calculator?

A

Sin (60) x 10

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67
Q

Sin 0* = ?

A

0

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68
Q

Sin 30* = ?

A

1/2

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69
Q

Sin 45* = ?

A

(Square root of 2) / 2

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70
Q

Sin 60* = ?

A

(Square root of 3) / 2

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71
Q

Sin 90* = ?

A

1

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72
Q

Cos 0* = ?

A

1

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73
Q

Cos 30* = ?

A

(Square root of 3) / 2

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74
Q

Cos 45* = ?

A

(Square root of 2)/2

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75
Q

Cos 60* = ?

A

1/2

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76
Q

Cos 90* = ?

A

0

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77
Q

Tan 0* = ?

A

0

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78
Q

Tan 30* = ?

A

(Square root of 3)/3

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79
Q

Tan 45* = ?

A

1

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80
Q

Tan 60* = ?

A

Square root of 3

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81
Q

Tan 90* = ?

A

Error

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82
Q

If you have cos theta = 6/12, how would you work out theta?

A

Cos -1

Theta = cos -1 (6/12)

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83
Q

What’s the perimeter?

A

Total length around the outside of a shape

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84
Q

What’s area?

A

The total space inside a shape

85
Q

Equation for area of rectangle

A

Base x height = area

86
Q

Equation for area of triangle

A

(Base x perpendicular height) / 2 = area

87
Q

What’s a parallelogram

A

4 sided shape with 2 pairs of parallel sides

88
Q

What’s a rhombus?

A

A parallelogram where all sides are the same length

89
Q

Equation for area of parallelogram?

A

Base x perpendicular height = area

90
Q

What’s the origin on a circle?

A

The centre of the circle

91
Q

What’s a sector on a circle?

A

A section of the circle. Has to go from the centre (to the circumference)

92
Q

What’s a chord in a circle?

A

A line that goes across, but not through the middle of the circle

93
Q

What’s a segment in a circle?

A

A section of a circle (the area between a chord and the circumference)

94
Q

What’s an arc in a circle?

A

A section of the circumference

95
Q

On a circle, what’s the circumference?

A

The distance around the edge of a circle

96
Q

On a circle, what’s the diameter?

A

The distance from one edge of the circle to the other, passing through the centre

97
Q

On a circle, what’s the radius?

A

The distance from the centre of the circle to one edge

98
Q

What’s equation for circumference of a circle?

A

2 x pi x radius

99
Q

What’s 1 revolution of a circle?

A

1 journey round the whole circumference

100
Q

Equation for area of circle

A

Area = r^2 x pi

101
Q

What’s a trapezium?

A

Any 4 sided shape with 1 pair of parallel lines

102
Q

Area of a trapezium?

A

1/2 (a+b) x h

a and b are lengths of parallel sides

103
Q

How do you work out a fraction of an amount

A

Divide amount by denominator and times answer by numerator

104
Q

What’s an outlier?

A

A value different to the pattern/trend. An anomaly.

105
Q

What’s a sample space diagram?

A

Diagram showing all probabilities in what looks like a multiplication square

106
Q

What’s a set?

A

A collection of objects or numbers

107
Q

What are the objects in a set called?

A

Members or elements of the set

108
Q

What does the set notation AnB mean?

A

Where A and B both exist at the same time

109
Q

What does the set notation AuB mean?

A

Everything that is A and everything that is B

110
Q

What does the set notation A’ mean?

A

Everything that is not A

111
Q

If you have a set of numbers that are in a diagram, and then within that set are multiple sets of types of number, what’s the rule?

A

Each number should only appear once in the diagram

112
Q

Equation for volume of a prism?

A

Volume of prism = csa x length

113
Q

Density equation and unit

A

Density = mass / volume

g/cm^3 or kg/m^3

114
Q

Equation for volume of any pyramid?

A

Volume = 1/3 x area of base x height

115
Q

How do you do compound interest?

A

You times by the increase to the power of how many years it’s over

116
Q

How do you do simple interest?

A

Work out the total after 1 year then just times that by number of years

117
Q

Equation for percentage profit

A

Percentage profit = (profit/ original amount ) x 100

118
Q

Equation for percentage loss

A

Percentage loss = (loss/original amount) x 100

119
Q

What are the four types of transformation?

A

Rotation, reflection, enlargement, translation

120
Q

How does translation work?

A

Uses a vector to describe how the shape is moved

121
Q

How does reflection work?

A

Tells you the line shape is reflected on, like a mirror line

122
Q

How does rotation Work?

A

Give centre of enlargement, direction of turn (clockwise, anti-clockwise) and angle of rotation (amount of turn)

123
Q

How does enlargement work?

A

Has a scale factor and centre of enlargement. He lengths change size, angles stay the same. Of scale factor negative, shape goes in opposite direction.

124
Q

On a distance time graph, what’s the gradient tell you?

A

The average speed

125
Q

Equation for average speed (on a distance time graph)

A

Average speed = total distance / total time

126
Q

On a velocity time graph, what does the area under the graph tell you?

A

Total distance travelled

127
Q

On velocity time graph, what does gradient tell you?

A

Acceleration

128
Q

What’s the general formula linking two things in direct proportion!

A

y (direct proportion sign) x

y = k x X

129
Q

How are two things that are inversely proportional written?

A

y (proportion sign) 1/x

y = k/x

130
Q

What’s the mode?

A

Value that appears most often

131
Q

What’s the median?

A

Middle value when set of data in order

132
Q

What’s the mean?

A

add up all values and divide by how many there are

133
Q

What’s the range?

A

Represents the spread of data: largest value - smallest value

134
Q

How do you work out interquartile range

A

Upper quartile - lower quartile

135
Q

In a table of scores and frequency of these scores, how do you work out the modal score?

A

The one with the highest frequency

136
Q

In a table of scores and frequency of these scores, how do you work out the range?

A

Highest score - lowest score

137
Q

In a table of scores and frequency of these scores, how do you work out the mean score

A

OKAY SO you times score and frequency along the tables in a new column then add this column up and then also add up values in frequency column
Mean score is new column total / frequency total

138
Q

In a class interval table how do you work out an estimate of the mean?

A

Do same as you would with regular table but use midpoints of the modal classes

139
Q

Equation for median position

A

(Total frequency + 1)/2

140
Q

Equation for lower quartile position

A

(Total frequency + 1) / 4

141
Q

Equation for upper quartile position

A

(Media position + 1) / 4 x 3

142
Q

What’s the two rules for stem and leaf diagrams?

A

Leaf is always 1 digit in size, diagram must be in size order of values

143
Q

What’s an arithmetic/linear sequence?

A

The terms go up or down by the same amount (add or subtracting the same each time) this amount is known as the constant difference

144
Q

What’s the start of the nth term rule in a quadratic sequence

A

It’s (half the repeated difference) n^2

145
Q

When’s a sequence a Fibonacci sequence

A

You add previous two numbers to create the next one

146
Q

When’s a sequence a auadratic sequence

A

Takes two sets of difference to get a repeated difference

147
Q

When’s a sequence a geometric sequence

A

Multiply the terms by the same amount each time. This amount is known as the common ratio

148
Q

In inequalities on a number line, what does it mean if the circle is coloured in and what does it mean when the circle is not coloured in

A

Coloured in = value can equal it

Not coloured in= value can’t equal it

149
Q

When’s the only time multiplying or dividing both sides of an inequality by a negative works?

A

When it switches the inequality sign round

150
Q

When solving inequalities graphically, what direction will the region be in when the inequality is < and when the inequality is >

A

< will always be below

> will always be above

151
Q

What’s the line y = x look like?

A

Diagonal line from bottom left to top right /

152
Q

What are similar shapes?

A

The same shape but different in size. All the angles are the same. The lengths are all multiplied or divided by the same amount.

153
Q

How do you go from length scale factor to area scale factor

A

asf is lsf^2

154
Q

How do you go from length scale factor to volume scale factor

A

vsf = lsf^3

155
Q

How do you draw the gradient of a cumulative frequency graph

A

A smooth curve going through every point

156
Q

What does a box plot have to have and how is it drawn?

A

Minimum mark is it’s own line, connecting to lower quartile, median and upper quartile which make a rectangle, then maximum mark is it’s own line

157
Q

When told to ‘compare data’, what do you compare?

A

An average with a Range of interquartile range (usually median with range)
Use IQR if data anomalous

158
Q

What’s the equation for frequency density when interpreting Variable Width Histograms

A

Frequency density = frequency / class width

159
Q

What’s the area of a rectangle on a variable width histogram tell you?

A

The frequency

160
Q

If told ‘make R the subject of the formula’, what do you want to do?

A

Get R by itself

161
Q

What’s random sampling

A

Where everything selected has an equal chance of being selected

162
Q

What’s stratified sampling?

A

Where the sample has the same proportions as the total population

163
Q

What’s a frequency polygon?

A

A graph (usually with frequency on the y axis and other value on the x axis). Plot the data as points, then connect the points in order with a line (not 1 continuous line)

164
Q

When asked to draw a graph with a positive x^2, what shape will the graph be?

A

U shaped

165
Q

When asked to draw a graph with a negative x^2, what shape will the graph be?

A

An n shape

166
Q

What does the graph for y in direct proportion to x look like

A

Four section graph. A line going from middle diagonally to corner of top right section

167
Q

What does the graph for y in direct proportion to x^2 look like

A

Four section graph. A U shape in middle top. Tops of U go to middle of top right section and middle of top left section

168
Q

What does the graph for y inversely proportional to x look like

A

Four section graph.
1 curve from a tiny bit right of top vertical line to a tiny bit up from the right horizontal line
Another curve (the diagonal reflection of the above)

169
Q

What does the graph for y inversely proportional to x^2 look like

A

Four section graph
1 curve from slightly right of top vertical line to slightly above right horizontal line
1 curve, the above Reflected on the top left section

170
Q

What’s the quadratic formula?

A

[-b + or - (the square root of: (b)^2 -4ac) ] / 2a

Where ax^2 + bx + c = 0
(Only works if quadratic = 0)

Give both answers

171
Q

What does iteration in maths mean?

A

A repeating process

172
Q

In iteration, what do values of X1, X2 and X3 represent

A

Approximations to the root

Also where it crosses the xaxis in a graph

173
Q

How do you write consecutive integers using algebra?

A

n n+1 n+2

174
Q

How do you write an even number using algebra?

A

2n

175
Q

How do you write an odd number using algebra?

A

2n+1

176
Q

How do you write consecutive even numbers using algebra?

A

2n 2n+2 2n+4 2n+6

177
Q

How do you write consecutive odd numbers using algebra?

A

2n+1 2n+3 2n+5

178
Q

How do you write a multiple of 3 using algebra?

A

3n

179
Q

What’s a product?

A

What you get when you multiply numbers together

180
Q

What’s the general form for the equation of a circle with centre (0,0)

A

x^2 + y^2 = r^2

R is radius

181
Q

What does it mean for two shapes to be congruent?

A

Then they are identical in both shape and size even if rotated or reflected

182
Q

When are two triangles congruent?

A

Three sides are the same length OR
two sides and the angle in between are the same
OR
Two angles and one side are the same OR
Two sides in a right angle are the same (one side is the hypotenuse)

183
Q

If something is bisecting something, what’s it doing?

A

Cutting it in half

184
Q

(a b)^ 2 = ?

A

= a^2 b^2

185
Q

What do inverse functions do

A

Undoes what was done by the function

186
Q

How can a vector be labelled?

A

With single bold letters or with an underline letter

187
Q

EF (arrow above both letters) = (6 [2 underneath 6])
a(underlined) = (6 [2 underneath 6])

What does the above mean

A

To get from E to F you move 6 right and 2 up. This movement can be described as the vector a

188
Q

What’s the magnitude (when talking about movement and vectors) and how do you write it with a vector

A

The length of the journey

(vector letter underlined) | = magnitude

189
Q

When are vectors parallel?

A

If one is a multiple of the other

190
Q

What rule links volume and litres?

A
1cm^3 = 1ml^3
1litre = 1000cm^3
191
Q

What’s ‘the root’ on a quadratic graph?

A

Where they cross the x axis

192
Q

What’s the ‘turning point’ on a quadratic graph

A

The lowest point of the dip

193
Q

What does the graph of y = sin x look like?

A
Smooth curve from point to point 
0,0
90,1
180,0
270,-1
360,0

This curve then repeats

194
Q

What does the graph of y = cos x look like?

A
Smooth curve from point to point 
0,1
90,0
180,-1
270,0
360,1

This curve then repeats

195
Q

What does the graph of y = tan x look like?

A

from 0,0, to the asymptote line x = 90
Curve from asymptote line x=90 to point 180,0. Curve from 180,0 to asymptote line x = 270
Curve from asymptote line x = 270 to point 360,0

This curve pattern repeats

196
Q

What are asymptotes?

A

The curve approaches the asymptote line but never touches it. As such, they are ‘infinite’

197
Q

If y = x is drawn f(x)+ a, what happens to the graph?

A

Always affects y coordinates

Graph moves up by ‘a’

198
Q

If y = x is drawn f(x)- a, what happens to the graph?

A

Always affects y coordinates

Moves down by ‘a’

199
Q

If y = x is drawn -f(x), what happens to the graph?

A

Always affects y coordinates

Reflects graph in the x-axis

200
Q

If y = x is drawn f(x+a), what happens to the graph?

A

Always affects x coordinates

Graph moves left by ‘a’

201
Q

If y = x is drawn f(x-a), what happens to the graph?

A

Always affects x coordinates, graph moves right by a

202
Q

If y = x is drawn f(-x), what happens to the graph?

A

Graph reflects in the y-axis

203
Q

What is the sine rule and when is it used

A

a/ Sin A = b/Sin B = c/Sin C

Used for trigonometry when the triangle isn’t a right angled triangle

The capital letters represent the inside angles , small letters the sides

204
Q

What is the Sine Rule for a missing angle?

A

Sin A/a = Sin B/b = Sin C/c

Could just use regular ol’ sine rule, but that needs more steps

205
Q

What’s the Cosine Rule

A

a^2 = b^2 + c^2 - 2bc x CosA

Capital letters = angles
Small letters = sides

a^2 is what you’re trying to work out, squared

206
Q

Is 0 an even or odd number

A

Even

207
Q

What digit number is 00

A

2 digit

208
Q

When asked to complete the square by writing it in the form ‘(x+p)^2+q

What do you do?

A

P will be 1/2 the value of the co-efficient of x. Then subtract the square of the number in the bracket

Only true for quadratic with 2 terms