Maths Flashcards
1
Q
What’s the rule for angles on a straight line?
A
They add up to 180*
2
Q
What’s the rule for angles around a point?
A
They add up to 360*
3
Q
What’s the rule for vertically opposite angles?
A
They’re equal
4
Q
What’s the rule for angles in a triangle
A
They add up to 180*
5
Q
What does an isosceles triangle have?
A
Two equal sides/lengths and two equal base angles
6
Q
What’s a quadrilateral?
A
Shape with 4 sides
7
Q
What’s the rule for angles on a quadrilateral?
A
They add up to 360*
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
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.
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
11
Q
When’s a shape regular?
A
When all sides are the same shape and all angles are the same size
12
Q
What’s equation for sum of interior angles in any polygon?
A
(n-2)x180*
13
Q
An interior angle + an exterior angle =?
A
180*
14
Q
What’s the rule for Exterior angles of a polygon?
A
They add up to 360*
15
Q
What’s a polygon?
A
Shape with at least 3 sides and angles
16
Q
What’s a tangent?
A
Line that touches the edge of a curve at one point
17
Q
What’s the rule for circle theorem for tangent and radius?
A
A tangent and radius meet to make a 90* angle
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
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
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
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
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
23
Q
What are the two rules for bearings?
A
Always measured clockwise from north, must always have 3 digits
24
Q
How do you work out HCF from a Venn diagram?
A
Multiply together numbers in middle
25
How do you work out LCF from a Venn diagram?
Multiply all numbers in diagram together
26
X^4 x X^3 =?
= X^7
27
P^8 / p^2 = ?
P^6
28
(X^4)^3 =?
X^12
29
X^4/X^4 = ?
X^0 = 1
30
9 ^ 1/2 = ?
(Little 2) (Square Root of 9)
31
16 ^ 3/2 = ?
(Little 2) (Square Root of 16^3 ) = 4^3 = 64
32
4^-2 = ?
1/(4^2) = 1/16
33
When asked to evaluate, what does it want you to do?
Work out
34
When using bus stop method, which number needs to be an integer?
The number inside the bus stop
35
How do you multiply two numbers that are both in standard form?
Time the first integers, add the indices. Write answer in standard form
36
When do you factorise into double brackets?
When expanding quadratics
37
When do you use smiley face method to factorise?
When the quadratic has an integer before it
38
What’s the rule of difference of two squares?
a^2-b^2= (a-b)(a+b)
39
What’s a surd?
A square root of an integer that doesn’t give you an integer answer
40
What’s the surd law?
(Square Root of a b) = (Square Root of a) (Square Root of b)
41
What does it mean to rationalise the denominator?
Getting rid of the surd on the denominator
42
What’s the first signification figure of a number?
The first non zero digit of a number when reading from the left
43
How do you estimate.
Round each number to 1sf, then work out the calculation
44
How do you convert from a percentage to a decimal?
Divide by 100
45
How do you convert from a percentage to a fraction?
Write it over 100
46
How do you convert from decimal to percentage.
Times by 100
47
How do you convert from decimal to fraction
Multiply by 100 and write over 100
48
How do you convert from fraction into decimal
Try writing it over 100, or divide numerator by denominator
49
How do you convert from fraction to percentage?
Write it over 100
50
Speed equation?
Speed = distance / time
51
Density equation?
Density (g/cm^3) = mass / volume
52
Pressure equation?
Pressure = force / area
| Pressure is measured in N/m^2
53
1m^2 = ?^2 cm^2 = ? Cm?
1m^2 = 100^2 cm^2 = 10000cm^2
54
What does an expression have?
No equal sign
55
How do you solve fractional equations?
Make a common denominator (put numerator into foil brackets) Expand brackets. Solve.
56
What’s the basic equation of a line? And what do the parts mean
Y = mx +/- c
m is gradient
Y and x are coordinates
+/- c is the y intercept (where line crosses y axis)
57
What’s the rule for gradient of lines that are parallel?
They have the same gradient
58
What’s the rule for gradient of lines that are perpendicular?
Lines a and b are perpendicular
| Gradient of line b will be the negative reciprocal of line a
59
Equation of gradient of a line between two points?
Difference in ys / difference in xs
60
How do you work out midpoint of two coordinates
( (x1 + x2)/2 , (y1+y2)/2 )
61
What’s Pythagoras theorem?
a^2 + b^2 = c^2
Only works on right angle triangles. C = hypotenuse, the line opposite the right angle
62
In trigonometry, what are the opposite and adjacent, what is theta.
```
Opposite = the length opposite theta
Adjacent = the side adjacent to theta, but not the hypotenuse
Theta = an angle that’s not the right angle
```
63
Sin theta = ?
Sin theta = opposite / hypotenuse
64
Cos theta = ?
Cos theta = adjacent / hypotenuse
65
Tan theta = ?
Tan theta = opposite / hypotenuse
66
If you end up with 10 x sin 60 = x, what do you enter into your calculator?
Sin (60) x 10
67
Sin 0* = ?
0
68
Sin 30* = ?
1/2
69
Sin 45* = ?
(Square root of 2) / 2
70
Sin 60* = ?
(Square root of 3) / 2
71
Sin 90* = ?
1
72
Cos 0* = ?
1
73
Cos 30* = ?
(Square root of 3) / 2
74
Cos 45* = ?
(Square root of 2)/2
75
Cos 60* = ?
1/2
76
Cos 90* = ?
0
77
Tan 0* = ?
0
78
Tan 30* = ?
(Square root of 3)/3
79
Tan 45* = ?
1
80
Tan 60* = ?
Square root of 3
81
Tan 90* = ?
Error
82
If you have cos theta = 6/12, how would you work out theta?
Cos -1
| Theta = cos -1 (6/12)
83
What’s the perimeter?
Total length around the outside of a shape
84
What’s area?
The total space inside a shape
85
Equation for area of rectangle
Base x height = area
86
Equation for area of triangle
(Base x perpendicular height) / 2 = area
87
What’s a parallelogram
4 sided shape with 2 pairs of parallel sides
88
What’s a rhombus?
A parallelogram where all sides are the same length
89
Equation for area of parallelogram?
Base x perpendicular height = area
90
What’s the origin on a circle?
The centre of the circle
91
What’s a sector on a circle?
A section of the circle. Has to go from the centre (to the circumference)
92
What’s a chord in a circle?
A line that goes across, but not through the middle of the circle
93
What’s a segment in a circle?
A section of a circle (the area between a chord and the circumference)
94
What’s an arc in a circle?
A section of the circumference
95
On a circle, what’s the circumference?
The distance around the edge of a circle
96
On a circle, what’s the diameter?
The distance from one edge of the circle to the other, passing through the centre
97
On a circle, what’s the radius?
The distance from the centre of the circle to one edge
98
What’s equation for circumference of a circle?
2 x pi x radius
99
What’s 1 revolution of a circle?
1 journey round the whole circumference
100
Equation for area of circle
Area = r^2 x pi
101
What’s a trapezium?
Any 4 sided shape with 1 pair of parallel lines
102
Area of a trapezium?
1/2 (a+b) x h
| a and b are lengths of parallel sides
103
How do you work out a fraction of an amount
Divide amount by denominator and times answer by numerator
104
What’s an outlier?
A value different to the pattern/trend. An anomaly.
105
What’s a sample space diagram?
Diagram showing all probabilities in what looks like a multiplication square
106
What’s a set?
A collection of objects or numbers
107
What are the objects in a set called?
Members or elements of the set
108
What does the set notation AnB mean?
Where A and B both exist at the same time
109
What does the set notation AuB mean?
Everything that is A and everything that is B
110
What does the set notation A’ mean?
Everything that is not A
111
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?
Each number should only appear once in the diagram
112
Equation for volume of a prism?
Volume of prism = csa x length
113
Density equation and unit
Density = mass / volume
| g/cm^3 or kg/m^3
114
Equation for volume of any pyramid?
Volume = 1/3 x area of base x height
115
How do you do compound interest?
You times by the increase to the power of how many years it’s over
116
How do you do simple interest?
Work out the total after 1 year then just times that by number of years
117
Equation for percentage profit
Percentage profit = (profit/ original amount ) x 100
118
Equation for percentage loss
Percentage loss = (loss/original amount) x 100
119
What are the four types of transformation?
Rotation, reflection, enlargement, translation
120
How does translation work?
Uses a vector to describe how the shape is moved
121
How does reflection work?
Tells you the line shape is reflected on, like a mirror line
122
How does rotation Work?
Give centre of enlargement, direction of turn (clockwise, anti-clockwise) and angle of rotation (amount of turn)
123
How does enlargement work?
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
On a distance time graph, what’s the gradient tell you?
The average speed
125
Equation for average speed (on a distance time graph)
Average speed = total distance / total time
126
On a velocity time graph, what does the area under the graph tell you?
Total distance travelled
127
On velocity time graph, what does gradient tell you?
Acceleration
128
What’s the general formula linking two things in direct proportion!
y (direct proportion sign) x
| y = k x X
129
How are two things that are inversely proportional written?
y (proportion sign) 1/x
| y = k/x
130
What’s the mode?
Value that appears most often
131
What’s the median?
Middle value when set of data in order
132
What’s the mean?
add up all values and divide by how many there are
133
What’s the range?
Represents the spread of data: largest value - smallest value
134
How do you work out interquartile range
Upper quartile - lower quartile
135
In a table of scores and frequency of these scores, how do you work out the modal score?
The one with the highest frequency
136
In a table of scores and frequency of these scores, how do you work out the range?
Highest score - lowest score
137
In a table of scores and frequency of these scores, how do you work out the mean score
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
In a class interval table how do you work out an estimate of the mean?
Do same as you would with regular table but use midpoints of the modal classes
139
Equation for median position
(Total frequency + 1)/2
140
Equation for lower quartile position
(Total frequency + 1) / 4
141
Equation for upper quartile position
(Media position + 1) / 4 x 3
142
What’s the two rules for stem and leaf diagrams?
Leaf is always 1 digit in size, diagram must be in size order of values
143
What’s an arithmetic/linear sequence?
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
What’s the start of the nth term rule in a quadratic sequence
It’s (half the repeated difference) n^2
145
When’s a sequence a Fibonacci sequence
You add previous two numbers to create the next one
146
When’s a sequence a auadratic sequence
Takes two sets of difference to get a repeated difference
147
When’s a sequence a geometric sequence
Multiply the terms by the same amount each time. This amount is known as the common ratio
148
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
Coloured in = value can equal it
| Not coloured in= value can’t equal it
149
When’s the only time multiplying or dividing both sides of an inequality by a negative works?
When it switches the inequality sign round
150
When solving inequalities graphically, what direction will the region be in when the inequality is < and when the inequality is >
< will always be below
| > will always be above
151
What’s the line y = x look like?
Diagonal line from bottom left to top right /
152
What are similar shapes?
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
How do you go from length scale factor to area scale factor
asf is lsf^2
154
How do you go from length scale factor to volume scale factor
vsf = lsf^3
155
How do you draw the gradient of a cumulative frequency graph
A smooth curve going through every point
156
What does a box plot have to have and how is it drawn?
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
When told to ‘compare data’, what do you compare?
An average with a Range of interquartile range (usually median with range)
Use IQR if data anomalous
158
What’s the equation for frequency density when interpreting Variable Width Histograms
Frequency density = frequency / class width
159
What’s the area of a rectangle on a variable width histogram tell you?
The frequency
160
If told ‘make R the subject of the formula’, what do you want to do?
Get R by itself
161
What’s random sampling
Where everything selected has an equal chance of being selected
162
What’s stratified sampling?
Where the sample has the same proportions as the total population
163
What’s a frequency polygon?
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
When asked to draw a graph with a positive x^2, what shape will the graph be?
U shaped
165
When asked to draw a graph with a negative x^2, what shape will the graph be?
An n shape
166
What does the graph for y in direct proportion to x look like
Four section graph. A line going from middle diagonally to corner of top right section
167
What does the graph for y in direct proportion to x^2 look like
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
What does the graph for y inversely proportional to x look like
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
What does the graph for y inversely proportional to x^2 look like
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
What’s the quadratic formula?
[-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
What does iteration in maths mean?
A repeating process
172
In iteration, what do values of X1, X2 and X3 represent
Approximations to the root
| Also where it crosses the xaxis in a graph
173
How do you write consecutive integers using algebra?
n n+1 n+2
174
How do you write an even number using algebra?
2n
175
How do you write an odd number using algebra?
2n+1
176
How do you write consecutive even numbers using algebra?
2n 2n+2 2n+4 2n+6
177
How do you write consecutive odd numbers using algebra?
2n+1 2n+3 2n+5
178
How do you write a multiple of 3 using algebra?
3n
179
What’s a product?
What you get when you multiply numbers together
180
What’s the general form for the equation of a circle with centre (0,0)
x^2 + y^2 = r^2
| R is radius
181
What does it mean for two shapes to be congruent?
Then they are identical in both shape and size even if rotated or reflected
182
When are two triangles congruent?
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
If something is bisecting something, what’s it doing?
Cutting it in half
184
(a b)^ 2 = ?
= a^2 b^2
185
What do inverse functions do
Undoes what was done by the function
186
How can a vector be labelled?
With single bold letters or with an underline letter
187
EF (arrow above both letters) = (6 [2 underneath 6])
a(underlined) = (6 [2 underneath 6])
What does the above mean
To get from E to F you move 6 right and 2 up. This movement can be described as the vector a
188
What’s the magnitude (when talking about movement and vectors) and how do you write it with a vector
The length of the journey
| (vector letter underlined) | = magnitude
189
When are vectors parallel?
If one is a multiple of the other
190
What rule links volume and litres?
```
1cm^3 = 1ml^3
1litre = 1000cm^3
```
191
What’s ‘the root’ on a quadratic graph?
Where they cross the x axis
192
What’s the ‘turning point’ on a quadratic graph
The lowest point of the dip
193
What does the graph of y = sin x look like?
```
Smooth curve from point to point
0,0
90,1
180,0
270,-1
360,0
```
This curve then repeats
194
What does the graph of y = cos x look like?
```
Smooth curve from point to point
0,1
90,0
180,-1
270,0
360,1
```
This curve then repeats
195
What does the graph of y = tan x look like?
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
What are asymptotes?
The curve approaches the asymptote line but never touches it. As such, they are ‘infinite’
197
If y = x is drawn f(x)+ a, what happens to the graph?
Always affects y coordinates
| Graph moves up by ‘a’
198
If y = x is drawn f(x)- a, what happens to the graph?
Always affects y coordinates
| Moves down by ‘a’
199
If y = x is drawn -f(x), what happens to the graph?
Always affects y coordinates
| Reflects graph in the x-axis
200
If y = x is drawn f(x+a), what happens to the graph?
Always affects x coordinates
| Graph moves left by ‘a’
201
If y = x is drawn f(x-a), what happens to the graph?
Always affects x coordinates, graph moves right by a
202
If y = x is drawn f(-x), what happens to the graph?
Graph reflects in the y-axis
203
What is the sine rule and when is it used
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
What is the Sine Rule for a missing angle?
Sin A/a = Sin B/b = Sin C/c
| Could just use regular ol’ sine rule, but that needs more steps
205
What’s the Cosine Rule
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
Is 0 an even or odd number
Even
207
What digit number is 00
2 digit
208
When asked to complete the square by writing it in the form ‘(x+p)^2+q
What do you do?
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
