Flashcards in Maths Deck (207):

1

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

### They add up to 180*

2

## What’s the rule for angles around a point?

### They add up to 360*

3

## What’s the rule for vertically opposite angles?

### They’re equal

4

## What’s the rule for angles in a triangle

### They add up to 180*

5

## What does an isosceles triangle have?

### Two equal sides/lengths and two equal base angles

6

## What’s a quadrilateral?

### Shape with 4 sides

7

## What’s the rule for angles on a quadrilateral?

### They add up to 360*

8

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

###
Alternative angles are equal

They’re an s or z shape with parallel arms

9

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

###
Corresponding angles are equal

F shape with parallel arms.

10

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

###
They add up to 180*

Look for c shape with parallel arms

11

## When’s a shape regular?

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

12

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

### (n-2)x180*

13

## An interior angle + an exterior angle =?

### 180*

14

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

### They add up to 360*

15

## What’s a polygon?

### Shape with at least 3 sides and angles

16

## What’s a tangent?

### Line that touches the edge of a curve at one point

17

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

### A tangent and radius meet to make a 90* angle

18

## What’s the circle theorem for two tangents?

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

19

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

###
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

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

###
Angles in the same segment are equal

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

21

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

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

22

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

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

23

## What are the two rules for bearings?

### Always measured clockwise from north, must always have 3 digits

24

## How do you work out HCF from a Venn diagram?

### 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