Maths Flashcards Preview

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Flashcards in Maths Deck (208):
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

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