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A Level / GCSE Maths > Key terms + facts > Flashcards

Key terms + facts Flashcards

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1
Q

Factor

A

A number that goes into another number without remainder

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2
Q

Multiple

A

Any numbers that are in the times table

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3
Q

Prime

A

A number that has exactly two factors: one and itself

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4
Q

LCM

A

Lowest Common Multiple

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5
Q

HCF

A

Highest Common Factor

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6
Q

How do you find the HCF when using a venn diagram?

A

Multiply the middle

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7
Q

How do you find the LCM when using a venn diagram?

A

Multiply everything

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8
Q

Anything to the power of 0 is …

A

1

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9
Q

Interior angle

A

Angle inside the shape

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10
Q

Exterior angle

A

Angle made from extending the side

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11
Q

Regular shape

A

All angles and sides are equal

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12
Q

Sum of interior angles =

A

(n-2) x 180

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13
Q

Sum of exterior angles =

A

360

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14
Q

Interior + exterior =

A

180

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15
Q

Each interior angle of regular shape =

A

((n - 2) x 180)/ n

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16
Q

Quadratics have …

A

Two answers

E.g x = -3 or x = -1

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17
Q

Expression

A

3x + 3y

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18
Q

Equation

A

3x + 4 = 12

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19
Q

Identity

A

3(2x + 3) = 6x + 9

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20
Q

Variable

A

Y

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21
Q

Formula

A

r = 3x + 3y

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22
Q

Write r in terms of a means …

A

Make r the subject
Or
r =

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23
Q

Percent means out of …

A

100

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24
Q

Multiplier

A

The percentage of an amount we want, but as a decimal

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25
Q

If you want to get to the original amount you …

A

Divide by the multiplier

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26
Q

If you want to get to the amount afterwards you …

A

Multiply by the multiplier

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27
Q

True or false? If you increase something by 10%, then decrease that by 10% you would get the same as decreasing by 10% then increasing by 10%.

A

True

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28
Q

Simple interest

A

Interest is calculated from original amount. Same amount added on every time

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29
Q

Compound interest

A

Interest is based on what is in there at that time

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30
Q

Direct proportion

A

As one value increases the other increases by the same rate (doubled/ x 10/ quartered)

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31
Q

Inverse proportion

A

As one value increases by a rate, the other decreases by the same rate (x2 and /2 / /5 and x5 / x8 and /8)

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32
Q

Mean

A

Add them all up and divide by however many there are (can be a decimal, doesn’t have to be in the list)

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33
Q

Mode

A

Most common (can have either no mode, 1 value or 2 values. Must be in list)

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34
Q

Median

A

The middle number when they’re in order (can be a decimal - in middle of two values on list or value on list)

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35
Q

How do you find the place value of the median?

A

(n+1) / 2

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36
Q

In the formula for finding the median, what is n?

A

The number of values in the list

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37
Q

IQR =

A

UQ - LQ

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38
Q

How do you find LQ?

A

(n+1) / 4

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39
Q

How do you find UQ?

A

3((n+1) / 4)

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40
Q

How do you find the mean from a table?

A

Sum of fx / sum of f

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41
Q

How do you find modal class/ mode from a table?

A

The one with the most frequency

42
Q

How do you find median from a table?

A

Sum of frequency + 1 / 2

This gives the place of the value

43
Q

How do you find the estimate of median? (When the table is in classes and answer is a number)

A 
~ find median class and the place of the value 
~ amount of numbers in (to get to the place of the value) / frequency of class
~ then times that by the class width
~ add that onto the lowest value of the class
44
Q

How do you know whether something is terminating or recurring?

A

A terminating fraction is a fraction that’s denominator has only 2 and 5 as prime factors

45
Q

Irrational

A

Cannot be expressed as a fraction: surds, pi, e

46
Q

Rational

A

Can be expressed as a fraction: ant terminating value/ decimal, any recurring decimal

47
Q

In probability with Venn diagrams, for ‘n’ thing, count the section(s) that has …

A

The most amount of ticks (2 if two circles, 3 if three circles e.g)

48
Q

In probability with Venn diagrams, for ‘u’ thing, count the section(s) that has …

A

A tick in (all sections with a tick)

49
Q

Probability can be written as …

A

A fraction, % or decimal

50
Q

Mutually exclusive

A

Cannot happen together

51
Q

Exhaustive

A

All outcomes are covered, probabilities add up to 1

52
Q

Independent events

A

Probability of one does not effect the other

53
Q

Dependent events (conditional probability)

A

The outcome of the first event, effects the probability of the second

54
Q

If the question using tree diagrams asks ‘or’ …

A

Add different outcomes

55
Q

If the question using tree diagrams asks ‘and’ …

A

Multiply along branches

56
Q

How do you calculate percentage profit?

A

(Profit / cost to make) x 100

57
Q

How do you calculate to find the percentage increase or decrease?

A

((Original - now) / original) x 100 ?????

58
Q

What is an arithmetic sequence?

A

Constant difference from one term to the next

Eg. 4, 7, 10, 13 (+3)

59
Q

What is a geometric sequence?

A

The ratio of one number and the next is the same

Eg. 3, 6, 12, 24 (x2)

60
Q

What is a Fibonacci sequence?

A

Uses previous terms to get the next

Eg. 1, 1, 2, 3, 5

61
Q

What is a quadratic sequence?

A

Second difference is constant
Eg. 2, 8, 18, 32, 50
+6 +10 +14 +18
+4 +4 +4

62
Q

With quadratic sequences, what do you do to the second difference?

A

Half it, and then write it out, and minus it from the original. Then find 0th term

63
Q

What kind of line does this give: y = 3x - 2

A

Straight line

64
Q

What kind of line does this give: y = x^2 + 1

A

‘U’ shape

65
Q

What kind of line does this give: y = 2x^3 + 1

A

Curved shape (like sideways S)

66
Q

How do you find gradient?

A

Change in y / change in x
Or
Rise / run

67
Q

If a line is perpendicular to a line with a gradient of -3/5, what is its gradient?

A

5/3 —> negative reciprocal

68
Q

What is the chord of a circle?

A

A line that cuts across the inside (doesn’t cross centre)

69
Q

What is a segment of a circle?

A

The area caused by a chord

70
Q

How do you find arc length?

A

(Angle/360) x (pi x diameter)

71
Q

How do you find sector area?

A

(Angle/360) x (pi x radius^2)

72
Q

Which axis is frequency ALWAYS on?

A

Y-axis

73
Q

What is cumulative frequency?

A

Frequency gets added as it goes along

74
Q

What is completing the square form?

A

(x+p)^2 - q

75
Q

Write x^2 + 10x + 3 in completing the square form

A

(x + 5)^2 - 22

76
Q

Write 2x^2 + 12x - 2 in completing the square form

A

2(x+3)^2 - 20

77
Q

What is the quadratic formula?

A

x = (-b +/- [root b^2 - 4ac]) / 2a

78
Q

In a quadratic equation, which numbers are the roots?

A

The two answers (x = … or x = …)

79
Q

What happens is you multiply or divide by a negative with an inequality?

A

The sign flips

80
Q

What is the Sine Rule?

A

a/SinA = b/SinB = c/SinC

81
Q

What is the Cosine Rule?

A

a^2 = b^2 + c^2 - 2bcCosA

82
Q

What is the ambiguous case?

A

Finding obtuse + acute versions in the triangle (subtract from 180)

83
Q

What is the other way to find area of a triangle?

A

Area = 1/2 abSinC

84
Q

What are the numbers (from thumb down) that you can use on your fingers for exact trigonometry values?

A

Above 0 - 30 - 45 - 60 - 90 Below

85
Q

What is the rule for Sin in exact trigonometry values?

A

Root amount of numbers above / 2

86
Q

What is the rule for Cos in exact trigonometry values?

A

Root amount of numbers below / 2

87
Q

What is the rule for Tan in exact trigonometry values?

A

Root amount of numbers above / root amount of numbers below

88
Q

What is Sin30?

A

1/2

89
Q

What is Cos90?

A

0

90
Q

What is Tan60?

A

Root 3

91
Q

How do you find density?

A

Density = mass / volume

92
Q

Volume of cone:

A

1/3 x pi x r^2 x h

93
Q

Surface area of cone (curved side):

A

Pi x r x l
(l = curved side)
(Add area of circle for whole surface area)

94
Q

Volume of sphere:

A

4/3 x pi x r^3

95
Q

Surface area of sphere:

A

4 x pi x r^2

96
Q

Volume of square-based pyramid:

A

1/3 x lwh
l = base length
w = base width
h = pyramid height

97
Q

Volume of triangular based pyramid:

A

1/3 x area of base x height

98
Q

When finding a turning point from (x+p)^2 + q, what’s the rule?

A

Opposite sign of inside one, same sign of outside one

-p,q

99
Q

If vectors can be written as multiples of each other, what does this mean?

A

They are parallel

100
Q

Start next ones at:

A

Rounding, estimating and using bounds : 6/7/20

A Level / GCSE Maths (4 decks)

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