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GCSE Maths > Facts And Terms > Flashcards

Facts And Terms Flashcards

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1
Q

Factor

A

A whole 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

Writing a number as product of primes

A

Use prime factor trees to find prime factors. Write them in a single line using multiplication (and powers if we choose.

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7
Q

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

A

Multiply the middle.

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8
Q

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

A

Multiply everything.

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9
Q

Factor decomposition

A

Product of primes

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10
Q

Dividing decimals

A

Use bus stop method when we know the times table. Include the decimal point in the same place and add in extra o’s as needed.

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11
Q

Negative numbers: adding and subtracting
5 - 6 = ?, 5 + -6 = ?
8 - -3= ?, 8 + 3 = ?

A

When there are 2 signs in the middle of the sum the operation changes and the second number becomes positive.
5 - 6 = -1, 5 + -6 = -1
8 - -3= 11, 8 + 3 = 11

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12
Q

Negative numbers: multiplying and dividing

  • 4 x 2 =
  • 3 x 8 =
  • 12 / -2 x -3 =
  • 20 / 5 x -2 =
A

If there is an odd number of negative signs in the sum the answer is negative, if there is an even number the answer is positive.

  • 4 x 2 = 8
  • 3 x 8 = -24
  • 12 / -2 x -3 = -18
  • 20 / 5 x -2 = 8
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13
Q

Anything to the power of 0 is…

A

1.

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14
Q

(Indices) Negative power -

Reciprocal is …

A

Negative power - reciprocal

Reciprocal is 1/number

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15
Q

Rules for indices - multiplying

A

a^m x a^m = a^m+n

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16
Q

Rules for indices - dividing

A

a^m / a^n = a^m-n

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17
Q

Indices (a/b)
A -
B -

A

A - new power

B - root

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18
Q

Rules for indices - brackets

A

(a^m)^n = a^mn

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19
Q

Calculating with standard form: multiplication

(4 x 10^6) x (5.1 x 10^3) =

A

x value + power

(4 x 5.1) x (10^6 x 10^3) = 2.04 x 10^10

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20
Q

Calculating with standard form: addition/subtraction

(4.7 x 10^3) + (2.1 x 10^2) =

A

Convert + or -, convert to standard form

= 4910 = 4.91 x 10

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21
Q

Calculating with standard form: division

3.6 x 10^4) / (9 x 10^6

A

(3.6/9) x (10^4 x 10^6) = 0.4 x 10^-2 = 4 x 10^-3

Divide values, - powers

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22
Q

Calculating with standard form: using brackets

(2 x 10^4)^3 =

A

Do the power to each part

2^3 x (10^4)^3 = 8 x 10^12

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23
Q

Expanding brackets

A

Times inside by outside.

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24
Q

Factorising

A

Means put back into brackets.

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25
Q

Interior angle

A

Angle inside the shape.

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26
Q

Exterior angle

A

Angle made from extending the side.

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27
Q

Regular shape

A

All angles and sides are equal.

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28
Q

Interior + exterior

A

= 180 degrees

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29
Q

Sum of interior

A

180(n-2)

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30
Q

Sure of exterior angles

A

360 degrees, no matter how many sides.

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31
Q

Each interior angle of regular shape =

A

(n - 2) x 180)/ n

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32
Q

Quadratics have…

A

Two answers

E.g. x = 8 or x = -2

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33
Q

Expression

A

3x + 3y

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34
Q

Equation

A

3x + 4 = 12

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35
Q

Identity

A

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

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36
Q

Variable

A

Y

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37
Q

Formula

A

r = 3x + 3y

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38
Q

Rearranging formulae

A

It is just like rearranging an equation. Rather than working to get an answer. We end up with algebra.

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39
Q

Write r terms of a means …

A

Make r the subject or r =

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40
Q

Percent means out of…

A

100

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41
Q

Multiplier

A

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

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42
Q

If you want to get to the original amount you…

A

Divide by the multiplier.

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43
Q

If you want to get to the amount afterwards you …

A

Multiply by the multiplier.

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44
Q

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

A

Yes.

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45
Q

Reverse percentages

A

Find the original amount after an increase or decrease. Get back to how much 100% is.

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46
Q

Percentage increase and decrease

A

Increase - add % to original
Decrease - take % from original
Find % first then + or -.

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47
Q

Simple interest

A

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

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48
Q

Compound interest

A

Interest is based on what is in there at that time.

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49
Q

Direct proportion

A

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

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50
Q

Inverse proportion

A

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

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51
Q

Other phrases for direct proportion

A 
. Directly proportion to
. Is proportional to
. Varies directly
. Y ∝ x
. Y = kx
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52
Q

Other phrases for inverse proportion

A

. Inversely proportional to
. Varies inversely
. Y ∝ 1/x
. Y = k/x

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53
Q

Types of average

A

Mean, mode and median.

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54
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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55
Q

Mode

A

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

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56
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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57
Q

Quartiles:

A

Split data up into quarters.

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58
Q

How do you find the median?

A

(n+1) / 2 or 1/2n + 0.5

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59
Q

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

A

The number of values in the list.

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60
Q

IQR =

A

UQ - LQ

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61
Q

How do you find LQ?

A

(n+1) / 4

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62
Q

How do you find UQ?

A

3((n+1) / 4)

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63
Q

How do you find the mean from a table?

A

Sum of fx / sum of f

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64
Q

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

A

The one with the most frequency.

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65
Q

How do you find median from a table?

A

Sum of frequency + 1 / 2

This gives the place of the value

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66
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.
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67
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.

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68
Q

Irrational

A

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

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69
Q

Rational

A

Can be expressed as a fraction e.g. any terminating value/ decimal, any recurring decimal

70
Q

Probability can be written as…

A

A fraction, % or decimal

71
Q

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

A

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

72
Q

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

A

A tick in (all sections with a tick).

73
Q

Mutually exclusive

A

Cannot happen together.

74
Q

Exhaustive

A

All outcomes are covered, probabilities add up to 1.

75
Q

Probability

A

We use a tree diagram to help find probabilities of combined events. Multiply along branches (and). Add different outcomes if needed (or).

76
Q

Independent events

A

Probability of one does not effect the other.

77
Q

Dependent events (conditional probability)

A

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

78
Q

Ratio

A

Allows us to see values in comparison with each other. It is usually in its simplified form. W can also have decimal inside a ratio if required.

79
Q

How do you calculate percentage profit?

A

(Profit / cost to make) x 100

80
Q

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

A

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

81
Q

Arithmetic sequence

A

Constant difference from one term to the next

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

82
Q

Geometric sequence

A

The ratio of one number and the next is the same

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

83
Q

Fibonacci sequence

A

Uses previous terms to get the next

Eg. 1, 1, 2, 3, 5

84
Q

Quadratic sequence

A

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

85
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.

86
Q

Term to term rule

A

From one term to the next.

87
Q

Nth term

A

Any term in the sequence (10th n =100).

88
Q

Quadratic sequence steps

A

. Find the common difference (2nd difference is equal, divide by 2)
This gives n^2
. Take of the n^2 part
. Find the nth term of whats left

89
Q

Fibonacci sequence

A

Series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … The next number is found by adding up the two numbers before it and so on.

90
Q

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

A

Straight line

91
Q

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

A

‘U’ shape

92
Q

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

A

Curved shape (like sideways S)

93
Q

How do you find gradient?

A

Change in y / change in x or Rise / run

94
Q

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

A

5/3 —> negative reciprocal

95
Q

Midpoint

E.g. (x, y) and (x2, y2)

A

The middle of the line

Mp = (x + x2/2 , y + y2/2)

96
Q

Parallel lines

A

Always have the same gradient. Make sure lines are in the same format before comparing (y=mx+c).

97
Q

Perpendicular lines

A

Their gradients multiply to make -1. Gradients are negative reciprocal of each other.

98
Q

Chord of a circle

A

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

99
Q

Segment of a circle

A

The area caused by a chord.

100
Q

How do you find arc length?

A

(Angle/360) x (pi x diameter)

101
Q

How do you find sector area?

A

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

102
Q

Which axis is frequency always on?

A

Y-axis

103
Q

What is cumulative frequency?

A

Frequency gets added as it goes along.

104
Q

Scatter graph

A

Allows us to compare different variables and shows us if there is any correlation (relationship) between them. Correlation is not the same as relationship.

105
Q

Positive correlation relationship

A

As x increases y also increases.

106
Q

Negative correlation relationship

A

As x increases y decreases.

107
Q

Completing the square form

A

(x+p)^2 - q

108
Q

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

A

First, factorise the x^2 and x term.
2(x^2 + 6x) - 2
Now write the x^2 + 6x part in completing the square form.
X^2 + 6 = (x + 3)^2 - 9
So, 2(x^2 + 6x) - 2 = 2[x + 3)^2 - 9] - 2
= 2 (x + 3)^2 - 18 - 2
= 2(x + 3)^2 - 20

109
Q

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

A

(x + 5)^2 - 22

110
Q

Quadratic formula

A

x = -b + or - √b^2 - 4ac / 2a

111
Q

In a quadratic equation, which numbers are the roots?

A

The two answers (x = … or x = …).

112
Q

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

A

The sign flips.

113
Q

What is the Sine Rule (missing sides)?

A

a/SinA = b/SinB = c/SinC

114
Q

What is the Sine Rule (missing angles)?

A

SinA/a= SinB/b= SinC/c

115
Q

Area of triangle with angle

A

1/2 x a x b x Sin C

116
Q

What is the Cosine Rule (missing sides)?

A

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

117
Q

What is the Cosine Rule (missing angles)?

A

Cos(A) = b^2 + c^2 - a^2 / 2bc

118
Q

Ambiguous case

A

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

119
Q

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

A

0, 30, 45, 60, 90

120
Q

What is the rule for Sin in exact trigonometry values?

A

√amount of numbers above / 2

121
Q

What is the rule for Cos in exact trigonometry values?

A

√amount of numbers below / 2

122
Q

What is the rule for Tan in exact trigonometry values?

A

√amount of numbers above / √amount of numbers below

123
Q

Sin of 0, 30, 45, 60, 90

A

0, 1/2, √2/2, √3/2, 1

124
Q

Cos of 0, 30, 45, 60, 90

A

1, √3/2, √2/2, 1/2, 0

125
Q

Tan of 0, 30, 45, 60, 90

A

0, 1/√3, 1, √3, not possible

126
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

127
Q

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

A

They are parallel.

128
Q

Density formula

A

Density = mass / volume

129
Q

Similar shapes

A

Same shape, different size.

130
Q

Congruent

A

Same shape and same size.

131
Q

Linear scale factor

A

Side lengths of large shape / corresponding side length of small shape

132
Q

Volume of square based pyramid.

A

V = 1/3 x ba x h

133
Q

Vector

A

Way of representing movement between two places. We visualise a vector with a straight line, the direction indicated by an arrow. We can use a matrix system to define a vector: x is the movement right, y is the movement up.

134
Q

Estimate

A

Round every value to 1sf.

135
Q

Discrete data

A

Data counted in a very basic sense.
E.g. number of siblings -3, 6, 2 etc.
Pens in a pencil case - 7, 12, 15, etc.
None of these could be made more accurate

136
Q

Continuous data

A

Data that has been measured.
E.g. temperature, length of a pencil, mass of a loaf of bread
Depending on how accurate we want to be, these could be more specific.

137
Q

How to get bounds.

A

Add or subtract half the accuracy.
E.g. 1cm / 2 = 0.5
7 - 0.5
7 + 0.5

138
Q

Sector

A

Area between two radi and an arc.

139
Q

Angle on circumference inside semi circle is…

A

90 degrees

140
Q

Angle at the centre from a chord is…

A

Double the angle at the circumference.

141
Q

Angles in a segment from a chord are…

A

The same

142
Q

Cyclic quadrilateral

A

Opposite angles add to 180 degrees

143
Q

Tangent meets radius at a…

A

Right angle

144
Q

Alternate segment theorem:

A

Alternate angles are equal

145
Q

Where two tangents to a circle meet…

A

The lengths are equal.

146
Q

When a number has been rounded, we use error intervals to…

A

Determine what it could have been before.

147
Q

When to use sohcahtoa

A

Right angle triangle

148
Q

When to use sine rule

A

. 2 angles known + 1 length known + 1 unknown length.

. 2 lengths known + 1 angle known + 1 unknown angle.

149
Q

When to use cosine rule:

A

. 3 lengths known + 1 unknown angle

. 2 lengths known + 1 angle known + 1 unknown length

150
Q

n

A

And

151
Q

U

A

Or

152
Q

A’

A

Not in set

153
Q

When are tree diagrams used in probability?

A

Used when the probabilities are not equally likely or if the probabilities change part way through.

154
Q

When are probability space diagrams used?

A

Used when probabilities of event A and event B are all equally likely (e.g. roll a dice and flip a coin)

155
Q

Conversion graphs

A

These allow us to convert between currencies/measurements. They are limited to working with the scales we have on them.

156
Q

Asymptote

A

A point/line that the graph approaches but does not meet.

157
Q

Circle graph

A

X^2 + y^2 = r^2
No asymptotes
Google picture to check if your right

158
Q

Linear graph

A

y = mx + c

Google picture to check if your right

159
Q

Quadratic graph

A

x^2 is the biggest power

Google picture to check if your right

160
Q

Reciprocal graph

A

y = k/x
Asymptote = y=x-axis/y-axis
Google picture to check if your right

161
Q

Cubic graph

A

x^3 is biggest

Google picture to check if your right

162
Q

Exponential graph

A

y = k^x
Asymptote = y=0/x-axis
Google picture to check if your right

163
Q

Speed formula

A

Speed = distance / time

Average speed = total distance / total time

164
Q

Completing the square steps

A
  1. Identify perfect square

2. Adjust it so expressions are equal

165
Q

What does gradient line tell you?

A

In general, the gradient line tells you the rate of change of the y variable in relation to the rate of change of the x-variable.

166
Q

What does area under the graph tell you?

A

In general, the area under the graph tells you the product of the two units on the two axis.

167
Q

Gradient of curved line

A

. Draw a tangent that hits the line only at the point you are trying to find.
Work out the gradient of the tangent (rise/run)

168
Q

What does y = tan x look like on a graph?

A

Google picture to check if your right.

169
Q

What does y = sin x look like on a graph?

A

Google picture to check if your right.

170
Q

What does y = cos x look like on a graph?

A

Google picture to check if your right.

GCSE Maths (3 decks)

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