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GCSE MATHS ST ROBERT'S > If questions have an H then they are only Higher tier > Flashcards

If questions have an H then they are only Higher tier Flashcards

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1
Q

Define rotational symmetry

A

How often an object will fit into itself when rotated

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2
Q

Correct name for
a Z angle
an F angle
a C angle

A

Alternate
Corresponding
Supplementary

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3
Q

Bearings must always be measured from _______ and always measured in which direction

A

North and clockwise

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4
Q

A coloured in dot represents which inequality signs?
An empty dot represents which inequality signs?

A

≥, ≤

<, >

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5
Q

Explain how you multiply decimals

A

Ignore the decimal points, do the calculation, count how many decimal places were in the question and put this many in your answer.

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6
Q

Explain how you divide decimals

A

Write as a fraction, multiply numerator and denominator by 10 until no decimals in the question and then carry out calculation.

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7
Q

To estimate you need to round all the numbers to __________

A

1 significant figure

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8
Q

‘Express as a product of it’s primes’ wants you to do what?

A

A factor tree

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9
Q

To work out highest common factor create a venn diagram and then multiply which numbers together?

A

The numbers in the middle

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10
Q

To work out lowest common multiple create a venn diagram and then multiply which numbers together?

A

All the numbers in the venn diagram

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11
Q

How do you know if something is an
Expression
Equation
identity

A

It doesn’t have an =
Can solve it
One side of the = is the same as the others

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12
Q

If substituting into 3x² which order should you do the operations?

A

Square first, then multiply by 3

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13
Q

Factorise means _____________________

A

Put into brackets

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14
Q

Explain how you add and subtract fractions

A

Make the denominators the same

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15
Q

Explain how you multiply fractions

A

Multiply the numerators and multiply the denominators

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16
Q

Explain how you divide fractions

A

Leave the first fraction the same, change to a multiply and ‘flip’ the second (KFC)

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17
Q

To find a fraction of an amount __________________

A

Divide by the denominator and multiply by the numerator

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18
Q

To solve an equation with an unknown on both sides start by looking for ________________

A

The smallest (x)

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19
Q

To find the midpoint between two points ____________

A

Add the x coordinates and half, then add the y coordinates and half

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20
Q

If asked to plot a graph you need to
_________________

A

Draw a table of values

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21
Q

To find the gradient from a line on a graph
____________________

A

Draw a triangle, do height divided by base

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22
Q

The equation of a straight line is y = __________

A

y = mx + c

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23
Q

What do you know about the gradient of parallel lines?

A

Equal

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24
Q

What do you know about perpendicular gradients?

A

Negative reciprocal of each other (change the sign and ‘flip’)

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25
Q

H - Cumulative frequency is a _________________

A

Running total of values

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26
Q

H - How do you find interquartile range?

A

Upper quartile –
Lower quartile

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27
Q

H - For a histogram you need to work out frequency density – how?

A

Frequency density = Frequency ÷ Class Width

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28
Q

H - If you have a histogram so you know class width and frequency density, how do you calculate frequency?

A

Frequency =
Frequency density x Class width

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29
Q

How do you work out the 10th term of a sequence?

A

Substitute n = 10 into the rule given

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30
Q

Explain how you work out n’th term rule for a linear sequence

A

Look for the pattern, put this number in front of n, decide what you would need to add or subtract to get the first term

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31
Q

What is a geometric sequence?

A

Where you multiply or divide the term in front to get the next term
e.g. 2, 4, 8, 16, 32, 64, …

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32
Q

How do you convert a fraction to a percentage without a calculator?

A

Make your denominator 100

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33
Q

How do you calculate percentage change given a starting value and end value?

A

% change = 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆/𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍x100

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34
Q

What decimals would you multiply by to calculate
23%
15%
3%?

A

0.23
0.15
0.03

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35
Q

What decimals would you multiply by to increase by
25%
8%
2.5%?

A

1.25
1.08
1.025

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36
Q

What decimals would you multiply by to decrease by
7%
5%
15%?

A

0.93
0.95
0.85

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37
Q

Define
Faces
Vertices
Edges

A

The surfaces of a shape
Corners
Lines that make up the shape

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38
Q

Area of a rectangle = ________________________

A

Area of a rectangle =
Base x Height

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39
Q

Area of a triangle = ______________________

A

Area of a triangle =
Base x Height divided by 2

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40
Q

Area of a parallelogram = _____________________

A

Area of a parallelogram =
Base x Perpendicular height

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41
Q

Area of a trapezium = _____________________
Use a and b for parallel sides and h for height

A

Area of a trapezium =

(𝒂+𝒃)/𝟐x h

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42
Q

Area of a circle = _______________________

A

Area of a circle =
∏r²

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43
Q

Circumference of a circle = _______________________

A

Circumference of a circle =
∏d

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44
Q

Surface area of a cylinder = ________________________

A

Surface area of a cylinder =
2∏r² + 2∏rh

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45
Q

What is the triangle involving Speed, distance and time?

A

D is at the top

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46
Q

How do you calculate average speed?

A

Total distance divided byTotal time

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47
Q

For a speed time graph how do you calculate distance travelled?

A

Area under the graph

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48
Q

H - For a speed time graph how do you calculate acceleration?

A

Gradient so
Change in speed divided by Change in time

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49
Q

‘Rate of change’ means find the _______________________

A

Gradient

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50
Q

Angles
In a triangle add up to …?
On a straight line add up to …?
Around a point add up to …?
Opposite each other are …?

A

180°
180°
360°
Equal

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51
Q

To find what the angles in any polygon add up to ________________________

A

Subtract two from the number of sides and multiply by 180°

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52
Q

An interior and it’s exterior add to what?

A

180°

53
Q

The exterior angles, no matter how many sides the shape has, always add to what?

A

360°

54
Q

What would be the lower bound (minimum) and upper bound (maximum) of 45 if it has been rounded to the nearest whole number?

A

44.5 and 45.5

55
Q

When multiplying what do you do with indices / powers?

A

add

56
Q

When dividing what do you do with indices / powers?

A

subtract

57
Q

When you have a power to a bracket what do you do with powers?

A

multiply

58
Q

H - What does a power of a half want you to do?

A

Square root

59
Q

H - What does a power of a third want you to do?

A

Cube root

60
Q

H - What does a negative power want you to do?

A

Find the reciprocal / ‘flip’

61
Q

H - Any number to the power of 0 is what?

A

1

62
Q

H - Explain how you find the median from a cumulative frequency graph?

A

Go half way down your graph, draw a line along until you reach the graph and then down

63
Q

H - Explain how you find the lower and upper quartiles from a cumulative frequency graph?

A

Go a quarter of the way up your graph, draw a line along until you reach the graph and then down, upper quartile the same but three quarters

64
Q

H - What does rationalise the denominator mean?

A

No surd in the denominator

65
Q

What does relative frequency mean?

A

Probability using results of an experiment

66
Q

How do you calculate how many times you expect something to happen given the probability and how many times you will do the experiment?

A

Expected probability =
Number of times x probability

67
Q

Probabilities add up to what?

A

1

68
Q

The word ‘and’ in probability means do what?

A

Multiply

69
Q

The word ‘or’ in probability means do what?

A

Add

70
Q

In standard form the base number has to be between what?

A

1 and 10

71
Q

Explain how you add and subtract numbers in standard form

A

Turn into ordinary numbers, add them and convert the answer back into standard form

72
Q

Explain how you multiply and divide numbers in standard form

A

Multiply / divide big numbers and add / subtract indices on the power of 10

73
Q

How many millimetres are in a centimetre?

A

10

74
Q

How many centimetres are in a metre?

A

100

75
Q

How many metres are in a kilometre?

A

1000

76
Q

How many grams are in a kilogram?

A

1000

77
Q

What information do you need to give when describing a reflection?

A

Line of reflection e.g.
y = 2

78
Q

What information do you need to give when describing a rotation?

A

Centre of rotation, how many degrees, direction (clockwise, anticlockwise)

79
Q

What information do you need to give when describing a translation?

A

A vector e.g.
(¦)

80
Q

What information do you need to give when describing an enlargement?

A

Scale factor and centre of enlargement

81
Q

How do you find the centre of enlargement given two shapes?

A

Join corresponding corners together and where lines intersect is the centre of enlargement

82
Q

What does the word congruent mean?

A

Same shape and same size

83
Q

What rules can you use to prove congruency?

A

SSS, SAS, ASA, RHS

84
Q

What does it mean if two shapes are similar?

A

All of their corresponding lengths have the same scale factor

85
Q

H - If you know the scale factor of the lengths on two shapes which are similar to each other how do you find the scale factor for the
Area
Volume?

A

Length scale factor squared
Length scale factor cubed

86
Q

How do you know if a question is a reverse percentage question?

A

You know the new amount and want to work backwards to find the old

87
Q

Define
Mean
Median
Mode
range

A

Add the numbers up and divide by how many
The middle once in order
The most common
Biggest - smallest

88
Q

To find the modal class from a frequency table look for ________________

A

The highest frequency

89
Q

To estimate the mean from a grouped frequency table you need to add two extra columns called what?

A

Midpoint and
Midpoint x Frequency (Fx)

90
Q

H - What do the lower and upper quartiles mean in relation to a list or table of data?

A

Quarter of the way through the data and three quarters of the way through

91
Q

What do you do along the branches of a probability tree?

A

Multiply

92
Q

What do you do down the side of a probability tree?

A

Add

93
Q

What does it mean if two events are independent?

A

The outcome of one does not effect the outcome of the other

94
Q

How do you calculate the volume of a prism?

A

Area of the cross section (the front) multiplied by the length

95
Q

Give a method you can use to multiply brackets

A

Grid, smiley face, FOIL

96
Q

x² + 5x + 6
If you were factorising this the two numbers would have to add to ____ and multiply to give ____?

A

5, 6

97
Q

x² - 9
is an example of what?

A

The difference of two squares

98
Q

How do you know if a scatter graph has
Positive correlation
Negative correlation?

A

Points slope up
Points slope down

99
Q

What makes using a line of best fit on a scatter graph unreliable?

A

No data around that point

100
Q

H - How do you show there is a solution between 1 and 2?

A

Substitute 1 and 2 into the equation and show one answer is positive and the other negative

101
Q

H - Before you can solve a quadratic equation it needs to be equal to what?

A

0

102
Q

H - What is the quadratic formula?

A

x = (−𝒃±√(𝒃^𝟐−𝟒𝒂𝒄))/𝟐𝒂

103
Q

To solve two equations simultaneously using a graph look at where they what?

A

Meet / intersect

104
Q

If y is directly proportional to x what is the equation you can write down?

A

y = kx

105
Q

If y is inversely proportional to x what is the equation you can write down?

A

y = 𝒌/𝒙

106
Q

Explain how you solve an inequality

A

Solve like a normal equation but make sure put inequality sign in your answer

107
Q

What is Pythagoras’ theorem?

A

c² = a² + b²

108
Q

If you are using Pythagoras to work out a shorter side which equations should you use?

A

a² = c² - b²
b² = c² - a²

109
Q

How do you know when to use Pythagoras?

A

Right angled triangle, you know two lengths and are working out the third

110
Q

What is the phrase to help you remember trigonometry?

A

SOHCAHTOA

111
Q

How do you know to use trigonometry rather than Pythagoras?

A

Right angled triangle, working with angles as well as lengths

112
Q

If you are using trigonometry to work out a missing length how do you know which rule to use?

A

Look at the side you know and the side you want

113
Q

If you are using trigonometry to work out a missing angle how do you know which rule to use?

A

Look at the two sides you know

114
Q

What does a quadratic graph look like?

A

A U or n shape

115
Q

If I invest £300 at a rate of 5% compound interest for 4 years, what calculation would I do to find how much money I have?

A

300 x 1.05 to the power of 4

116
Q

What is simple interest?

A

Whatever interest you get in the first year you will get the same every year

117
Q

What is a plan view?

A

From above

118
Q

When solving simultaneous equations what is the first thing to try and do?

A

Make the ‘x’s’ the same (or whatever the first letter is)

119
Q

H - How do you find a stratified sample?

A

Sample size divided by total x group

120
Q

What does the word inverse mean?

A

Going backwards (reversing)

121
Q

H - Equation of a circle with centre (0,0)

A

x^2 + y^2 = radius^2

122
Q

H - If you have completed the square and got
y = (x – 3)² + 2 then the turning point of the graph is what?

A

(3,2)

123
Q

H - What is the formula for working out the area of a triangle where you don’t know base and perpendicular height?

A

𝟏/𝟐 𝒂𝒃𝒔𝒊𝒏𝑪

124
Q

H - The angle at the centre of the circle is _________ the angle at the circumference

A

Half

125
Q

H - The diameter makes a ____________ with the circumference

A

Right angle

126
Q

H - Opposite angles in a cyclic quadrilateral add to what?

A

180 degrees

127
Q

H - A tangent creates a ______________ with the radius

A

Right angle

128
Q

H - Explain how you find the gradient of a curved graph at a particular point

A

Draw a tangent at that point and find the gradient of the line

129
Q

H - Explain how you simplify an algebraic fraction

A

Factorise and cancel common brackets

GCSE MATHS ST ROBERT'S (1 decks)

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