If questions have an H then they are only Higher tier Flashcards
Define rotational symmetry
How often an object will fit into itself when rotated
Correct name for
a Z angle
an F angle
a C angle
Alternate
Corresponding
Supplementary
Bearings must always be measured from _______ and always measured in which direction
North and clockwise
A coloured in dot represents which inequality signs?
An empty dot represents which inequality signs?
≥, ≤
<, >
Explain how you multiply decimals
Ignore the decimal points, do the calculation, count how many decimal places were in the question and put this many in your answer.
Explain how you divide decimals
Write as a fraction, multiply numerator and denominator by 10 until no decimals in the question and then carry out calculation.
To estimate you need to round all the numbers to __________
1 significant figure
‘Express as a product of it’s primes’ wants you to do what?
A factor tree
To work out highest common factor create a venn diagram and then multiply which numbers together?
The numbers in the middle
To work out lowest common multiple create a venn diagram and then multiply which numbers together?
All the numbers in the venn diagram
How do you know if something is an
Expression
Equation
identity
It doesn’t have an =
Can solve it
One side of the = is the same as the others
If substituting into 3x² which order should you do the operations?
Square first, then multiply by 3
Factorise means _____________________
Put into brackets
Explain how you add and subtract fractions
Make the denominators the same
Explain how you multiply fractions
Multiply the numerators and multiply the denominators
Explain how you divide fractions
Leave the first fraction the same, change to a multiply and ‘flip’ the second (KFC)
To find a fraction of an amount __________________
Divide by the denominator and multiply by the numerator
To solve an equation with an unknown on both sides start by looking for ________________
The smallest (x)
To find the midpoint between two points ____________
Add the x coordinates and half, then add the y coordinates and half
If asked to plot a graph you need to
_________________
Draw a table of values
To find the gradient from a line on a graph
____________________
Draw a triangle, do height divided by base
The equation of a straight line is y = __________
y = mx + c
What do you know about the gradient of parallel lines?
Equal
What do you know about perpendicular gradients?
Negative reciprocal of each other (change the sign and ‘flip’)
H - Cumulative frequency is a _________________
Running total of values
H - How do you find interquartile range?
Upper quartile –
Lower quartile
H - For a histogram you need to work out frequency density – how?
Frequency density = Frequency ÷ Class Width
H - If you have a histogram so you know class width and frequency density, how do you calculate frequency?
Frequency =
Frequency density x Class width
How do you work out the 10th term of a sequence?
Substitute n = 10 into the rule given
Explain how you work out n’th term rule for a linear sequence
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
What is a geometric sequence?
Where you multiply or divide the term in front to get the next term
e.g. 2, 4, 8, 16, 32, 64, …
How do you convert a fraction to a percentage without a calculator?
Make your denominator 100
How do you calculate percentage change given a starting value and end value?
% change = 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆/𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍x100
What decimals would you multiply by to calculate
23%
15%
3%?
0.23
0.15
0.03
What decimals would you multiply by to increase by
25%
8%
2.5%?
1.25
1.08
1.025
What decimals would you multiply by to decrease by
7%
5%
15%?
0.93
0.95
0.85
Define
Faces
Vertices
Edges
The surfaces of a shape
Corners
Lines that make up the shape
Area of a rectangle = ________________________
Area of a rectangle =
Base x Height
Area of a triangle = ______________________
Area of a triangle =
Base x Height divided by 2
Area of a parallelogram = _____________________
Area of a parallelogram =
Base x Perpendicular height
Area of a trapezium = _____________________
Use a and b for parallel sides and h for height
Area of a trapezium =
(𝒂+𝒃)/𝟐x h
Area of a circle = _______________________
Area of a circle =
∏r²
Circumference of a circle = _______________________
Circumference of a circle =
∏d
Surface area of a cylinder = ________________________
Surface area of a cylinder =
2∏r² + 2∏rh
What is the triangle involving Speed, distance and time?
D is at the top
How do you calculate average speed?
Total distance divided byTotal time
For a speed time graph how do you calculate distance travelled?
Area under the graph
H - For a speed time graph how do you calculate acceleration?
Gradient so
Change in speed divided by Change in time
‘Rate of change’ means find the _______________________
Gradient
Angles
In a triangle add up to …?
On a straight line add up to …?
Around a point add up to …?
Opposite each other are …?
180°
180°
360°
Equal
To find what the angles in any polygon add up to ________________________
Subtract two from the number of sides and multiply by 180°
An interior and it’s exterior add to what?
180°
The exterior angles, no matter how many sides the shape has, always add to what?
360°
What would be the lower bound (minimum) and upper bound (maximum) of 45 if it has been rounded to the nearest whole number?
44.5 and 45.5
When multiplying what do you do with indices / powers?
add
When dividing what do you do with indices / powers?
subtract
When you have a power to a bracket what do you do with powers?
multiply
H - What does a power of a half want you to do?
Square root
H - What does a power of a third want you to do?
Cube root
H - What does a negative power want you to do?
Find the reciprocal / ‘flip’
H - Any number to the power of 0 is what?
1
H - Explain how you find the median from a cumulative frequency graph?
Go half way down your graph, draw a line along until you reach the graph and then down
H - Explain how you find the lower and upper quartiles from a cumulative frequency graph?
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
H - What does rationalise the denominator mean?
No surd in the denominator
What does relative frequency mean?
Probability using results of an experiment
How do you calculate how many times you expect something to happen given the probability and how many times you will do the experiment?
Expected probability =
Number of times x probability
Probabilities add up to what?
1
The word ‘and’ in probability means do what?
Multiply
The word ‘or’ in probability means do what?
Add
In standard form the base number has to be between what?
1 and 10
Explain how you add and subtract numbers in standard form
Turn into ordinary numbers, add them and convert the answer back into standard form
Explain how you multiply and divide numbers in standard form
Multiply / divide big numbers and add / subtract indices on the power of 10
How many millimetres are in a centimetre?
10
How many centimetres are in a metre?
100
How many metres are in a kilometre?
1000
How many grams are in a kilogram?
1000
What information do you need to give when describing a reflection?
Line of reflection e.g.
y = 2
What information do you need to give when describing a rotation?
Centre of rotation, how many degrees, direction (clockwise, anticlockwise)
What information do you need to give when describing a translation?
A vector e.g.
(¦)
What information do you need to give when describing an enlargement?
Scale factor and centre of enlargement
How do you find the centre of enlargement given two shapes?
Join corresponding corners together and where lines intersect is the centre of enlargement
What does the word congruent mean?
Same shape and same size
What rules can you use to prove congruency?
SSS, SAS, ASA, RHS
What does it mean if two shapes are similar?
All of their corresponding lengths have the same scale factor
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?
Length scale factor squared
Length scale factor cubed
How do you know if a question is a reverse percentage question?
You know the new amount and want to work backwards to find the old
Define
Mean
Median
Mode
range
Add the numbers up and divide by how many
The middle once in order
The most common
Biggest - smallest
To find the modal class from a frequency table look for ________________
The highest frequency
To estimate the mean from a grouped frequency table you need to add two extra columns called what?
Midpoint and
Midpoint x Frequency (Fx)
H - What do the lower and upper quartiles mean in relation to a list or table of data?
Quarter of the way through the data and three quarters of the way through
What do you do along the branches of a probability tree?
Multiply
What do you do down the side of a probability tree?
Add
What does it mean if two events are independent?
The outcome of one does not effect the outcome of the other
How do you calculate the volume of a prism?
Area of the cross section (the front) multiplied by the length
Give a method you can use to multiply brackets
Grid, smiley face, FOIL
x² + 5x + 6
If you were factorising this the two numbers would have to add to ____ and multiply to give ____?
5, 6
x² - 9
is an example of what?
The difference of two squares
How do you know if a scatter graph has
Positive correlation
Negative correlation?
Points slope up
Points slope down
What makes using a line of best fit on a scatter graph unreliable?
No data around that point
H - How do you show there is a solution between 1 and 2?
Substitute 1 and 2 into the equation and show one answer is positive and the other negative
H - Before you can solve a quadratic equation it needs to be equal to what?
0
H - What is the quadratic formula?
x = (−𝒃±√(𝒃^𝟐−𝟒𝒂𝒄))/𝟐𝒂
To solve two equations simultaneously using a graph look at where they what?
Meet / intersect
If y is directly proportional to x what is the equation you can write down?
y = kx
If y is inversely proportional to x what is the equation you can write down?
y = 𝒌/𝒙
Explain how you solve an inequality
Solve like a normal equation but make sure put inequality sign in your answer
What is Pythagoras’ theorem?
c² = a² + b²
If you are using Pythagoras to work out a shorter side which equations should you use?
a² = c² - b²
b² = c² - a²
How do you know when to use Pythagoras?
Right angled triangle, you know two lengths and are working out the third
What is the phrase to help you remember trigonometry?
SOHCAHTOA
How do you know to use trigonometry rather than Pythagoras?
Right angled triangle, working with angles as well as lengths
If you are using trigonometry to work out a missing length how do you know which rule to use?
Look at the side you know and the side you want
If you are using trigonometry to work out a missing angle how do you know which rule to use?
Look at the two sides you know
What does a quadratic graph look like?
A U or n shape
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?
300 x 1.05 to the power of 4
What is simple interest?
Whatever interest you get in the first year you will get the same every year
What is a plan view?
From above
When solving simultaneous equations what is the first thing to try and do?
Make the ‘x’s’ the same (or whatever the first letter is)
H - How do you find a stratified sample?
Sample size divided by total x group
What does the word inverse mean?
Going backwards (reversing)
H - Equation of a circle with centre (0,0)
x^2 + y^2 = radius^2
H - If you have completed the square and got
y = (x – 3)² + 2 then the turning point of the graph is what?
(3,2)
H - What is the formula for working out the area of a triangle where you don’t know base and perpendicular height?
𝟏/𝟐 𝒂𝒃𝒔𝒊𝒏𝑪
H - The angle at the centre of the circle is _________ the angle at the circumference
Half
H - The diameter makes a ____________ with the circumference
Right angle
H - Opposite angles in a cyclic quadrilateral add to what?
180 degrees
H - A tangent creates a ______________ with the radius
Right angle
H - Explain how you find the gradient of a curved graph at a particular point
Draw a tangent at that point and find the gradient of the line
H - Explain how you simplify an algebraic fraction
Factorise and cancel common brackets
