Key Maths Flashcards
What’s an equivalent fraction?
Fractions that look different but are equal to each other
How do you make an equivalent fraction
You times/divide the numerator and denominator by the same number
What’s an integer
A whole number
How do you add fractions?
Get common denominator then add numerators, then convert back to mixed. Subtracting is the same
How do you work out a fraction of an amount?
Divide by the denominator then times by the numerator
‘4/7 of 81’ what does the of mean?
4/7 x 81
What’s the rule for angles on a straight line?
Add up to 180*
What’s the rule for angles around a point?
Add up to 360*
What’s the rule for vertically opposite angles?
They’re equal
What’s the rule for angles in a triangle?
Add up to 180*
What’s an isosceles triangle?
Has two equal sides (lengths) and two equal base angles
What’s a quadrilateral?
Shape with 4 sides
What’s the rule for angles in a quadrilateral?
Add up to 360*
What’s the rule for alternative angles? What do these angles look like?
Are equal
Look for the S shape. As long as arms of S are parallel, angles in the S are equal
What’s the rule for corresponding angles? What do these angles look like?
Are equal
Look for the F shape, if arms of F are parallel then angles in the arm of F are equal
What’s the rule for co interior angles? What do these angles look like?
Add up to 180*
Look for C shape, if arms of c are parallel angles in the C add up to 180*
What does it mean for a shape to be Regular?
All sides are the same shape and all angles are the same size
What’s a quick way to work out how many triangles are in a regular shape?
Number of sides - 2
What’s the equation for the sum of the interior angles of any polygon?
(Number of sides - 2) x 180*
What’s a polygon?
A shape with at least three straight sides and angles
What do an exterior angle + an interior angle add up to?
180*
What do the exterior angles of a polygon add up to?
360*
What do a tangent and radius meet to make?
90*
Tangents from an extended point to a circle are what?
Equal in length
whats the circle theorem for when there’s an angle in the centre and the other three angles are touching the circumference of the circle?
Angle at centre is twice the angle of circumference
When does the circle Theorem ‘Angle at centre is twice the angle of circumference ‘ apply?
when there’s an angle in the centre and the other three angles are touching the circumference of the circle
What’s the circle theorem when all points of a ‘bow tie’ shape are touching the circumference?
Angles in the same segment are equal
What’s the circle theorem when one length of triangle is going through centre of circle, all vertices are touching circumference
The angle in a semicircle is always 90*
What’s the circle theorem for a cyclic quadrilateral
Opposite angles in a Cyclic quadrilateral add up to 180*
When is a quadrilateral cyclic?
All points of quadrilateral must be touching the circumference of a circle
What are the 2 rules for bearings?
Bearings are always measured clockwise from North, must always have 3 digits
How do you work out the HCF from a Venn diagram?
Multiply numbers in the middle
How do you work out the LCM using a Venn diagram?
Multiply all numbers in diagram together
A^m x a^n = ?
A^m x a^n = a ^m+n
A^m / a^n = ?
A^m / a^n = a ^m-n
(A^m)^n = ?
(A^m)^n = a^mxn
A^0 = ?
A^0 = 1
A^1/m = ?
A^1/m = m(square root of a)
A ^ n/m = ?
A^n/m = m(square root of a^n)
A^-n = ?
A^-n = 1/(a^n)
What does it mean when the question asks you to ‘evaluate’?
Work out
When dividing decimals using bus stop, which numbers need to be integers?
The number inside the busstop
When multiplying numbers in standard form what do you do?
Times the first integers, add the indices. Give answer in standard form
What are terms separated by?
Plus and minus signs
What are like terms?
Terms with the same letter
How do you expand triple brackets?
Expand first 2 brackets, then simplify answer, then expand with last bracket
How do you do simple factorising?
Look for HCF, rewrite but take HCF outside brackets
When do u use smiley face method to factorise?
When quadratic has number in front of x^2
What is the difference of two squares rule?
A^2-b^2 = (a-b)(a+b)
What’s a surd?
A square root of an integer that doesn’t give you an integer answer, eg square root of 5
What’s the surd law?
Square root of ab = square root of a square root of b
What does rationalising the denominator mean?
To get rid of the surd on the denominator
What’s the first significant figure of a number?
The first non zero figure reading from the left
How do you estimate?
Round each number to 1sf. Then work out the new calculation
How do you convert from a percentage to a decimal?
Divide by 100
How do you convert from a percentage to a fraction?
Write it over 100
How do you convert from a decimal to a percentage?
Times by 100
How do you convert from a decimal to a fraction
Multiply by 100 and write over 100
How do you convert from a fraction to a decimal?
Divide denominator by numerator OR try writing it over 100
How do you convert from a fraction to a percentage
Write over 100 OR change to decimal and x 100
What’s equation for speed?
Speed = distance / time
What’s equation for density?
Density = mass / volume
What is equation for pressure? What’s it usually measured in?
Pressure = force / area
N/m^2 or N/cm^2
1 m^2 = ? Cm^2
1m^2 = 100^2 cm^2 = 10000 cm^2
1 m^3 = ? Cm^3
1m^3 = 100^3 cm^3 = 1,000,000 cm^3
What’s an expression?
Has no equal sign
How do you solve fractional equations?
Make a common denominator, times by it, expand brackets, solve
What do you do to solve a quadratic equation that equals 0
Factorise. Has 2 answers (usually opposite of numbers made when factorising)
How do you solve a quadratic?
Make it equal 0
When factorising a quadratic,which number do the numbers in brackets want to add to make?
The one with an unknown
What do you use to solve simultaneous equations?
Substitution
What is the equation for a straight line?
Y = mx + c
C = y intercept, where it crosses y axis M = the gradient
What’s the rule for the gradient of parallel lines?
Parallel lines have the same gradient
What’s the rule for the gradient of perpendicular lines?
If you know the gradient of a line, the gradient of the line perpendicular to it will be the negative reciprocal of the first lines gradient
What are perpendicular lines?
Lines which cross each other at right angles
What’s the equation for the gradient of a line?
Change in y / change in x
What’s the equation for the midpoint of two coordinates
( [x1 + x2]/2 , [y1+y2]/2)
What’s the equation of Pythagoras theorem?
What are the three rules for when Pythagoras theorem?
a^2 + b^2 = c^2
Only works on right angled triangles
Hypotenuse = c, it is opposite the right angle
a and b can be any line
What are the five rules for trigonometry?
Only work o night angled triangles
Hypotenuse is the length opposite right angle
Theta is an angle in the triangle which isn’t the right angle
Opposite is the length opposite theta
Adjacent is the side adjacent to theta, but not the hypotenuse
What are the three trigonometry equations?
Sin theta = opposite / hypotenuse
Cos theta = adjacent / hypotenuse
Tan theta = opposite / hypotenuse
How do you enter 10xsin60=x into the calculator
Sin (60) x 10
When you have cos theta = number/number, how do you get the theta on its own?
Cos -1, giving theta = cos^-1 (6/12)
What’s the equation for area of a triangle?
(Base x perpendicular height) / 2 = area
What’s the equation for area of a parallelogram?
Base x perpendicular height = area
What’s a parallelogram?
4 sided shape with 2 pairs of parallel sides
What is the value of sin theta 90*
1
What is the value of cos theta 0*
1
What is the value of cos theta 30*
(Square root of 3)/2
What is the value of cos theta 45*
1/(square root of 2) / (square root of 2)/2
What is the value of sin 0*
0
What is the value of sin 30*
1/2
What is the value of sin 45*
1/square root of 2
What is the value of sin 60*
(Square root of 3)/2
What is the value of sin 90*
1
What is the value of cos 0*
1
What is the value of cos 30*
(Square root of 3)/2
What is the value of cos 45*
1/(square root of 2)
What is the value of cos 60*
1/2
What is the value of cos 90*
0
What is the value of tan 0*
0
What is the value of tan 30*
1/(square root of 3)
What is the value of tan 45*
1
What is the value of tan 60*
Square room of 3
What is the value of tan 90*
Undefined
What’s a rhombus?
A parallelogram where all the sides are the same length
What’s a sector (in a circle)?
A section that goes from the centre to the circumference
What’s a origin (in a circle)?
Centre of the circle
What’s an arc (in a circle)?
A part of the circumference
What’s a segment (in a circle)?
A section of the circle not from the centre
What’s a tangent (in a circle)?
Outside circle, Touches circumference at one point
What’s a chord (in a circle)?
Line that goes across the circle but doesn’t go through the middle of the circle
What’s the diameter?
The distance from one edge of the circle to the other, passing through the centre
What’s the radius?
The distance from the centre of the circle to the edge
What’s the equation for circumference?
2 x pi x radius
What’s a revolution?
1 full turn or a circle
What’s equation for area of a circle
r^2 x pi
What’s a trapezium?
A 4 sides shape with 1 pair of parallel lines
What’s the equation for area of a trapezium
(a+b)/2 x height
A and b are the parallel lines
How do you work out the fraction of an amount
Divide amount by denominator and times answer by numerator
What’s an outlier?
Something different to the pattern/trend. An anomaly
What must probability do?
Add up to 1 whole
What do sample space diagrams allow you to do?
List our every probability using something that looks like a multiplication square
How do you use a probability tree diagram to work out probability?
Multiply along the branches and add together if you get multiple answers. Answer will be a fraction
What is relative frequency?
The same as probability
What is a set? (In set notation)
A collection of objects or numbers
What are the objects in a set called? (In set notation)
Members or elements of the set
Notation A = {1,2,3,4} means?
Set A with elements 1,2,3,4 and 5
The set notation 3 € A means? (€ should only have one horizontal line)
Means 3 is an element/member of set A
What does (in a vent diagram) the set notation AnB mean?
Where they both exist at the same time.
What does (in a vent diagram) the set notation AuB mean?
Where A or B exists
What does (in a vent diagram) the set notation A’ mean?
Everything outside of A
What does (in a vent diagram) the set notation (A) mean?
Everything that’s A
What does (in a vent diagram) the set notation (A’) mean?
Everything not A
What does (in a vent diagram) the set notation AuB’ mean
Everything that is A or outside of B
What does (in a vent diagram) the set notation (AuB)’ mean
Everything outside of A or B
What does (in a vent diagram) the set notation (B) mean
Everything that is B
What does (in a vent diagram) the set notation (AnB) mean
Everything that is A and B at the same time
What does (in a vent diagram) the set notation AnB’ mean
Everything that is A and not B
What does (in a vent diagram) the set notation A’nB’ mean
Everything that is not A and B
What does (in a vent diagram) the set notation A’nB mean?
Everything that is B and not A
When you’re putting set notation into a diagram, what is the rule?
Each number can only appear once in the diagram
What’s the difference between frequency trees and probability trees?
Probability trees show chance outcomes of different information, frequency trees just display data
What’s equation for volume of a prism?
Volume of a prism = cross sectional area x length
How do you work out surface area?
Find area of all faces, add together
What’s equation for density?
Density (g/cm^3 or kg/m^3) = mass / volume
If asked for the capacity of something, what do you work out?
It’s volume
What’s the equation for volume of any pyramid?
Volume = 1/3 x area of base x height
How do you do a percentage increase using a multiplier?
Original value x (100% + eg 35% = 135% > x 1,35) = ans
(For decrease by it’d be 100% - 35%
How do you work out simple interest over a given period of time?
Starting amount x percentage increase (6% every year = x 0.06) = ans
Ans x number of years = ans 2
Starting amount + ans 2 = final ans
What’s the equation for percentage profit?
Percentage profit = (profit / original amount) x 100
What’s the equation for percentage loss?
Percentage loss = (loss / original amount) x 100
What are the four types of transformation?
Rotation
Reflection
Enlargement
Translation
What are translations? If the translation is
( 3 ) [with the brackets going down over the -2 as well]
-2
What does it mean?
Translations use a vector to describe how the shape has moved.
It means three right, two down. (All the vertexes move like this)
How do you do reflection? How would you give an answer?
Measure from the ‘mirror’ at a right angle, even if it’s diagonal to the mirror line
Answer eg ‘reflection in the line x = -0.5’
What are the three requirements/things to give in rotation?
Centre of enlargement
Direction of turn is clockwise or anti-clockwise
Amount of turn/angle of rotation
What happens in enlargement with a positive scale factor? What are the two things you have to give in enlargement ?
The lengths get bigger, however angles stay the same size
Scale factor and centre
How do you do enlargement with a negative scale factor?
Times distance between point and centre of enlargement by the negative scale factor
What’s the equation for acceleration?
a= (v-u)/t
On velocity time graphs what does area under graph tell u?
Total distance travelled
On a velocity time graph what does the gradient (line) tell you?
The acceleration
How do you work out gradient of a curved graph?
Use a tangent to work out an estimation. Tangent touch graph at time you want to estimate acceleration at.
How do you simplify a ratio?
Change to same unit and Find a common factor and divide both by it
What’s the general formula for two things in direct proportion
(Y direct proportion symbol x)
y= k x
What do we write for inverse proportion
y (direct proportion sign) 1/x
So y = k/x (k is constant of proportionality)
‘Rearrange the formula to find E in terms of s’
What do you do?
Make E the subject
What’s the mode/modal value of a set of data?
Value that occurs most often
What’s the median of a set of data?
The middle value when in order
If there are 2 in the middle, add them up and divide by 2
How do you work out the mean of a set of data?
Add up the values and divide by how many there are
What does the range represent?
The spread of data
Largest - smallest = range
How do you work out the interquartile range?
Upper quartile - lowest quartile
Middle left of median - middle right of median
How do you work out the modal value from a table?
The one with the highest frequency
If there’s a score and a frequency in a table, how do you work out the range?
Highest score - lowest score
If there’s a score and a frequency in a table, how do you work out the mean score?
Times score and frequency together. Add all these answers up. Add up all frequencies. Mean is (total of frequency x score) / total frequency
What’s the equation for median position from tables?
Median position = (total frequency + 1) / 2
its 2 because you’re finding the middle
How do you work out the interquartile range of a set of data?
Make sure the data is in smallest to largest order
LQ position = (how many there are +1) / 4 [invisible x 1] = position
UQ position = (how many there are + 1) /4 x 3 [3 because 3/4] = position
IQR = number at UQ position - number at LQ position = IQR
How do you do stem and leaf diagrams?
Leaf always 1 digit in side, steam and leaf diagrams must be in order
The first number of it goes in stem, the second number goes in its section in leaf
Stem and leaf diagrams must be in order
What’s an arithmetic/ linear sequence?
In 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
When’s a sequence quadratic?
If it takes two differences to get a repeated difference
How do you write the start of the nth term rule for a quadratic sequence?
The start of the nth term rule is half of the second repeated difference
What’s a Fibonacci sequence?
You add previous two numbers to create the next one
What are Geometric sequences?
Multiply the terms by the same amount each time, this amount is known as the common ratio
In inequalities on a number line, if there’s a solid circle under the number, what does that mean for the value?
x can equal it
In inequalities on a number line, if there’s a circle with under the number, what does that mean for the value?
X can’t equal the number
When does multiplying or dividing both sides of an inequality by a negative work? (It usually doesn’t)
When the inequality sign is switched round when multiplying or dividing both sides by a negative
If you’re solving an inequality graphically, and the grid needs to satisfy the inequality which is
Below
If you’re solving an inequality graphically, and the grid needs to satisfy the inequality which is >, will the region be above or below a horizontal line?
Above
How do you simplify fractions?
Divide the numerator and denominator by the same value
When adding/subtracting fractions, what does the denominator do if common?
Stays the same
When are shapes similar?
The same but different in size. All angles are the same. The lengths are all multiplied or divided by the same amount
How do you get from the length scale factor to volume scale factor?
Vsf = (lsf)^3
How do you draw the gradient on a cumulative frequency graph?
Draw a smooth curve which goes through every point
What features do a box plot need to have?
A minimum mark, lower quartile, median, upper quartile and maximum mark
When you’re asked to compare data, what two things should you comparE?
An average together with the range or inter-quartile range (usually median with range)
What’s the equation for frequency density? (Variable width histograms)
Frequency density = frequency / class width
On a variable width histogram, what does the area of a rectangle tell you?
The frequency
How would you draw a frequency polygon given height and frequency?
Midpoint value of heights give x coordinates, frequency is y coordinates. Plot and join dots with straight lines between them
What does the quadratic formula do?
Used to work out x without factorising. Only works when quadratic = 0
What are the three steps to sketching quadratics?
Solve to find where it crosses the x axis
Complete square to find the turning point (vertex)
Sketch it
How do you write consecutive integers using algebra?
n
n+1
n+2
How do you write an even number using algebra?
2n
How do you write an odd number using algebra?
2n + 1
How do you write consecutive even numbers using algebra?
2n
2n+2
2n+4
2n+6
How do you write consecutive odd numbers using algebra?
2n+1
2n+3
2n+5
How do you write a multiple of 3 using algebra?
3n
How do you write a multiple of 8 using algebra?
8n
What does a box plot HAVE to have? How are they drawn?
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