Key terms + facts Flashcards
Factor
A number that goes into another number without remainder
Multiple
Any numbers that are in the times table
Prime
A number that has exactly two factors: one and itself
LCM
Lowest Common Multiple
HCF
Highest Common Factor
How do you find the HCF when using a venn diagram?
Multiply the middle
How do you find the LCM when using a venn diagram?
Multiply everything
Anything to the power of 0 is …
1
Interior angle
Angle inside the shape
Exterior angle
Angle made from extending the side
Regular shape
All angles and sides are equal
Sum of interior angles =
(n-2) x 180
Sum of exterior angles =
360
Interior + exterior =
180
Each interior angle of regular shape =
((n - 2) x 180)/ n
Quadratics have …
Two answers
E.g x = -3 or x = -1
Expression
3x + 3y
Equation
3x + 4 = 12
Identity
3(2x + 3) = 6x + 9
Variable
Y
Formula
r = 3x + 3y
Write r in terms of a means …
Make r the subject
Or
r =
Percent means out of …
100
Multiplier
The percentage of an amount we want, but as a decimal
If you want to get to the original amount you …
Divide by the multiplier
If you want to get to the amount afterwards you …
Multiply by the multiplier
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%.
True
Simple interest
Interest is calculated from original amount. Same amount added on every time
Compound interest
Interest is based on what is in there at that time
Direct proportion
As one value increases the other increases by the same rate (doubled/ x 10/ quartered)
Inverse proportion
As one value increases by a rate, the other decreases by the same rate (x2 and /2 / /5 and x5 / x8 and /8)
Mean
Add them all up and divide by however many there are (can be a decimal, doesn’t have to be in the list)
Mode
Most common (can have either no mode, 1 value or 2 values. Must be in list)
Median
The middle number when they’re in order (can be a decimal - in middle of two values on list or value on list)
How do you find the place value of the median?
(n+1) / 2
In the formula for finding the median, what is n?
The number of values in the list
IQR =
UQ - LQ
How do you find LQ?
(n+1) / 4
How do you find UQ?
3((n+1) / 4)
How do you find the mean from a table?
Sum of fx / sum of f
How do you find modal class/ mode from a table?
The one with the most frequency
How do you find median from a table?
Sum of frequency + 1 / 2
This gives the place of the value
How do you find the estimate of median? (When the table is in classes and answer is a number)
~ 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
How do you know whether something is terminating or recurring?
A terminating fraction is a fraction that’s denominator has only 2 and 5 as prime factors
Irrational
Cannot be expressed as a fraction: surds, pi, e
Rational
Can be expressed as a fraction: ant terminating value/ decimal, any recurring decimal
In probability with Venn diagrams, for ‘n’ thing, count the section(s) that has …
The most amount of ticks (2 if two circles, 3 if three circles e.g)
In probability with Venn diagrams, for ‘u’ thing, count the section(s) that has …
A tick in (all sections with a tick)
Probability can be written as …
A fraction, % or decimal
Mutually exclusive
Cannot happen together
Exhaustive
All outcomes are covered, probabilities add up to 1
Independent events
Probability of one does not effect the other
Dependent events (conditional probability)
The outcome of the first event, effects the probability of the second
If the question using tree diagrams asks ‘or’ …
Add different outcomes
If the question using tree diagrams asks ‘and’ …
Multiply along branches
How do you calculate percentage profit?
(Profit / cost to make) x 100
How do you calculate to find the percentage increase or decrease?
((Original - now) / original) x 100 ?????
What is an arithmetic sequence?
Constant difference from one term to the next
Eg. 4, 7, 10, 13 (+3)
What is a geometric sequence?
The ratio of one number and the next is the same
Eg. 3, 6, 12, 24 (x2)
What is a Fibonacci sequence?
Uses previous terms to get the next
Eg. 1, 1, 2, 3, 5
What is a quadratic sequence?
Second difference is constant
Eg. 2, 8, 18, 32, 50
+6 +10 +14 +18
+4 +4 +4
With quadratic sequences, what do you do to the second difference?
Half it, and then write it out, and minus it from the original. Then find 0th term
What kind of line does this give: y = 3x - 2
Straight line
What kind of line does this give: y = x^2 + 1
‘U’ shape
What kind of line does this give: y = 2x^3 + 1
Curved shape (like sideways S)
How do you find gradient?
Change in y / change in x
Or
Rise / run
If a line is perpendicular to a line with a gradient of -3/5, what is its gradient?
5/3 —> negative reciprocal
What is the chord of a circle?
A line that cuts across the inside (doesn’t cross centre)
What is a segment of a circle?
The area caused by a chord
How do you find arc length?
(Angle/360) x (pi x diameter)
How do you find sector area?
(Angle/360) x (pi x radius^2)
Which axis is frequency ALWAYS on?
Y-axis
What is cumulative frequency?
Frequency gets added as it goes along
What is completing the square form?
(x+p)^2 - q
Write x^2 + 10x + 3 in completing the square form
(x + 5)^2 - 22
Write 2x^2 + 12x - 2 in completing the square form
2(x+3)^2 - 20
What is the quadratic formula?
x = (-b +/- [root b^2 - 4ac]) / 2a
In a quadratic equation, which numbers are the roots?
The two answers (x = … or x = …)
What happens is you multiply or divide by a negative with an inequality?
The sign flips
What is the Sine Rule?
a/SinA = b/SinB = c/SinC
What is the Cosine Rule?
a^2 = b^2 + c^2 - 2bcCosA
What is the ambiguous case?
Finding obtuse + acute versions in the triangle (subtract from 180)
What is the other way to find area of a triangle?
Area = 1/2 abSinC
What are the numbers (from thumb down) that you can use on your fingers for exact trigonometry values?
Above 0 - 30 - 45 - 60 - 90 Below
What is the rule for Sin in exact trigonometry values?
Root amount of numbers above / 2
What is the rule for Cos in exact trigonometry values?
Root amount of numbers below / 2
What is the rule for Tan in exact trigonometry values?
Root amount of numbers above / root amount of numbers below
What is Sin30?
1/2
What is Cos90?
0
What is Tan60?
Root 3
How do you find density?
Density = mass / volume
Volume of cone:
1/3 x pi x r^2 x h
Surface area of cone (curved side):
Pi x r x l
(l = curved side)
(Add area of circle for whole surface area)
Volume of sphere:
4/3 x pi x r^3
Surface area of sphere:
4 x pi x r^2
Volume of square-based pyramid:
1/3 x lwh
l = base length
w = base width
h = pyramid height
Volume of triangular based pyramid:
1/3 x area of base x height
When finding a turning point from (x+p)^2 + q, what’s the rule?
Opposite sign of inside one, same sign of outside one
-p,q
If vectors can be written as multiples of each other, what does this mean?
They are parallel
Start next ones at:
Rounding, estimating and using bounds : 6/7/20
