END OF TERM TEST Flashcards
What is mode?
The one that occurs most often
What us the range?
The highest value-lowest value
What is the median?
The value in the exact middle after putting numbers in order
What is the mean?
Add all the values/how many values
What would be the median if u had an even amount of numbers?
Find the midpoint of the 2 numbers (add the numbers/2)
What is the equation for total?
Total=mean x frequency
What is the equation for mean?
Mean=total/frequency
What is the fx column?
The frequency column x the X column (other column)
How to work out range in FT?
Look in the first column (X).
Highest value-lowest value
How to work out the mode in FT?
Look in the first column (X). It id the value with the highest frequency
How to work out median in FT?
Mp=sum of f+1/2
Find the mp then count down the f column. Remember the answer is in the X column.
How to work out mean in FT?
Mean=sum of FX column / sum of F column
If it is class wdith then find the midpoint and multiply midpoint with frequency to get fx column. Find sum of fx and sum of f. Do sum of fx/ sum of f to get mean
What to do when you have a class width instead of X column?
Modal class (class width answer)
Range (biggest number-smallest number- dont take away all the class width just one number)
Median class (class width answer)
ARE THE SAME
MEAN-
work out midpoint. Middle number of class width 0<h<_10
Midpoint-5
Work out FX (FREQUENCY X MIDPOINT)
SUM OF FX/SUM OF F
What to do if u have to find x value in f or fx and u are given the mean
M=sum of fx/sum of x
Sum if f X mean
This = sum of fx
Solve for x
Recurring decimals into fractions
Lex x= 0.88888
X10
Let 10x= 8.8888
10x-x=9x
8.888-0.888=8
9x=8
/9
X=8 over 9
Index laws
BASES STAY THE SAME
if its a x u add
If its a / u takeaway
If theyre in brackets u times
ANYTHING TO POWER OF 0 IS 1
1 TO THE POWER OF ANYTHING IS 1
NEGATIVE POWERS IS RECIPROCAL
FRACTION POWER ROOT BY DENOMINATOR POWER BY NUMERATOR
Pythagoras theorem
USE WHEN GIVEN 2 SIDES INORDER TO WORK OUT 3RD
RIGHT ANGLE TRIANGLE
LONG SIDE- S S A SR a^2+b^2=c^2
SHORT SIDE- S S D SR. c^2-b^2=a^2
Quadratic nth term
Find first and then second differences
Second difference-2a
First difference-3a+b
First term-a+b+c
an^2 + bn + c
HCF AND LCM
Draw prime factor tree in order to find the 2 numbers as a product of their primes
Draw a venn diagram
Start in the overlap ans weite any common numbers in it
Write remaining numbers on each side
HCF-TIMES EVERY NUMBER IN OVERLAP
LCM-TIMES EVERY NUMBER IN WHOLE BENN DIAGRAM
Itteration
Xn+1= next answer
Xo-1st number u substitute/starting point
Step1 - input ur Xo num inti calc press EXE then press ON
step2- type ur expression into ur calc but replace Xn with ANS
step3- press EXE to find x1 x2 x3
Solving inequalities
solve like regualr equation then replace w crocodile signs
Have to solve till u get x on its own- do inverse
NUMBER LINE
draw circle on number before x and cirlce on number after x
IF EQUAL TO THEN COLOUR IN OTHERWISE LEAVE BLANK
if only 1 number with x then draw circle on that number if equal to then colour
And draw arrow in direction depending on if number is less than or more than x
EXPANDING
Use the grid method for both double and triple brackets
Remeber to times not add and simplify
FACTORISE
X^2 -6x +5=0
3 TERMS 2 BRACKETS
(X-5) (x-1)=0
X= 5 or X=1
TIMES TO LAST NUMBER
IGNORE THE MINUS SIGNS IF ANY
UR ANSWER WOULD BE OPPOOSITE SIGN TO WHSTS IN BRSCKET
2 TERMS = 1 BRACKET (EXCEPT DOTS)
3 TERME = 2 BRACEKETS
2 brackets- add to the number infront of x
Times to the mumber at the end
1 bracket common HCF
DOTS-square root of each number 2 brackets 1 plus 1 minus
Reverse percentage
ORIGNAL ALWYAS EWUAL TO 100%
Find 10% FURST TO WORK OUT 100%
PERCENTAGE INCREASE x1.number
PERCENTAGE INCREASE X0. 100/1000-NUNBER
Compound interest
Final = oringial value x (1+ interest rate /annum as a decimal) ^ number of years
IF RHE WUESTION ASKS FOR A INTEREST RATE AS PERCENTAGE REMEBRR TO GIVE AS PERCENTAGE
Simplifying algebraic fractions
Factorise both the top and bottom in either double bracket or single bracket
You should have one bracket which is the same on both the top and the bottom. They should cancel each other out, leaving you with your answer.
Eg.3x^2+11x-4.
X^2 +3x-4
Fibonacci sequence
The two terms add to get rhe next one
In order to work out avlue of the letter add all sequences and divide by rhe coeffiecient
Turn into simultaneous ewuation by timsing to get same a value to cancel out
Scatter graphs first
Correlation- positive negative no
Cirlce off point (annomaly)
Line if best fit - line foloows pattern starting from first point to last point
Use line of best fut to work out estimate
Error intervals
If number begins with eg 8.3 then
8.3<_ y <8.4
Say ur nunber is 3.7
Ur nunbers before and after will be between 3.6-3.7 and 3.7-3.8
So 3.65 <_ x <3.75
Frequency polygons
Work our midpoint of class width
Y axis is frequency and x axis is number data
Plot the midpoint (x) against frequency (y) for whole table
Join the coordinates (NOT FROM 0,0) BUT FROM FIRST POINT TILL LAST POINT WITH LINES TO CREATE A SHAPE DONT JOIN FIRST AND LAST POINTS
Coordinate geometry -length if line
Y=mx+c
Midpoint
To find length- use pythagoras
Turn into right angle eith hupotenuse beinf x. See how far u gone along x axis by finding difference of 2 points
See how far along the y acis u gone by finding difference of 2 points
Use them to do pythagoras
Can leave answer as square root
Coordinate geometry-gradient of line
Repsent graduent as m=
So how ever much we go up when we go 1 across
Draw small triangles go one across and see how much up u go to reach the line can be a half or if negative correlation then - number
Couldn’t geometry-perpendicular and parrallel
Perpendicular meet a right angle-opposite gradient
Parrallel lines- same gradient
Opposite sign fraction into whole number or number into fraction 1/ denominator number
Coordinate geometry-equation of line
Y=mx+c
M is gradient
C is y intercept where the y acis is crossed
Leave x and y as x and y
Given two coordinates
M=y2-y1/x2-x1 should get 1 number as answer after simplify
Thats gradient
Substitute coordinate 1 into the equation to find c (y intercept)
(2,5)
Y=3x+c
5=3x2+c
5=6+c
C=-1
Equation- y=3x-1
IF ANDWER (GRADIENT) IS FRACTION
THEN WRITE IT INTO EQUATION Y=mx+c
Substitute y and x for coordinates
Times every term by rhe denominattor of fraction
Then solve to get c on its own and thats ur y gradient
Then write into ewution y=mx+ c with x snd y ad x and y
