quick maths

to find a term in a normal sequence (re arrange), to find a term in a quadratic factorise and take positive term

cubic graph

exponetional (y=ab^x)

reciprocal (fraction graph)

finding mean with table

find the mp

do mp x freq

do mp x freq totoal

mp x freq total divided by tot freq

pie charts

add freq to find tot

divide by 360

get the number from above and times each one by individual freq

thats the degrees your going to draw your pie chart at

notation

A n B (a and b), intersection

A U B (A or b), union

A’ (not a) (including intersections)

cumalative freq

6 cum freq, 6

22 28

36 64

median, get tot, divide by 2

iq, find quater of tot, ¾ of tot, substract for iqr

harder box plots

median 1+n/ 2

lq n+1/4

¾ of n+1

histograms

class width

frequ density - frequency / class width , rearrange this equation in the exam PLEASE (FOR LQ UQ MEDIAN IQR ETC)

mean- draw a freq table, class widths and freq

mp x freq

tot of mp x freq/ tot freq

vt graphs

distance travelled - area under the graph: trapezium, triangles, rectangles

accelration - gradient change in y over change in x

transormation of graphs

plus outside (up) plus inside (left)

minus outside (down) minus inside (right)

-f, flip the Y vals and draw

-x, flip x vals and draw

for -f , relfect then translate

for -x inside, translate then reflect

quadratic inequalities

< < normal, if < is pointing to 0

>, always points to FIRST negative number, then opposite for second (poitive incld)

if u times or divide with a negative number (FLIP)

TO SOLVE inequalities with 3 sections, whatever done in middle, do to all of them

bearings

bearings always has 3 figures (090)

bearings are always measured clockwise

bearings are always measured FROM north

from (ur starting point

error intervals

1 dp of 6.4, 6.34 <(line underneath it)n< 6.45 (go down one whole dp and go up 1dp, half it!!)

2DP

8.42 is 8.415 and 8.425 (same notation as above) (go down 2 whole dp and up 2dp, HALF)

17000, 16500 and 17500 (nearest 2sf, go down a whole sf , go up a whole sf, half)

8350 , 8325, 8375 (nearest 50, go up 50 go down 50 half)

120, (nearest integer), 119.5, 121.5 (go down one integer, go up one integer, find half)

Truncation up to 1dp (chop the number), so 8.8 is 8.8 including and up to 8.9

truncation to 2 dp (9.41 to 9.42

loci

angle bisector (cut angle in half), draw arc, extend and draw second arc, connect 2 points forming a criss cross in arc, draw line

perpendicular biesctor, measure the line, get compass (draw one line at one end - past the center) and do the same on the other sides, dont change compass length, draw line in the middle

perpendicular bisector with point, draw cirlcearound point, remove everything else except the 2 lines on either side of p intersecting the line , and do what u did above ^

perpendicluar bisector with point not on line, take point draw half a semicircle (intersecting the line), only nide the 2 points on the line which intersect , then draw arcs from each side of the smaller line youve created like the semicricles, drop a perpinduclar

estimation

round to 1 sf

indices u will forget

fraction, sqrt

x^A/B becomes (x^1/b)^a

if fraction with 2/3, and theres letters, u divide by 3 and times by 2 (not sqrt and then power)

x u add

divide u subtract

together separted by a bracket multiply

to the minus, becomes 1/x to positive power

transformation

translation by clumn vector please x

number by f, enlargement by sf 4 parallel to the y axis

inside, enlargement by ¼ paralell to x axis

draw quadratic

need y intercept (constant at the end is Y ntercept)

complete square

take eq (x-4)² - 11 = 0 (make equal to 0 no need to factorise)

solve for x is 4 plus or minus root 11

equation of line of symmetry , x is 4

proof

even number 2n

odd n

consecutive, 2n-2, 2n+2, 2n + 4 (USE NEGATIVE SO THEY CANCEL OUT)

then factorise , therfore multiple of 3 write it

vector

total

= mean times freq

cylinder

pie r squared h

pyramid

1/3 base area x h