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Grade 10 Math Formula Sheet

Linear Systems y=mx +b

Substitution

Step1: isolate a variable with the coefficient of 1

Step2: substitute isolated variable into 2nd

equation

With ractions

Step1: !et rid of fractions by multiplyin!

denominators by all

Step2: isolate variable with coefficient 1

Step": substitution isolated variable into 2nd

equation

#limination 1 $ if you don%t already have one

variable with the same coefficient with opposite

si!ns in both equations

Step1: identify which variable to be eliminated

Step2: need to multiply one or both equations beinte!ers so that both equations would have one

variable with the same coefficient with opposite

si!ns

#limination 2Step1: if there is a positive and ne!ative variable&

line them up and add columns

Step2: substitute the found variable into otherequation' chec( LS = )S

*nalytic eometry

,idpoint-. ,/x& y0 = /x1 + x2& y1 +y20

2 2

Slope-. rise -. y2- y1

run x2- x1

Len!th -. *= /x2- x10 + /y2-y10

,edian

Step1: find midpoint of line opposin! the

identified vertex

Step2: connect them& find len!th of median

Step": find slope of the median

Step: find the equation of the line for median

eometric 3roperties

4entroid: the point where all three medians

intersect

ormula-. /x1+ x2 + x"& y1+ y2+ y"0

" "4ircles

4entred at the ori!in )adius-. x + y

4entred at a random point )adius-.x + y = r

5iameter-. d=2r

6uadratic )elations

Simplest quadratic-. y=x

inite differences- differences found from the y-

values in tables with evenly spaced x-values

irst differences are the same means its linear

Second differences are the same means its

quadratic

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y =a/x-h0 + (

(- vertical translation' vertex%s y value

if (7 -. move up ( units #x: y=/x-80 -9

a- vertical stretch or compression

if 71 -. vertical stretch#x: y="/x+20-8if a is ne!ative-. flips !raph on x-axis#x: y=-2/x-0 /x+0

h- horiontal translation' vertex%s x value

if he!ative exponents

When a non-ero base is raised to a ne!ative

exponent& the result is the reciprocal of the base

raised to the positive of the exponent

#very number with exponent of 7 equals 1

6uadratic #xpressions

5istributive 3roperty /x-?0/x+?0 or /x-@+?0

Step1: multiply the two binomials

Step2: simplify by collectin! terms

/a+b0 = a + 2ab + b or /a-b0 = a $ 2ab + b

x + bx + c -. /x+r0/x+s0

Step1: find 2 inte!ers whose product is c and

whose sum is b

ax +bx +c = 7

Step1: multiply a by c

Step2: brea( up middle term& solve

6uadratic #quations

4ompletin! the square is ma(in! y=ax + bx + c

into y=a/x-h0 +(or find vertex-. -b

2a

6uadratic ormula-.

Ari!onometry of )i!ht Arian!les

4on!ruent-. identical shape and sie

Similar-. identical shape but different sie

Scale actor (-. the factors that relate

correspondin! side len!ths of two similar

trian!les *4 5#

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Aan!ent )atio /only ri!ht an!le trian!les0

Step1: identify what is to be found

Side len!th- cross multiply& to !et the variable

isolated& solve

*n!le- divide opposite side len!th by adBacent or

opposite side len!th& inverse Aan to !et an!leAan=opposite

adBacent

Sine )atio /only ri!ht an!le trian!les0

Step1: identify what is to be found

Side len!th- cross multiply& to !et the variableisolated& solve

*n!le-divide opposite side len!th by hypotenuseside len!th& inverse sine to !et an!le

Sin= opposite

hypotenuse

4osine )atio /only ri!ht an!le trian!les0

Step1: identify what is to be found

Side len!th- cross multiply& to !et the variable

isolated& solve*n!le- divide opposite side len!th by hypotenuse

side len!th& inverse cosine to !et an!le

4os= adBacent

hypotenuse

3roper labels for a trian!le

*4 *

c b

b

4

a

Ari!onometry of *cute *n!les

Sine Law /all trian!les0

When have an an!le& side& an!le /*S*0

* = = 4sin* sin sin4

4osine Law /all trian!les0

Cnly two situations that we use this law:

side& an!le& side /S*S0 or " sides /SSS0

a = b + c $ 2bc 4os*

b = a + c $ 2ac 4os

c = c + b $ 2cb 4os4

3ytha!orean Aheorem c

a + b = c a

b

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,edian

*ltitude

3erpendicular isector

Square

)ectan!le

3arallelo!ram

)hombus

Dite

Arapeoid

)i!ht *n!le Arian!le

Esosceles Arian!le

Scalene Arian!le

#quilateral Arian!le