PSAT formulas

how to solve linear inequalities in 1 variable

standard form: ax + b < 0

solve by isolating variable

how to solve linear inequalities in 2 variable

standard form: ax + by < 0

• rewrite into y=mx+b

• graph line

• check (0,0) then shade

distributive property

a(b+c)=ab+ac

associative property

grouping doesn't change answer 

commutative property

order does change answer

solving equivalent expressions

combine like terms

solving quadratic equations

• factoring 

  • difference of sqaures

  • difference of cubes

  • grouping

• quadratic formula

you factor when

3 terms

group when

4 terms

solve when

its set as “ =0”

difference of sqaures

a² - b² = (a-b)(a+b)

difference of cubes POSITIVE

(a³ + b³ )(a² - ab + b²)

difference of cubes NEGATIVE

(a³ - b³ )(a² + ab + b²)

quadratic formula standard form

ax² + bx + c = 0

quadratic formula usage

when equation is unfactorable

quadratic formula

x = -b ± √(b² - 4ac) / 2a

turning radicals into normal equations

1. remove the square root by squaring both sides

2. apply squaring

3. rearrange into quadratic standard form

4. set equal to zero if it says solve

5. factor or put into quadratic formula

axis of symmetry formula

-b/2a

how to find vertex

plug in axis symmetry (x) into original equation

roots are

where it crosses the x axis

grwoth formula

y = a x (l+r)^t

a is

initial value

r is

growth / decay rate

t is

time

decay formula

y = a x (l-r)^t

compound interest formula

a = p(1+r/n)^(n/t)

variables explained compound interest formula

p - initial amount

r - growth rate

n - number of times its compounded per YEAR

t - time

r is always a

DECIMAL

how to solve proportions

• use butterfly method

• known over know and unknown over 100

percent to decimal

move decimal 2 to the left

decimal to percent

move decimal 2 to the right

decimal to a fraction

put over 100 or 1000 and simplify

what is 18% of 250?

• convert 18 to a decimal

• multiply 250 by that decimal 

44 is what percent of 80?

• divide 44 by 80

• convert decimals to a percent

percent change formula

new - old / old x 100

interest formula

i = PRT

p - initial rate

r - annual rate

t - years

probability formula

favorable outcomes / total outcomes

conditional probability formula

probability a & b occur / probability b occurs

area of a rectangle

l x w

area of a circle 

 𝜋 x r²

area of a square

s²

area of a parallelogram

b x h

area of a trapezoid

½ ( b₁ + b₂ ) x h

volume of a rectangular prism

l x w x h

volume of a cylinder 

πr²h

volume of a sphere

4/3πr³

volume of a pyramid

1/3(base) x h