Quantitative Reasoning formulas

currently missing central angles, inscribed angles, and exterior angles. remember "less than = less thAND" and "greater than = greatOR"

area for a circle

πr²

circumference

2πr=πd

sector area (of a circle)

πr²(theta/360)

arc length (of a circle)

2πr(theta/360)

equation for graph of circle

(x-h)²+(y-k)²=r² where h,k is circle center

Area for right angle triangle

½ bh

area for equilateral triangle

sqrt(3)/4 * s²

area for rectangle

lw

area for square

s²

surface area for rectangular prism

2(lw+lh+hw)

volume for rectangular prism

lwh

surface area for cylinder

2πrh+2πr²

volume for cylinder

πr²h

surface area for sphere

4πr²

volume for sphere

4/3πr²

arithmetic sequence

a(n)=a(1)+(n-1)d

sum of arithmetic sequence

s(n)=n*(a1+an)/2

finding x-coordinate of parabolic vertex x =

-b/2a

how to determine if parabola points up or down for y=ax²+bx+c

a>0 parabola points up, a<0 down

distance formula (on coordinate plane) d=

sqrt((x2-x1)²+(y2-y1)²)

midpoint formula (xm,ym)

(x1+x2)/2, (y1+y2)/2

work

rate x time

rate

work/time

two people working together

T=tAxtB/(tA+tB)

distance

speed x time

average speed

total distance/total time

concentration as percent

c=amount of solute/amount of solution

CtotVtot=

C1V1+C2V2

shortcut when C2>Ctot>C1

V2/V1=(Ctot-C1)/(C2-Ctot)

Simple interest

A=P(1+rt)

Compound interest

A=P(1+r/n)^nt

Book value depreciation

BV=P(1-r)^t

Interest

Final-initial

1 yard = how many feet

3

1 mi = how many feet

5280

1 in = how many centimeters

2.54

1 mile = how many kilometers

1.6

1 pound = how many ounces (oz)

16

1 cm³ = how many millileters (mL)

1

1 pint = how many cups

2

1 quart = how many pints

2

1 gallon = how many quarts

4

1 gallon = how many Liters

3.8

44 ft/sec = how many mi/hr

30

1 yard = how many meters

0.91

if 100 yards = 9100 centimeters, 100 yards³ (cubic yards) = how many cm³ (cubic centimeters

(9100)³

7 × 8=?

56

6 × 7 = ?

42

6 × 8 =?

48

2! = ?

2

3! = ?

6

4! = ?

24

0! = ?

1

permutation formula nPr = ?

n!/(n-r)!

combination formula nCr = ?

n!/r!(n-r)!

difference between nPr and nCr (NOT formulas)

the order of picking things matters for permutations but not for combinations