MATH 10C FORMULA SHEET
Metric & Imperial Conversion Factors
Relationships between
Imperial Units
Approximate Relationships between
Imperial Units and Metric Units
1 mile = 1760 yards
1 mile = 5280 feet
1 yard = 3 feet
1 yard = 36 inches
1 foot = 12 inches
1 mile = 1.609 km
1 km = 0.6214 miles
1 yard = 0.9144 m
1m
= 1.094 yd
1 foot = 0.3048 m = 30.48 cm
1m
= 3.281 ft
1 inch = 2.54 cm
1 cm = 0.3937 in
Relationships
between Metric
Units
1 km = 1000 m
1 m = 100 cm
1 cm =
10 mm
Area, Surface Area and Volume Formulas
Area:
Shape
Rectangle A  lw
Shape
1
Triangle A  bh
2
Circle A  r 2
Volume
Surface Area
Rectangular
prism
V  lwh
SA  2lw  lh  wh
or SA  2lw  2lh  2wh
Right pyramid
1
V  lwh
3
SA 
Cylinder
V  r 2 h
SA  2rh  2r 2
Cone
1
V  r 2 h
3
SA  rs  r 2
Sphere
4
V  r 3 or
3
1
V  d 3
6
1
( slant hgt )( perimeter of base)  (area of base)
2
SA  4r 2 or SA  d 2
Pythagorean Theorem
c2 = a2 + b2
Trigonometric Ratios
sin A 
opposite
hypotenuse
cos A 
adjacent
hypotenuse
tan A 
opposite
adjacent
Exponent Laws
Exponent Law
Product of Powers
Quotient of Powers
xm  xn
 xmn
Rule
xm
 xmn
n
x
( xm ) n  xm  n
( xy)m  xm ym
Power of a Power
Power of a Product
Power of a Quotient



Zero Exponent
Negative Exponent
m
x
xm
  m
y
y
x0  1
xm 
Fractional Exponent
1
xm
m
x n  n xm or
n x 
m
Linear Functions
slope 
rise
run
m
y2  y1
x2  x1
slope-intercept form
y  mx  b
general form
Ax  By  C  0
standard form
Ax  By  C
slope 
y
x
slope-point form
( y  y1 )  m( x  x1 )