MATH 10C FORMULA SHEET

MATH 10C FORMULA SHEET
Metric & Imperial Conversion Factors
Relationships
between Imperial
Units
1 mile = 1760 yards
1 mile = 5280 feet
1 yard = 3 feet
1 yard = 36 inches
Approximate Relationships between
Imperial Units and Metric Units
1 mile = 1.609 km
1 km = 0.6214 miles
1 yard = 0.9144 m
1 m = 1.094 yd
1 foot = 12 inches 1 foot = 0.3048 m = 30.48 cm
1 m = 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
1
Area: Rectangle A = lw Triangle A = bh Circle
2
2
A = πr
Shape Shape Volume Surface Area
Rectangular
prism
V = lwh SA = 2( lw + lh + wh)
or SA = 2lw + 2lh + 2wh
Square
pyramid
1
V = lwh 3
1
SA = ( slant hgt )( perimeter of base ) + ( area of base )
2
Cylinder
V
= πr
2
h
SA = 2π rh + 2πr
2
Cone
Sphere
Pythagorean Theorem
c 2 = a 2 + b 2
V
V
V
2
1 = π
2
r h
SA = π rs + π r
3
4 r 3
1 π d 6
= π
3
or
SA = 4πr
or
2
=
3
2
SA = πd

Trigonometric Ratios
sin A =
opposite
hypotenuse
cos A =
adjacent
hypotenuse
tan A =
opposite
adjacent
Exponent Laws
Exponent Law
m n m n
Product of Powers x × x = x +
Quotient of Powers
x m n
n
= x
−
x
Power of a Power x ) = x ×
Power of a Product xy)
Power of a Quotient
m
( m n m n
(
m
= xm ym
m
⎛ x ⎞ xm
=
⎜ y ⎟ ym
⎝ ⎠
Zero Exponent x
0
= 1
Negative Exponent m 1
x− =
xm
Fractional Exponent
m
n
x n = xm or
n
x
Rule
( )
m
Linear Functions
y = mx + b
+ By + C = 0
Ax y − y1 = m x − x1
( ) ( )
rise
slope =
run
y − y
m = x − x
2 1
2 1
differencein y ' s ∆y
slope = =
differencein x ' s ∆ x