FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS 10
DATA PAGES
UNIT CONVERSION
Common Imperial
Imperial and SI
1 mile = 1760 yards
1 mile = 5280 feet
Length
1 yard = 3 feet
1 yard = 36 inches
1 foot = 12 inches
Mass
(Weight)
1 ton = 2000 pounds
1 pound = 16 ounces
Common
Abbreviations
mile = mi
yard = yd
feet = ' or ft
SI
1 mile ! 1.609 km
1 km = 1000 m
1 yard = 0.9144 m
1 foot = 30.48 cm
1 m = 100 cm
1 cm = 10 mm
1 inch = 2.54 cm
1 t = 1000 kg
1 kg = 1000 g
2.2 pounds ! 1 kg
1 pound ! 454 g
1 ounce ! 28.35 g
kilometre = km
metre = m
centimetre = cm
millimetre = mm
inch = " or in
ton = tn
tonne (metric ton) = t
gram = g
pound = lb
ounce = oz
FORMULAE
(Put your calculator in Degree Mode)
• Right triangles
sin A =
cos A =
• The equation of a line:
y = mx + b
Ax + By + C = 0
y ! y1 = m ( x ! x1 )
opposite
hypotenuse
adjacent
hypotenuse
• The slope of a line:
rise !y y2 ! y1
m=
=
=
run !x x 2 ! x1
B
c
a
tan A =
opposite
adjacent
Math Tiles Legend
C
b
A
Pythagorean Theorem
a2 + b2 = c2
+x2
–x2
+x
–x
distance = speed × time
+1
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2012/13 School Year
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Foundations of Mathematics and Pre-Calculus 10
Data Pages
GEOMETRIC FORMULAE
7
8
Key Legend
l = length
P = perimeter
w = width
C = circumference
b = base
A = area
h = height
SA = surface area
s = slant height
V = volume
6
r = radius
d = diameter
Geometric Figure
5
Rectangle
Perimeter
Area
P = 2l + 2w
or
A = lw
P = 2 (l + w )
4
Triangle
P = a+b+c
3
Circle
A=
bh
2
C = !d
A = !r 2
or
NOTE: Use the value of ! programmed in your calculator
rather than the approximation of 3.14.
Inches
1
2
C = 2!r
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Foundations of Mathematics and Pre-Calculus 10
Data Pages
Cylinder
Surface Area
20
Geometric Solid
Volume
19
Atop = !r 2
Abase = !r 2
h
18
r
•
V = (area of base ) × h
17
Aside = 2!rh
16
SA = 2!r 2 + 2!rh
Sphere
or
•
V=
4 3
!r
3
V=
1
× ( area of base ) × h
3
V=
1
× ( area of base ) × h
3
14
r
15
SA = 4!r 2
Cone
13
SA = !d 2
Abase = !r 2
s
h
11
12
Aside = !rs
10
SA = !r 2 + !rs
Abase = b 2
s
SA = 2bs + b 2
b
6
b
1
bs ( for each triangle )
2
7
h
Atriangle =
8
Square-Based Pyramid
9
r
Rectangular Prism
or
w
l
V = (area of base ) × h
SA = 2 ( wh + lw + lh )
4
h
5
SA = wh + wh + lw + lw + lh + lh
V = ( area of base ) × h
SA = the sum of the areas
of all the faces
V=
cm
1
SA = the sum of the areas
of all the faces
2
3
General Right Prism
General Right Pyramid
1
× ( area of base ) × h
3
NOTE: Use the value of ! programmed in your calculator rather than the
approximation of 3.14.
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Foundations of Mathematics and Pre-Calculus 10
Data Pages
ROUGH WORK SPACE
(No marks will be given for work done on this page.)
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Foundations of Mathematics and Pre-Calculus 10
Data Pages