FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS 10
DATA PAGES
UNIT CONVERSION
Common Imperial
Length
Mass
(Weight)
Imperial and SI
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 yard = 0.9144 m
1 ton = 2000 pounds
1 pound = 16 ounces
2.2 pounds ≈ 1 kg
1 pound ≈ 454 g
1 ounce ≈ 28.35 g
SI
1 km = 1000 m
1 m = 100 cm
1 foot = 30.48 cm
1 inch = 2.54 cm
1 cm = 10 mm
1 t = 1000 kg
1 kg = 1000 g
kilometre = km
metre = m
centimetre = cm
mile = mi
yard = yd
feet = ' or ft
inch = " or in
ton = tn
pound = lb
ounce = oz
Common
Abbreviations
millimetre = mm
tonne (metric ton) = t
gram = g
FORMULAE
(Put your calculator in Degree Mode)
• Right triangles
sin A =
cos A =
tan A =
• The equation of a line:
y = mx + b
Ax + By + C = 0
y − y1 = m ( x − x1 )
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
• The slope of a line:
rise y y2 − y1
m=
=
=
run x x 2 − x1
B
c
a
C
b
Math Tiles Legend
A
Pythagorean Theorem
a2 + b2 = c2
+x2
–x2
+x
–x
distance = speed × time
+1
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2015/16 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
A = lw
or
P = 2 (l + w )
4
Triangle
P = a+b+c
3
Circle
A=
bh
2
C = πd
A = πr 2
or
NOTE: Use the value of π programmed in your calculator
rather than the approximation of 3.14.
Inches
1
2
C = 2πr
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Foundations of Mathematics and Pre-Calculus 10
Data Pages
Surface Area
Volume
20
Geometric Solid
Abase = πr 2
•
h
18
r
19
Atop = πr 2
Cylinder
V = (area of base ) × h
17
Aside = 2πrh
16
SA = 2πr 2 + 2πrh
Sphere
or
•
V=
4 3
πr
3
V=
1
× ( area of base ) × h
3
V=
1
× ( area of base ) × h
3
14
r
15
SA = 4πr 2
13
SA = πd 2
Cone
Abase = πr 2
s
h
10
SA = πr 2 + πrs
11
12
Aside = πrs
7
Abase = b 2
s
SA = wh + wh + lw + lw + lh + lh
Rectangular Prism
V = (area of base ) × h
or
w
l
SA = 2 ( wh + lw + lh )
4
h
6
SA = 2bs + b 2
b
b
1
bs ( for each triangle )
2
5
h
Atriangle =
8
Square-Based Pyramid
9
r
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 π programmed in your calculator rather than the
approximation of 3.14.
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2015/16 School Year
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Foundations of Mathematics and Pre-Calculus 10
Data Pages
ROUGH W ORK S PACE
(No marks will be given for work done on this page.)
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Foundations of Mathematics and Pre-Calculus 10
Data Pages