TMTH 111
MIDTERM FORMULA SHEET
CHAPTER 1: Numerical Computation
Distance = Rate × Time
% change
Amount = Rate × Base (where rate is in decimal form)
new value − original value
Measured Value − Known value
=
× 100 % error
× 100
original value
Known value
% efficiency
=
output
× 100
input
Amount of A
× 100
Total Amount of Mixture
% conc. of A
=
Metric Prefixes.
1012
109
106
103
10
10-1
10-2
10-3
10-6
10-9
10-12
tera
giga
mega
kilo
deca
deci
centi
milli
micro
nano
pico
CHAPTER 6: Geometry
NAME
FORMULA
Circle
Circumference = 2𝜋𝜋 or 𝜋𝜋
2
Square
Rectangle
Parallelogram
Rhombus
Trapezoid
Area = 𝜋𝑟 or
Hero’s
Formula
4
Perimeter = 4s
Area = s 2
Perimeter = 2(l + w)
Area = 𝑙 ⋅ 𝑤
Perimeter = 2(a + b)
Area = 𝑏 ⋅ ℎ
Perimeter = 4s
Area = 𝑠 ⋅ ℎ
Perimeter = a + b + c + d
Area =
Triangle
𝜋𝑑 2
Area =
(𝑎+𝑏)∙ℎ
𝑏∙ℎ
2
2
Area = �𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐) where 𝑠
=
𝑎+𝑏+𝑐
2
Compiled by: Humber College Math Department
Last revision: 06/2015
NAME
Cube
FORMULA
Rectangular
Parallelepiped
Volume = 𝑎 3
Surface Area = 6𝑎 2
Volume = lwh
Any cylinder or prism
Volume = (area of base)⋅(altitude)
Right cylinder or
prism
Sphere
Lateral Area = (perimeter of base) ⋅ (altitude)
(not including bases)
4
Volume = 𝜋𝑟 3
3
Surface area = 4𝜋𝑟2
Surface Area = 2(lw + hw + lh)
Any cone or pyramid
Volume =
Right circular cone or
regular pyramid
Frustum
ℎ
3
●
(area of base)
Lateral area =
ℎ
𝑠
●
2
(perimeter of base)
(A 1 + A 2 + �𝐴1 𝐴2 )
𝑠
Lateral area = ● (sum of base perimeters)
2
𝑠
= ● (𝑃1 + 𝑃2 )
2
Volume =
Frustum
3
●
CHAPTER 7: Right Triangles and Vectors
1 rev = 360° = 2𝜋 radians
sin 𝜃 =
csc 𝜃 =
opp
hyp
1
1 radian = 57.3°
sec 𝜃 =
sin 𝜃
adj
cos 𝜃 =
𝑐 2 = 𝑎2 + 𝑏 2
tan 𝜃 =
hyp
1
cot 𝜃 =
cos 𝜃
opp
adj
1
tan 𝜃
CHAPTER 15: Oblique Triangles and Vectors
Law of Sines:
Law of Cosines:
a
sin A
=
b
sin B
=
c
sin C
𝑎2 = 𝑏 2 + 𝑐 2 − 2𝑏𝑏 ⋅ 𝑐𝑐𝑐 𝐴
or
𝑐 2 = 𝑎2 + 𝑏 2 − 2𝑎𝑎 ⋅ 𝑐𝑐𝑐 𝐶
or
2
2
2
𝑏 = 𝑎 + 𝑐 − 2𝑎𝑎 ⋅ 𝑐𝑐𝑐 𝐵
or
𝑐𝑐𝑐 𝐴 =
𝑐𝑐𝑐 𝐵 =
𝑐𝑐𝑐 𝐶 =
𝑏 2 +𝑐 2 −𝑎2
2𝑏𝑏
𝑎2 +𝑐 2 − 𝑏 2
2𝑎𝑎
𝑎2 + 𝑏 2 −𝑐 2
2𝑎𝑎
Compiled by: Humber College Math Department
Last revision: 06/2015