MATH 1030-008: Final Exam Review Sheet, Fall 2007
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Venn Diagrams
• Know how to draw 2 and 3 set Venn diagrams.
• Be able to take information about set relationships from Venn diagrams.
2
Unit Conversions
• Be able to convert various measurements to different units given a conversion factor.
• Know what the prefixes kilo (103 ), centi (10−2 ), and milli (10−3 )mean and know how to
use them to convert metric units.
3
Percentages
•
New Value − Reference Value
= Relative Difference.
Reference Value
•
Reference Value × (100 ± P )% = New Value.
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Chapter 4
• Know the General Compound Interest Formula:
nY
AP R
A=P 1+
n
Note:
daily compounding means n = 365
monthly compounding means n = 12
quarterly compounding means n = 4
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• Know the Compound interest formula for continuous compounding:
A = P × e(AP R×Y )
• Use the compound interest formulas for problems that ask how a single deposit of money
accumulates wealth over a period of time.
• Know what the annual percentage yield (APY) is and be able to find it, given an APR
and an amount of money deposited, using:
relative increase =
absolute increase
starting principal
• Know how and when to use the Savings Plan and Loan Payment formulas. The formulas
will be given to you on the exam, but you will need to be able to use them to solve word
problems.
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Chapter 8
• Know the “Rule of 70” and when it is a valid approximation (when the P in P% is less
than 15%) for the Doubling and Half-Life times.
Td ≈
70
P
Th ≈
70
P
• Know the Doubling Time Formula for Exponential growth:
Q = Q0 × 2t/Td
or
new value = initial value × 2t/Td
• Know the Half-Life Formula for Exponential decay:
t/Th
1
Q = Q0 ×
2
or
t/Th
1
new value = initial value ×
2
• Know the two logarithm rules:
log10 (x + y) = log10 (x) + log10 (y)
2
log10 (xy ) = y × log (x)
• Know the Exact Doubling time and Half-life formulas or be able to manipulate the general
exponential formula to get them.
Td =
Th =
6
log (2)
,
log (1 + r)
− log (2)
log (1/2)
=
.
log (1 − r)
log (1 − r)
Linear and Exponential Models
• If given two points, be able to solve for the slope and then the y-intercept (when x=0) in
order to create a linear function for your problem, using:
y = mx + b
m=
y2 − y1
change in y value
=
x2 − x1
change in x value
• Know how to use logarithms to solve for an exponent.
• Be able to find the fractional growth rate r given the doubling time or the half-life time
of a function:
2Q0 = Q0 (1 + r)Td ⇒ 2 = (1 + r)Td ⇒ r = 21/Td − 1
and
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1
1
Q0 = Q0 (1 − r)Th ⇒ = (1 − r)Th ⇒ r = 21/Th − 1
2
2
Geometry
• Know the formulas for the areas and perimeters of 2-D objects, and the formulas for the
surface area and volume of 3-D objects.
2D
Rectangle
Circle
Triangle
3D
Box
Sphere
Cylinder
Area
l×w
πr2
1
b×h
2
Volume
l×w×h
4
πr3
3
πr2 h
3
Perimeter
2l + 2w
2πr or πd
side1 + side2 + side3
Surface Area
2lw + 2wh + 2lh
4πr2
2πr2 + 2πrh
• Know that length scales like the scaling factor, area scales like the square of the scaling
factor, and volume scales like the cube of the scaling factor.
• Be able to create scaled models of each of the above objects if you are given the measurements.
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Problems to Review
• Exam 1: 1, Extra Credit.
• Exam 2: 1, 2 (with monthly and quarterly deposits), 3, 4, 5, 6.
• Quiz 2: 2.
• Quiz 4: 1, 2, 3 (figure out for compounding continuously too), 4.
• Quiz 5: 1, 2.
• Exam 1 Review: 2b, 8.
• Exam 2 Review: 1-4, 6-13, 15, 17, 18.
• Section 2.A, exercises 62-64.
• Section 3.A, exercises 113, 116, 118, 119.
• Section 8.B, exercises 37, 39-42, 55, 56.
• Section 9.B, exercises 35-37, 39, 43, 53.
• Section 9.C, exercises 51, 52.
• Section 10.A, 47-52, 57, 63-77.
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