Summer Session, Worksheet for Lesson 29
For the following formulas: S is future value, P is present value, r is the annual interest
rate, k is the number of compounding periods in a year, t is time in years, A is the amount
of money, and R is the amount o
MA 15200
Practice Questions for the Final Exam
1)
Simplify: 2 x 3 y + 2[3 x (2 y + 5 x)]
A. 2 x 7 y
B. 18 x 7 y C. 30 x 2 12 xy + 2 x 3 y
D. 2 x 5 y
E. None of these
2)
07/10
Which number is irrational?
A.
3)
2
3
B. 3.4848.
1
4
B.
(
x5
)
1
2
1
2
2
5
C.
MA 15200 Exam 3 Memo, Summer 2012
1. Exam 3 is during the regular class time on Wednesday, July 25th in MATH 175 (notice the
same location as exam 2, not the regular classroom). You will be given an assigned seat in this
lecture hall before the exam and a
Summer Lesson 28
MA 15200, Appendix I Sections 5.5 and 5.6
You are familiar with the simple interest formula, I = prt . However, in many accounts
the interest is left in the account and earns interest also. We say the account earns
compound interest.
For
Summer MA 15200 Lesson 27, Sections 3.1 and Appexdix H
If a parabola opens downward, the vertex is the highest point of the graph. The ycoordinate of that vertex is the largest value in the range of the function. That ycoordinate value is called the maxim
Summer Lesson 26
MA 152, Section 3.1
I
Quadratic Functions
A quadratic function of the form y = ax 2 + bx + c , where a, b, and c are real numbers
(general form) has the shape of a parabola when graphed. The parabola will open
upward if the value of a is
Summer Lesson 25
MA 152, Appendix G, Section 2.8
Many application problems can be solved by using a system of equations. Usually the
addition method or the substitution method is used to solve the problem.
STEPS:
1. Define two variables for the problem.
2
Summer MA 15200
Lesson 24, Section 5.1
A linear equation with two variables has infinite solutions (many ordered pairs, example
2 x 3 y = 6 ) However, if a second equation is also considered, and we want to know
what ordered pairs they may have in common,
Summer MA 15200
Lesson 23, Section 4.4
An exponential equation is an equation with a variable in one of its exponents.
A logarithmic equation is an equation with one or more logarithmic expressions that
contain a variable.
Solving an exponential equations
Summer MA 15200 Lesson 22
Section 4.3
This lesson is on the properties of logarithms. Properties of logarithms model the
properties of exponents.
I
Product Rule
Product Rule of Exponents: bmbn bmn
Notice: When the bases were the same, the exponents were a
Summer MA 15200 Lesson 21
Section 4.2 and Applied Problems
Remember the following information about inverse functions.
1. In order for a function to have an inverse, it must be one-to-one and pass a
horizontal line test.
2. The inverse function can be fou
Summer MA 15200 Lesson 20
Section 2.7 (part 2), Section 4.1
Definition of the Inverse of a Function:
Let f and g be two functions such that f ( g ( x) = x for every x in the domain of g and
g ( f ( x) = x for every x in the domain of f.
The function g is
Summer MA 15200 Lesson 17
Parts of Sections 2.3 and 2.4
Equations of Lines can be written several ways. In the last lesson, the slope-intercept
form was discussed, y mx b .
I
Point-Slope Form of the Equation of a Line
Begin with the slope formula and drop
Lesson 38 MA 15200, Appendix I Section 5.5
You are familiar with the simple interest formula, I prt and the accumulated amount
formula (where interest in only determined at the end) A = P + Prt. However, in many
accounts, the interest is added into the ac
Worksheet Lesson Section 3.1 Find the following for each quadratic equation. (a) vertex (b) direction of opening (c) equation for axis of symmetry (d) y-intercept (e) x-intercepts, if possible (f) maximum or minimum value and where it occurs 1) 2) 3) 4) y
MA 15200
Lesson 40, Appendix I, Section 5.6
When an individual borrows money from a bank, he or she signs a promissory note, a contract that promises to repay the money loaned. In a previous lesson, we discussed a formula that could be used to repay a loa
Lesson 39 Appendix I Section 5.6 (part 1)
Any of you who are familiar with financial plans or retirement investments know about annuities. An annuity is a plan involving payments made at regular intervals. An ordinary annuity is one in which the payments
Lesson 38 MA 15200, Appendix I Section 5.5
You are familiar with the simple interest formula, I = prt . However, in many accounts the interest is left in the account and earns interest also. We say the account earns compound interest. For example: Suppose
MA 15200
Lesson 37, Sections 3.1 and Appexdix H
If a parabola opens downward, the vertex is the highest point of the graph. The ycoordinate of that vertex is the largest value in the range of the function. That ycoordinate value is called the maximum of t
Lesson 36 MA 152, Section 3.1
I Quadratic Functions A quadratic function of the form y = f ( x) = ax 2 + bx + c , where a, b, and c are real numbers (general form) has the shape of a parabola when graphed. The parabola will open upward if the value of a i
Formula Sheet for the Final Exam 1. Circle: ( x h) 2 + ( y k )2 = r 2 2. Parabola (Quadratic function): y = f ( x) = a ( x h) + k f ( x) = ax 2 + bx + c 3. Distance formula: d = ( x2 x1 )2 + ( y2 y1 )2
2
b b2 h = , k = f (h) or k = c 2a 4a
4. Quadratic fo
Formulas for Applied Problems with Exponential or Logarithmic Formulas
or A = A0 2 where A is the final Radioactive Decay Formula: A = A0 2 amount, A0 is the initial amount present at time 0, t is the time, and h is the half-life of the material.
Populati
Answers to Applications of Exponential and Logarithmic Functions Worksheet 1) 2) 3) 4)
5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)
6.1 grams 829.5 grams a) a)
a) a) a) a)
42,000
b)
3642.9 thousand or 3,642,900
b) 84,562 b) 87.7 years 0.
Answers to Worksheet for Section 3.1
1) a ) V (0, 1) b) opens up c) x = 0 d ) 1 e) 1, 1 f ) minimum value is 1 when x = 0 2) a ) V (3, 12) b) opens up c ) x = 3 d) 3 e) f ) minimum is 12 when x = 3 3) a ) V (1.5, 24.5) b) opens down c) x = 1.5 d ) 20 e) 5
Applications of Exponential and Logarithmic Functions
1)
Tritium has a half-life of 12.4 years. If a sample contains 100 grams, how many grams (rounded to the nearest tenth of a gram) will be remaining in 50 years? The half-life of cobolt-56 is 78.76 days
MA 15200 or MA 15200X Supplemental Worksheet, Lesson 38 Formulas that may be used (found on the course formula sheet): For the following formulas: S is future value, P is present value, r is the annual interest rate, k is the number of compounding periods
MA 15200
I
Lesson 22
Sections 2.3 and 2.4
Slope of a Line
A measure of the steepness of a line is called the slope of the line. Slope compares a
vertical change (called the rise) to the horizontal change (called the run) when moving
from one point to anot
MA 15200
Lesson 20
Section 2.1
A relation is any set of ordered pairs. The set of all first components of the ordered pairs
is called the domain. The set of all second components is called the range.
Relations can be represented by tables, sets, equations
Summer MA 15200 Lesson 5
I
Section P.4
Polynomials
A Monomial or Term is a number or the product of a number and one or more variables
with whole-number exponents. The number factor is called a Coefficient of the term.
The Degree of the monomial (or term)