My Mathematical Equations
By Kathleen Rossi
MAT 222 Intermediate Algebra
Instructor: Mohamed Elseifieen
May 12, 2013

My Mathematical Equations
This paper will show two mathematical problems, the first is “To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?” (Dugopolski, 2013, pp. 437, probem 56). The second will be to complete problem 10 on page 444 of Elementary and Intermediate Algebra. Here all steps in solving the problem will be explained step by step. The first problem is to estimate the size of the bear population located on the Keweenaw Peninsula conservation. In reading over the “Bear Population” method #56 on page 437you will notice we are to assume that the ratio of originally tagged bears to the whole population is equal to the ratio of recaptured bears to the size of the sample. The ratio of the originally tagged bears to the whole population is 2100 The ration of the recaptured tagged bears to the sample size is 50x 2100=50x Since x is on the right-hand side of the equation, we need to switch the sides so it is on the left-hand side. 50x=2100 This is the proportion set up and ready to solve. I will cross multiply setting the extremes equal to the means. 100(50) = 2x Here 100 and 50 are the extreme, while x and 2 are the means. 50002=2x2 Next we must divide each term in the equation by 2. X=50002 Cancel out the common factor

X=2500 The bear population in Keweenaw Peninsula is estimated to be around 2500. For the second problem in this assignment I am asked to solve this equation for y. The first thing I notice is that it is a single fraction (ratio) on both sides of the equal sign so basically it is a proportion which can be solved by cross multiplying the extremes and...

...Mathematics Exam Examples Math Diagnostic Testing Project (MDTP)
revised 8-2010
There are four math exam levels. You'll be asked to choose one level that is at your skills and abilities that you feel will best challenge your math competency. The results will be used for prerequisite clearance and will not be part of your permanent record. Calculators are not needed and will not be allowed during the test.
Level 1 - Pre - Algebra Competency
This exam measures how well you understand basic math principles. Examples include addition, subtraction, multiplication, and division of fractions, signed numbers and decimals, as well as solutions of basic algebraic equations. (50 questions - 45 minutes). Possible placements are Math 251 or 351.
Level 2 - Elementary Algebra Competency
This exam measures how well you understand the material covered in an elementary algebra course. (50 questions - 45 minutes). Possible placements are Math 253, 205, 251 or take lower test.
Integers (1) Jim wrote a check for $318.00. If his balance was then $2126.00, what was his balance before he wrote this check? A) $808 B) $1808 C) $2444 D) 5306 (2) What number multiplied by 6 gives -18 as a result? A) -12 B) -3 C) 3 D) -54 Decimals (3) 7.20 = 2.4 A) 0.03 B) 0.30 C) 3.00 D) 30.0 (4) Which of the following best approximates 1.147 - 114.7 A) -100 B) -10 C)10 D) 100 Fractions (5) The ratio of winning...

...the degree of denominator is called
a) equation b) improper c) proper d) identity
5) A histogram is a set of adjustment
a) Square b) rectangular c)circle d)a,b both
6) The different ways of describing a set
a) 1 b) 2 c) 3 d) 4
7) 3π/4 radians=
a) 1150 b)1350 c)1500 d)300
8) +
a) 2sec2 b) 2cos2 c)sec2 d) cos2
9) The observation that divide a data into four equal parts are called
a) Median b) mode c) mean d) a, b both
10) If A and B are disjoint then AUB is equal to
a) A b) B c) null d) BUA
11) If =the componendo property is
a) = b) = c) d) none of these
12) If α , β are the roots of x2-x-1=0 the product of 2αβ is
a) -2 b)2 c) ±2 d) -4
13) The solution of equation of 4x2-16=0 is
a) ±4 b) 4 c) ±2 d) 0
14) An expression of form with D(x) ≠ 0 and D(x), N(x) are
a) Fraction b) polynomial c) partial fraction d) a,b both
15) Mean is effected by change in
a) Value b) scale v) rate d) place
BAHRIA FOUNDATION HIGH SCHOOL SARGODHA
Paper: Mathematics 2nd PHASE PAPER.201 Class: 10th
Total Marks: 60 Time Allowed: 2 :10 min
حصہ۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔ I
Part اول۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔۔
Note: Total 27 shorts questions are given in Q#2, 3, and 4. Attempt any 18 questions according to given instruction in question.
Q # 2: Attempt any six (6) questions from the following. 6
1) Define quadratic equation with one example?
2) What is meant by...

...Quadratic Equation:
Quadratic equations have many applications in the arts and sciences, business, economics, medicine and engineering. Quadratic Equation is a second-order polynomial equation in a single variable x.
A general quadratic equation is:
ax2 + bx + c = 0,
Where,
x is an unknown variable
a, b, and c are constants (Not equal to zero)
Special Forms:
* x² = n if n < 0, then x has no real value
* x² = n if n > 0, then x = ± n
* ax² + bx = 0 x = 0, x = -b/a
WAYS TO SOLVE QUADRATIC EQUATION
The ways through which quadratic equation can be solved are:
* Factorizing
* Completing the square
* Derivation of the quadratic formula
* Graphing for real roots
Quadratic Formula:
Completing the square can be used to derive a general formula for solving quadratic equations, the quadratic formula. The quadratic formula is in these two forms separately:
Steps to derive the quadratic formula:
All Quadratic Equations have the general form, aX² + bX + c = 0
The steps to derive quadratic formula are as follows:
Quadratic equations and functions are very important in business mathematics. Questions related to quadratic equations and functions cover a wide range of business concepts that includes COST-REVENUE, BREAKEVEN ANALYSIS, SUPPLY/DEMAND & MARKET EQUILIBRIUM....

...While the ultimate goal is the same, to determine the value(s) that hold true for the equation, solving quadratic equations requires much more than simply isolating the variable, as is required in solving linear equations. This piece will outline the different types of quadratic equations, strategies for solving each type, as well as other methods of solutions such as Completing the Square and using the Quadratic Formula. Knowledge of factoring perfect square trinomials and simplifying radical expression are needed for this piece. Let’s take a look!
Standard Form of a Quadratic Equation
ax2+ bx+c=0
Where a, b, and c are integers
and a≥1
I. To solve an equation in the form ax2+c=k, for some value k. This is the simplest quadratic equation to solve, because the middle term is missing.
Strategy: To isolate the square term and then take the square root of both sides.
Ex. 1) Isolate the square term, divide both sides by 2
Take the square root of both sides
2x2=40
2x22= 40 2
x2 =20
Remember there are two possible solutions
x2= 20
Simplify radical; Solutions
x= ± 20
x=± 25
(Please refer to previous instructional materials Simplifying Radical Expressions )
II. To solve a quadratic equation arranged in the form ax2+ bx=0.
Strategy: To factor the binomial using...

...Quadratic equation
In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, the quadratic coefficient, the linear coefficient and the constant or free term.
Solving the quadratic equation
A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.
Factoring by inspection
It may be possible to express a quadratic equation ax2 + bx + c = 0 as a product (px + q)(rx + s) = 0. In some cases, it is possible, by simple inspection, to determine values of p, q, r, and s that make the two forms equivalent to one another. If the quadratic equation is written in the second form, then the "Zero Factor Property" states that the quadratic equation is satisfied if px + q = 0 or rx + s = 0. Solving these two linear equations provides the roots of the quadratic.
Completing the square
The process of completing the square makes use of the algebraic identity...

...Summer 2010-3 CLASS NOTES CHAPTER 1
Section 1.1: Linear Equations
Learning Objectives:
1. Solve a linear equation
2. Solve equations that lead to linear equations
3. Solve applied problems involving linear equations
Examples:
1. [pic]
[pic]
3. A total of $51,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment?
4. Shannon, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $608 for 56 hours worked. What is her regular hourly wage?
Answers: 1. [pic]
2. [pic]
3. $24,000 in CDs, $27,000 in bonds 4. $9.50/hour
Section 1.2: Quadratic Equations
Learning Objectives:
1. Solve a quadratic equation by (a) factoring, (b) completing the square, (c) the
quadratic formula
2. Solve applied problems involving quadratic equations
Examples:
1. Find the real solutions by factoring: [pic]
2. Find the real solutions by using the square root method: [pic]
3. Find the real solutions by completing the square: [pic]
4. Find the real solutions by using the quadratic formula: [pic]
5. A ball is thrown vertically upward from the top of a...

...MATH 209 — FINAL EXAM
This is an open book quiz – feel free to use all the material at your disposal.
Please remember to show your methodology as well as the answer. How you solve the problems counts almost as much as your correct answer – in other words, even if you get the wrong answer, partial credit is available if you can show that you know how to approach the problem!
These are not difficult – just remember to follow logical rules
AND PLEASE BE CAREFUL — CHECK YOUR ARITHMETIC
WATCH OUT FOR THOSE QUESTIONS THAT NEED ± SOLUTIONS
There are 20 questions.
For questions 1 through 5, perform the indicated operations. If possible, simplify the answer.
1. [2 – 5(6 – 2)²] ÷ (8 – 4•3)
parens
[2-5(4)^2]/(8-12)
Powers
[2-5(16)]/-4
multiplication
(2-80)/-4
parens
-78/-4
Cancel the minus
78/4
simplify
39/2
2.
Expand:
27x^6 * 2x^-3 / 6x^3
Simplify:
54x^3 / 6x^3
Cancel x^3:
54/6
Simplify:
9
3.
Common denominators:
3x/x + 3/x
-------------
4x/x + 4/x
Simplify:
(3x+3)/x
-----------
(4x+4)/x
Cancel the x:
(3x+3)/(4x+4)
Factor:
3(x+1)/4(x+1)
Cancel the x+1:
3/4
4.
Factor:
(y-3)(y-1) / (y-3)(y+3)
---------------------------
(y+6)(y+1) / (y+6)(y-3)
Flip the second fraction and multiply:
(y-3)(y-1)(y+6)(y-3)
-------------------------
(y-3)(y+3)(y+6)(y+1)
Cancel like terms:
(y-3)(y-1)
---------------
(y+3)(y+1)
5.
= 1 / 16^3/4
= 1 / 2^3
= 1/8
6....

... in the game of Math Time, the contestants are given an answer and they must come up with the question that corresponds to the given answer.
Your task for this portion of the assignment is to create two different “answers” (and the questions that accompany them) that the host could use for the final round of Math Time. The questions and answers you create must be unique. Check out the example and hint below, if needed.
x^2 - 100 is the product of these two binomials.
(x + 10) (x -10)
x^2 -10x +10x -100
My Solution: c = current of river b = rate of boat d = s(t) will represent (distance = speed X time) Upstream: 60 = 6(b-c)
Downstream: 60 = 3(b+c)
There are now two separate equations: 60 = 6b - 6c and 60 = 3b + 3c
Solve both equations for b: b = 10 + c b = 10 - c
Now make both equations equal each other and solve for c: 10 + c = 10 - c 2c = 0 c = 0
The speed of the current was 0 mph Now, plug the numbers into one of either the original equations to find the speed of the boat in still water.
I chose the first equation: b = 10 + c or b = 10 + 0 b = 10
The speed of the boat in still water must remain a consistent 10 mph or more in order for Wayne and his daughter to make it home in time or dinner.
My Solution: c = current of river b = rate of boat d = s(t) will represent (distance = speed X time) Upstream: 60 = 6(b-c)
Downstream: 60 = 3(b+c)
There...