Buried treasure. Ahmed has half of a treasure map,which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?

The Pythagorean Theorem states to find the missing side of a right triangle you can square to know lengths and add the two together. The result will be the distance of the missing length squared.

A^2+b^2=C^2

We know that Ahmed has a map with a distance to the treasure of 2x+6.

We know that Vanessa has a map with a distance of 2x+4, after walking x paces north.

We are looking to solve for the number of paces north Vanessa must walk.

(number of paces north)^2+ (Vanessa’s distance)^2=(Ahmed’s distance)^2

Now we have a quadratic equation to solve by factoring and using the zero factor.

x^2-8x-20=0

(x – ) (x + ) = 0

Since the coefficient of x2 is 1 we can start with a pair of parenthesis with an x in each. Since the 20 is negative we know there will be one + and one – in the binomials. We need two factors of -20 which add up to -8. -1, 20; -2, 10; -4, 5; -5, 4; -10, 2; -20, 1

-10 and 2 will work

(x – 10)(x + 2) = 0 Use the zero factor property to solve each binomial, x – 10 = 0 or x + 2 = 0 creating a compound equation. x = 10 or x =...

...
Algebra 1
Schools in California now have higher expectations to make it necessary for students to take a Algebra 1 course in order to graduate from high school. This requirement issues that it will help students achieve higher expectations and great problem solving skills in future references. People like Mitchell Rosen a licensed family counselor who also disagrees with having Algebra 1 be a requirement for high schools. In one of Rosens articles “Finding X is not a factor of living,” he explains that algebra is not a reliable subject because it not used in the real world. Rosen argues that students should better life training skills in other subjects, students “need more [fundamental] training, not the fine-tuning.” Rosen argues that algebra can be discouraging to students and causes their self-esteem to decrease, also causing unnecessary stress for the student; algebra isn't required for most jobs in the real world; algebra has caused high school dropout rates to increase; due to low grades in algebra. Furthermore, algebra should not be a requirement in order to graduate from high school.
First and for most, If asked, most people would not say that they have personally never used algebraic problems outside of class room walls and isn't important to their professions, so Algebra 1 should not be a requirement in high...

...ALGEBRA
In all three of these problems there is use of all of the terms required: simplify, like terms, coefficient, distribution, and removing parentheses. There is also use with the real number properties of the commutative property of addition and the commutative property of multiplication. In what ways are the properties of real numbers useful for simplifying algebraic expression? The properties are useful for identifying what should go where and with what, to make it simpler to understand and to solve the equation properly. When we break things down to a simplified process, it is much easier to see how the real numbers are placed and why they are placed that way. Real numbers do not actually show the value of something real in the “real world”. For example, in mathematics if we write 0.5 we mean exactly half, but in the real world half may not be exactly half. In all reality, we use mathematics every single day, whether we consciously realize it or not. Math is the key subject that applies to our everyday lives in the “real world”.
Expression number one like terms are combined by adding coefficients, the removal of parentheses, and the use of commutative property of addition and multiplication. Expression number two has the use of quite a bit of distribution, combining like terms, and removal of parentheses. Expression number three like terms are combined by adding coefficients also. In this expression there is a temporary addition of...

...Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis.
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
• As a single word without article, "algebra" names a broad part of mathematics (see below).
• As a single word with article or in plural, "algebra" denotes a specific mathematical structure. Seealgebra (ring theory) and algebra over a field.
• With a qualifier, there is the same distinction:
• Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
• With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
• Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all arecommutative algebras over the integers.
• Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to...

...Accelerated Coordinate Algebra / Analytic Geometry Part A
Dr. Khan, Ph.D., Fall 2012
ekhan@marietta-city.k12.ga.us
WHY ARE YOU TAKING THIS COURSE?
All Georgia high school students are required to take four years of mathematics. Taking Accelerated Coordinate Algebra / Analytic Geometry Part A is comparable to taking the typical ninth grade course, Coordinate Algebra AND the first half of the tenth grade course, Analytic Geometry. The reason for acceleration of the first three courses is to provide ample room in a student’s schedule to incorporate higher level mathematics classes in future years.
WHAT WILL YOU LEARN?
Accelerated Coordinate Algebra / Analytic Geometry Part A covers topics in algebra, geometry, and statistics.
Unit 1: Relationships Between Quantities
Unit 2: Reasoning with Equations and Inequalities
Unit 3: Linear and Exponential Functions
Unit 4: Describing Data
Unit 5: Transformations in the Coordinate Plane
Unit 6: Connecting Algebra and Geometry Through Coordinates
Unit 7: Similarity, Congruence, and Proofs
Unit 8: Right Triangle Trigonometry
Unit 9: Circles and Volume
The first semester of Accelerated Coordinate Algebra / Analytic Geometry Part A will cover the first five units. Second semester will include the last four units. During the second semester students will take the End of Course Test in Coordinate...

...that there are many aspects of Algebra that the majority of people do not use on a daily basis. I think that this fact is what leads people to the false conclusion that Algebra is useless.
To better understand our topic, let’s define what we mean when we say “Algebra”. Webster’s dictionary defines Algebra as “a form of mathematics dealing with symbols and equations.” A guest in the mathematics forum on xpmath.com states that “…the truth is that Algebra is not much more than arithmetic expanded to the point where you don’t have to do trial and error to get an answer.” This guest goes on to explain that “…if you view it from that perspective, and overlook the outdated nature of some problems’ data, then you’ll recognize that indeed math deserves a place in your career; the more competent you can become with it, the better you’ll be able to competently manage you life.” I wholeheartedly agree with the preceding statement.
However, I’m not completely certain that math is THE MOST important subject we’ll ever learn; I believe that English quite important as well.
Math describes how everything in our environment works. A working knowledge of mathematics enables us to make accurate measurements and predictions. Since Algebra uses letters to represent numbers, it forces us to leap from concrete to abstract thinking. This “new thinking” method is, I believe, the reason Algebra...

...The CENTRE for EDUCATION in MATHEMATICS and COMPUTING
PATTERNING
AND
ALGEBRA: ALGEBRAIC EXPRESSIONS
This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo.
Play the Late Delivery game first! Levels 1 and 2 are recommended. Click on http://www.bbc.co.uk/education/mathsfile/shockwave/games/postie.html or go to www.wiredmath.ca for the link. 1. a. Write each of the following expression as a single number. i. 20 + 5 ii. 15 ÷ 3
iii. 11 × 9
b. For each question in (a) write 3 equivalent expressions using 3 different operations. 2. Match up the equivalent expressions below:
4+3 1+ 2 6×2+2 16 ÷ 2
55 − 52
2×2×2 49 ÷ 7 7×2
Did You Know?
A cheetah can run 76 km/h. The fastest human can only run about 37 km/h!
3.
The scale balances because the mass on the left side is equal to the mass on the right side. A number sentence can be written to describe the picture: 10 + 10 + 1 = 10 + 5 + 5 + 1 or 2 × 10 + 1 = 2 × 5 + 10 + 1 . a. Draw 3 different combinations of masses on a scale that would balance.
b. Write a number sentence to describe each of the 3 new combinations.
4.
a. Balance the scale using a combination of 10 g, 5 g and 1 g weights. Assume you have many different masses. Compare your solution with your classmates.
b. Write an equivalent expression, which is...

...
Financial Polynomials
MAT 221 Introduction to Algebra
Instructor: Neal Johnson
April 7, 2013
Problem 1
p=200
r=10
n=1
p(1+r)1
Reorder the polynomial 1+r alphabetically from left to right, starting with the highest order term.
p(r+1)
Multiply p by each term inside the parentheses.
pr+p
Replace the variable r with 10 in the expression.
p(10)+p
Replace the variable p with 200 in the expression.
(200)(10)+(200)
Divide 200 by 10 to get 20. This will be the Dividend for the year.
(20)+200
Add 200 to 20 to get 220.
220.00
Problem 2
p=5670
r=3.5
n=1
p(1+r)1
Reorder the polynomial 1+r alphabetically from left to right, starting with the highest order term.
p(r+1)
Multiply p by each term inside the parentheses.
pr+p
Replace the variable r with 3.5 in the expression.
p(3.5)+p
Replace the variable p with 5670 in the expression.
(5670)(3.5)+(5670)
Divide 5670 by 3.5 to get 1620. This will be the Dividend for the year.
(1620)+5670
Add 5670 to 1620 to get 7290.
7,290.00
Problem 3
(-9x3+3x2-15x)/(-3x)
Move the minus sign from the denominator to the front of the expression.
-(-9x3+3x2-15x)/(3x)
Factor out the GCF of -3x from each term in the polynomial.
-(-3x(3x2)-3x(-x)-3x(5)/(3x)
Factor out the GCF of -3x from -9x3+3x2-15x.
-(-3x(3x2-x+5)/(3x)
Reduce the expression -(3x(3x2-x+5)/(3x) by removing a factor of 3x from the numerator and denominator....

...PROFICIENCY TEST STUDY GUIDE
With sample test questions
MATHEMATICS / ALGEBRA |
Key Words and Converting Words to EquationsFractions Adding, subtracting, multiplying, dividing Simplifying Writing decimals as fractions StatisticsReading Tables and ChartsExponentsPre-Algebra and Algebra Special notation for multiplication and division with variable Algebra word problems Order of operations Simplifying expressions Prime factorization Greatest common factor Least common multiple Factoring Sample algebra problemsCoordinate System Grid graph Slope coordinatesGeometry Basics Squares, rectangles, circles, trianglesMath Definitions |
ENGLISH |
Proof reading / spellingReading comprehensionMain theme of a paragraphLogical sequence of a paragraphKey wordEnglish grammarBasic word meanings |
ABILITY TO ASSIST |
Worker roles and responsibilitiesStudent discipline / behavior |
WRITING |
ContentFormatGrammarSpellingPunctuation |
MDUSD Proficiency Test Study Guide / Page 2
MATH
Key Words and Converting Words to Equations
Sometimes math questions use key words to indicate what operation to perform. Becoming familiar with these key words will help you determine what the question is asking for.
OPERATION | OTHER WORDS WHICH INDICATE THE OPERATION |
Addition | Increased by; more...