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CUMBERLAND
HIGH SCHOOL
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Math Assignment C
Summer Assignment for those students who are entering Algebra 2
Cumberland High School
2600 Mendon Road, Cumberland, Rhode Island 02864
401/658-2600 Fax No. 401/658-0880
June, 2015
Dear Student,
This year’s summer math assignment will focus on the things that you will need to know as you begin your next math course (this upcoming fall). The material in this assignment is designed to “refresh your memory” on the major concepts that you have learned in previous math classes. The math department has provided some examples and practice problems that will help reinforce these concepts to make sure you remember them before starting your class next year. If after reviewing the examples, you still do not remember how to do the problems, there are numerous websites available to help you which are provided below. When you return to school in the fall, your math teacher will be available for extra help after school for any questions that you may have. In addition, all teachers have school emails in the form: first name.last name @. Please feel free to email if you have questions. (Note: it is vacation time so some teachers may be away or not checking email as frequently as they would in school so please be patient if you email during the summer.)
This summer assignment will not be graded. However, within the first week of school, you will have a short summative assessment on the material in the packet. If you make an honest attempt at the packet, you will be allowed to revise this assessment if you perform below standard. Please make your best effort and be sure that you know this material since it will be important to your success in your next math class. Your math teachers are always happy to help you - all you need to do is ask!
Have an enjoyable summer! We look forward to working with you in the fall.
CHS Math Department
Core Values and Belief Statement
The Cumberland High School community promotes development of a culture in which students are respectful, responsible, and ready to succeed. We guide our students to be actively involved in a learning process that combines academic depth of understanding with higher-order thinking, problem-solving, risk-taking, and creativity. We offer opportunities for students, as members of a 21st century world society, to become life- long learners and informed, productive citizens.
Learner Expectations
Cumberland High School Students will:
1. Communicate effectively and critically through reading, writing and speaking
2. Exhibit a range of functional and critical thinking skills related to information media and technology
3. Apply effective reasoning and problem-solving skills independently and collaboratively
4. Analyze and evaluate a variety of sources for reliability and credibility
5. Act with respect, tolerance, courtesy and compassion
6. Act responsibly and display good citizenship
Directions:
• Complete each problem.
• Use the space provided to carry out the work (attach additional pages if necessary).
• Show all work.
REMEMBER: If you find that you are having difficulty completing any of the problems, try using some of the suggested online resources, or carry out a web search on the topic that is presenting you difficulty.
Topic 1: Factoring
|Are there Common Factors? |
To factor polynomial expressions, there are several approaches that can be used to simplify the process. While all of these approaches are not used for each problem, it is best to examine your expression for the possible existence of these situations. Ask yourself the following questions:
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|Factor out the Greatest Common Factor (GCF) of the expression, if one exists. This will make it simpler to factor the remaining expression. |
|Take care NOT to drop this GCF, as it is still part of the expression's answer. |
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|Does the expression have only 2 terms? |
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|If it does, is the expression a DIFFERENCE of PERFECT SQUARES? |
|If so, you should be able to write the expression as a product of the sum and difference of the square roots of the terms. |
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|Does the expression have exactly 3 terms? |
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|If yes, then the expression may factor into the product of two binomials. One way to solve this type of problem is to use trial and error, |
|keeping certain "hints" in mind. |
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|Hints: |
|With the trinomial arranged in proper order (highest to lowest powers): |
|• if the leading coefficient is 1, you are looking for two numbers that multiply to the last term and add to the coefficient of the middle|
|term. |
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|• if the leading coefficient is not 1, you will have to look more carefully to find the answer. |
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|For the examples below, use the hint above for factoring when the leading coefficient is 1, and the trial and error (guess and check) method|
|when the leading coefficient is 2. |
|Always check your work by multiplying the binomials to see if your center term matches the original problem. |
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Does the expression have only 4 terms?
If there are four terms, we use a method called grouping. Here, you group the first two terms, and the second two terms. Find the GCF of each, and rewrite.
Keep in mind, you may need to apply more than one factoring method, below are a few examples:
Ex.) GCF and the Difference of Squares Ex.) Quadratic Like Trinomials
Ex.) GCF and Trinomials Ex.) Quadratic Like and Difference of Square
Factor the following completely:
1) [pic] 2) [pic]
3) [pic] 4) [pic]
5) [pic] 6) [pic]
7) [pic] 8) [pic]
9) [pic] 10) [pic]
Topic 2: Manipulating Equations
Manipulating equations is just rearranging the equation to solve for a given variable. Below are some examples.
Ex.) Solve for a Ex.) Solve for x Ex.) Solve for y
Solve for the indicated variable:
1) Solve for a: [pic] 2) Solve for y: [pic]
3) Solve for x: [pic] 4) Solve for y: [pic]
5) Solve for x: [pic] 6) Solve for a: [pic]
7) Solve for x: [pic] 8) Solve for d: [pic]
9) Solve for a: [pic] 10) Solve for b: [pic]
11) Solve for E: [pic] 12) Solve for Q: HQM = H + M
Topic 3: Graphing
Ex. Vertical Line: x = 1 Ex.) Horizontal Line: 2y +1 = 3 ( 2y = 2 ( y = 1
It is easiest to graph from slope-intercept form: y = mx + b
• m = the slope
• b = the y-intercept (where the graph crosses the y-axis)
Ex.) [pic] *Start by graphing the y-intercept (0, 2)
* The use the slope [pic] [pic]
If an equation is NOT in slope-intercept form, then you can use two methods: finding the intercepts or rewriting in slope intercept form.
Ex.) Graph [pic] by finding the intercepts.
Ex.) Graph [pic] by putting it into slope-intercept form (hint: solve for y!)
Slope = [pic] y-intercept = (0, 0)
Graph the following lines each on a separate coordinate plane:
1) [pic] 2) [pic]
3) [pic] 4) [pic]
5) [pic] 6) [pic]
7) [pic] 8) 3y + 1 = 16
9) [pic] 10) [pic]
Topic 4: Order of Operations
Ex.) Order of Operations Ex.) Order of Operations and Exponents
Ex.) Order or Operations and Evaluating Ex.) Order or Operations and Exponents
Ex.) Order of Operations and Exponents Ex.) Order of Operations and Exponents
Simplify the following completely:
1) [pic] 2) [pic]
3) [pic] 4) [pic]
[pic]
5) [pic] 6) [pic]
7) [pic] 8) [pic]
9) [pic] 10) [pic]
Web Based Resources
Khan Acacademy – Modules/video tutorials that provide overviews and steps for completing math problems.
Factoring with Mr. Yang and Mosley the alien - A comics based lesson for Algebra students.
National Library of Virtual Mathematics -
The National Library of Virtual Mathematics, with K-12 activities in operations, geometry, algebra, measurement, data analysis, and probability.
Purplemath - Online algebra resource.
The Math Forum Home Page - This site can be searched by resource type (lesson plan), math topics, grade levels, and key sites.
CTAP Region 4: Middle School Math Project - CA Technology Assisted Program Region 4 has developed this site for middle school math.
Seeing Math - Seeing Math has developed interactive software Java tools to clarify key mathematical ideas in middle and high school mathematics. Each interactive provides a real-time connection between representations of the mathematics (symbolic, graphical, etc.), so that changes in one representation instantly cause changes in the other.
Enjoy Mathematics in 3D - This site, created by the Department of Mathematics Education, Faculty of Education, Shinshu University, welcomes users to the three-dimensional mathematics world described as "the world of space figures learned with the three-dimensional dynamic geometry software."
Math Slice - These math games (including Math Jeopardy and MathMillionaire) are complemented by a wide selection of online multiple choice activities that test class knowledge of math concepts from basic counting to algebra and statistics.
The Educator's Reference Desk - Hundreds of mathematics lesson plans organized by subject and grade level.
Geometry and its Applications (GeoMAP) - Eight complete high school geometry units created by the Consortium of Mathematics and its Applications.
Mudd Math Fun Facts - Fun math facts created by the Harvey Mudd College math department that teachers can use to enrich their lessons.
PBS TeacherSource - Math lessons and activities organized by grade and topic.
Johnny Money - Now available from the NFIB Young Entrepreneur Foundation, Johnny Money Online Game is a FREE Internet-based small business simulation game that engages students as they explore the risks and rewards of business ownership. Johnny Money is the newest of the Entrepreneur-in-the-Classroom programs, which are designed to enable educators to talk about entrepreneurship in their classrooms.
. This online community includes teachers, students, researchers, parents and educators who have an interest in math and math education. The site includes Ask Dr. Math, Problems of the Week, discussion groups and much more.
. Customized by grade level and topic, AAA Math features explanations of various mathematical topics, practice problems and fun, challenging games.
. This fully interactive site and allows the user to sharpen basic math skills, play games and explore new math concepts.
. Created by the National Council of Teachers of Mathematics, this site helps families enjoy mathematics outside school through a series of fun and engaging challenges.
. Math Cats provides playful explorations of important math concepts through games, crafts and interactive projects. Includes a magic chalkboard and an art gallery.
. This South African Community website for teachers, parents and students is complete with lessons, tests, exams, worksheets, study skills and much more.
bbc.co.uk/education/megamaths/tables.html. This lively, interactive Web site, based on the popular BBC Schools Television series “Megamaths,” is for practicing and testing times tables.
. The Math League, designed for students in fourth grade through high school, specializes in math contests, books and computer software. The “Help Facility” is handy reference guide for math topics complete with examples, definitions and explanations.
. FleetKids games teach elementary children several different aspect of money management. Games include Windfall, where a child can run an imaginary business and BuyLo/SellHi, where children can play the stock market. Students can sign up as an individual or as part of an elementary school team.
numbers.html. This site includes 17 original games based on soccer, car racing and much more Other games include Math Baseball, where a child can score runs with correct answers and Operation Order, where students can build pyramids with their knowledge of algebra.
The Math Dude Tutorials on various mathematical concepts. Videos are downloadable.
Math videos and pod casts.
Teacher who created a website that has various math concepts set to rap music. Check out “Fractions!”
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(A = D – C
2b
Y-intercept (set x = 0 and solve):
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(0, -3)
X-intercept (set y = 0 and solve):
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(5, 0)
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Exponent Rules:
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