# SUMMER MATH PACKET. Geometry A COURSE 227

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 SUMMER MATH PACKET Geometry A COURSE 7

4 Examples: Simplify the following a) 1 ( 5) b) 1 ( ) = 0 (9 ) () IV. Solving Equations & Inequalities Be able to solve multi-step equations using order of operations, distributive property and inverse operations. ex. Solve: 5x ( x 5) = 7x 5x x+ 10 = 7x x+ 10 = 7x 1 = x x = Be able to solve inequalities using the same process as solving equations. Just remember that if you multiply or divide by a negative, you must switch the inequality sign. ex. Solve: (y ) 9(y+ 5) 1y+ 1y+ 5 0y 7 7 y 0 Be able to solve proportions: 10 = x+ 1 x x= 10x+ 10 cross multiply x = 10 5 x = fraction reduced

5 V. Interval notation and conjunctions The word "and" corresponds to "intersection" and to the symbol " ". Any solution of a conjunction must make each part of the conjunction true. The word "or" corresponds to "union" and to the symbol " ". For a number to be a solution of a disjunction, it must be in at least one of the solutions sets of the individual sentences. Interval notation is used in inequalities, domain and range, solution sets, etc. For a boundary point to be included, the symbol "[ " or "]" is used. For a boundary point not to be included, the symbol "(" or ")" is used. Ex. Solve: x 5< or x < 10 x < or x < 7 x > or x < 7 Solution set is (, 7 ), solve each separately Ex. Solve: x 5 and x 5 11 Solution set is [,1] x 1 and x

6 VI. Solving Systems of Equations & Inequalities Methods to Solving Systems: Graphing, Substitution, Elimination 5

7

8 VII. Simplifying Radicals a Know that for any real number a, Simplifying radicals, means taking out the factors that are perfect squares. Be careful with simplifying algebraic expressions. x x x x instead = a x x x x + 1 = ( ) = Examples: Simplify the following = ( a+ 1) = a+ 1 5 = VIII. Solving Quadratics Standard form of a quadratic equation: ax + bx + c = 0 Be able to solve quadratics using factoring, quadratic formula and graphing Remember to set equations equal to 0 before solving Factoring: x = x x + x = 0 Set equation equal to 0 ( x )( x+ 1) = 0 Factor equation x = 0 and x + 1= 0 Set each factor equal to 0 x = and x = -1 Solve each equation Quadratic Formula: ex. Solve To solve ax bx c + + = 0 and a 0 b ± b ac Then x = a 5x + x= using the quadratic formula 5x x = a = 5, b =, c = ± x = (5)() (5) ± x = Split the plus and minus apart 10 x = or x = 1 5 7

9 Solving Quadratics by Graphing: Graph: y = x + x on your graphing calculator - the solution(s) are where the graph crosses the x-axis Solutions: x= & x = IX. Problem Solving Skills for Word Problems 1. Read the problem carefully.. Draw a picture (if you can) illustrating the problem.. Identify unknown quantities you're being asked to find.. Choose a variable to represent one quantity. 5. Write down, in words, what the variable (you chose in ) represents.. Represent other quantities to be found in terms of the variable (you chose in ). 7. Write the word problem as an equation (hard step--takes practice).. Solve the equation for the unknown quantity. 9. Answer the question asked in the word problem. 10. Check your solution in the original word problem.

10 X. Basic Formulas Formula Use Formula Use A = r Area of a circle. r is P = L + W Perimeter of a rectangle. the radius L is length, W is width C = r Circumference of a circle. r is the radius A=(1/)BH Area of a triangle. B is base length, H is height A = LW Area of a rectangle. L is length, W is width a + b = c Pythagorean theorem for a right triangle. a, b lengths of legs c length of hypotenuse A = s Area of a square 9

11 Review problems: Complete the following problems, showing work where necessary. Feel free to do your work on separate sheets of paper and remember you will be required to turn this in. An answer key is provided for you but in geometry the work is usually more important than the answer! *Problems should be completed by Geometry A students only I. Using the graphing calculator 1. Graph the following on your calculator and sketch the graph: a) y = x+ b) y = x c) x+ y = 5 x y =. Find the points of intersection of the following: y = x + 1 y = x+. Find the roots (y = 0) of the following: y x x = + 1 II. Cartesian Coordinate System. Which pair of lines are perpendicular? y = x+ y = x - a) b) c) y = x + 9 y = x y = 1 y = d) y = x y = x 5. Which pair of lines are parallel? y = x+ y = x - a) b) y = x + 9 y = x c) y = 1 y = d) y = x y = x 10

12 . Write an equation in point-slope form for the line through the given point and slope. a) (-, ), m = - b) (1,5), m = - 7. Write an equation for the line through the given points. Use the form given only.,1, 0,7 Slope Intercept Form a) ( 1, ),(,5 ) Point-slope form b) ( ) ( ). Find the equation of the line perpendicular to the given line that contains the 1 following point. Use slope intercept form. y = - x - ; ( 0,7) 9. Find the equation of the line parallel to the given line that contains the following point. Use point-slope form. y = - x + 7; ( 1,) 11

13 10. Graph the following lines: A. y + = B. y + x = C. x - y = D. (y - ) = 0.(x + ) 1

14 III. Simplifying Algebraic Expressions 11. Simplify the following expressions: a) 19 ( + ) b) c) Evaluate: ( x ) x if x = - IV. Solving Linear Equations and Inequalities 1. Solve the following equations: a) -9x + (x - ) = 5 (x-) + 7 b) 1 (5 y 1) = 15( y+ 1) c) 1 5 x = x+ 1

15 1. Solve the following inequalities: (write your answer in interval notation) a) x + 7 < 19 b) m+ 7 1( m ) c) 1 1 (y+ ) 17 < (y ) 1. Graph the solution to the following linear inequalities: A y x B. 5x y< V. Conjectures 15. Find the intersection of the sets: { 1,,5,7,9} {,5,11,1} 1. Find the union of the sets: { 1,,5,,9} { 1,,5,9} 1

16 17. Solve and graph the solution set: x > 1 or x 10 VI. Solving Systems of Linear Equations & Inequalities 1. Graph the following systems and state the solution A. x - y = x + y = B. x - y = 5x - y = C. y = x -1 y = x D. x - y = 9x - y = 1 15

17 19. Solve using Substitution or Elimination Method a). y = x+ 11 y = x+ 5 b). x 5y = 11 x+ 7y = 1 c). x + y = x= y+7 d). -x + 5y = x - y = 5 0. Substitution Only! 1. Elimination Only! -x + y = 1 x + y = 17 y = -x + x - y = -5.* x - y +5z = 1.* w + x - y + z = 0 5x + y + z = 1 w - x - y - z = -5 x + y + z = w - x -y + z = w -x - y +z = 7 VII. Simplifying Radicals. Simplify the following: a) 5 b) 19 c) 5 d) 5 11 a b 1

18 5. Rationalize the denominator for each expression. a) 5 b) 5b VIII. Solving Quadratic Equations. Multiply the following expressions: (write your answer in descending order) a). (a + )(a - 7) b). y(y - 5y - 10) c). (a + )(a - ) d). (d - 5)(d + d + 1) e). (y - 7y )(y + 7y ) f). (b - 1 )(b + ) g). (x + 7)(x + 7) h). (m - 1) 17

19 7. Factor the following polynomials a). y - 10y + 5 b). x + 1x + c). b d). c + 9 e). x + x + 5 f). x - 7x + 1 g). x - x - h). x x 5. Solve each equation. If the value is irrational, simplify the radical. a) x -1 = 0 b) x +1 = 0 c) x + = 7 d) x -10 = - e) x - = 50 f) 5x + 5 = 15 Solve by factoring: g) ( x - )( x +1 ) = 0 h) x +1x +1 = 0 i) x + 7x = j) x -11x +10 = 0 k) x - 1x - 5 = 0 l) 0x +11x - 1 = 0 1

20 IX. Problem Solving Skills 9. Kevin rolled a number cube (a die which is one of a pair of dice) 50 times and obtained the following results: Number which showed up 1 5 Number of times it showed up a) Based on this experiment, what s the probability of rolling a? b) What is the theoretical probability of rolling a? c) Based on these results, how many 5 s should Kevin expect to get in 00 rolls? d) Based on theoretical probability, how many 5 s should Kevin expect to get in 00 rolls? 0. Three times the greater of two consecutive odd integers is five less than four times the smaller. Find the two numbers. 1. Solve: v d d t = 1, solve for d 1 19

21 . Write and solve an inequality for the following: 5 times a number minus 7 is less than 11. Write an inequality for the following problem. One fourth of a number increased by 17 is at least. X. Using Basic Formulas. Use the formula P = l + w to find the length of a rectangle whose perimeter is 57 inches and whose width is 1 inches. 5. A rectangle has dimensions x + 5 and x +. Write an expression for the area of the rectangle as a product and as a polynomial in standard form.. Stephanie is planning to build a rectangular garden that is 5m longer than it is wide. If the flowerbed will have an area of 7500 m, find the dimensions of the garden. 0

22 7. Find the area of the shaded region: 1

23 ANSWER KEY Part 1: Graphing calculator a) b) c). x = and x =.705. x = 1, -1.1 and also x =.10 Part : Review Problems. D 5. A. a) y = ( x+ ) b) y 5 = ( x 1) 7. a) y = x 1 or y 5= x b) y = x+ 7. y = x y = ( x 1)

24 10. a) b) c) d) 11. a) - b) no solution c) - 1. a) x = b) no solution c) x = a) (,) b) [.9, ) 1. a) b) c. (,5) 15. {,5 }

25 1. { 1,,,5,,9 } 17. x < or 1. 5 x a) Solution (, 0) b) Solution (, ) c) Infinite # of Solutions d) No Solution 19. a) (-, 7) b) (, 1) c) (5, -) d) (7, ) 0. a) (-, 5) 1. 11,. (,, 1). (-, -1, 0, ) = (w, x, y, z). a) 5 b) c) 5 1 d) 5 a b ab

26 5. a) 15 b) 5b 5b. a) c) a a 1 b) a 9 d) 5 10 y y y d 1d d 5 e 9y + 1y f) 1b + 5b g) x x x x h) 9m m a) ( x 5) b) ( x + ) c) ( b 10)( b 10) + d) can t be factored e) ( x+ 5)( x+ 1) f) ( x )( x ) g) ( x )( x+ ) h) x ( x+ )( x ). a) x = ± 1 b) no solution c) x = ± d) x = ± e) 5 x = ± f) x = ± 5 g) 1 x =, h) x = { 1, 1} i) x = {,1} j) 5 x =, k) 5 x =,1 l) 1 1 x =, 5 9. a) 9 50 b) 1 c) d) & 1 5

27 1. d vt = d1. n < n +. l = 15.5 inches 5. A= x + x width = 75m length = 100m 7. A = 1 x + x 7x 10 units

### SUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 215

SUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 5 Updated May 0 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of

### Basic Fraction and Integer Operations (No calculators please!)

P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.

### FOR ALL STUDENTS TAKING ALGEBRA II Honors SUMMER REVIEW PACKET

FOR ALL STUDENTS TAKING ALGEBRA II Honors 01-014 SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants you to be successful in Algebra II.

### Basic ALGEBRA 2 SUMMER PACKET

Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout

### Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4)

NAME HONORS ALGEBRA II REVIEW PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their Algebra I course. In

### Herndon High School Geometry Honors Summer Assignment

Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in

### Rising Algebra Students. Stone Middle School

Algebra Summer Packet 017 Dear Future Algebra student, Rising Algebra Students Stone Middle School We hope that you enjoy your summer vacation to the fullest. We look forward to working with you next year.

### Anticipated workload: 6 hours Summer Packets are due Thursday, August 24, 2017 Summer Assignment Quiz (including a unit circle quiz) the same day

Dear AP Calculus BC student, Hello and welcome to the wonderful world of AP Calculus! I am excited that you have elected to take an accelerated mathematics course such as AP Calculus BC and would like

### Accelerated CP Geometry Summer Packet

Accelerated CP Geometry Summer Packet The math teachers at Cherry Creek High School want each student to be successful, no matter which level or math course the student is in. We know that it is critical

### ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t F o r S t u d e n t s E n t e r i n g A l g e b r a This summer packet is intended to be completed by the FIRST DAY of school. This packet will be

### Parenthesis and other grouping symbols. Exponential expressions. Multiplication & Division Addition & Subtraction.

NAME SADDLE BROOK HIGH SCHOOL HONORS ALGEBRA II SUMMER PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their

### STUDY GUIDE Math 20. To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition

STUDY GUIDE Math 0 To the students: To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition When you study Algebra, the material is presented to you in a logical sequence.

### When using interval notation use instead of open circles, and use instead of solid dots.

P.1 Real Numbers PreCalculus P.1 REAL NUMBERS Learning Targets for P1 1. Describe an interval on the number line using inequalities. Describe an interval on the number line using interval notation (closed

### Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher

Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work

### An equation is a statement that states that two expressions are equal. For example:

Section 0.1: Linear Equations Solving linear equation in one variable: An equation is a statement that states that two expressions are equal. For example: (1) 513 (2) 16 (3) 4252 (4) 64153 To solve the

### Mathematics Department. Summer Course Work. Algebra 2 Honors

Bergenfield High School Bergenfield, New Jersey Mathematics Department Summer Course Work in preparation for Algebra 2 Honors Completion of this summer work is required on the first day of the 2017-2018

### Geometry A & Geometry B & Honors Geometry Summer Packet

Geometry A & Geometry B & Honors Geometry Summer Packet RADICALS Radical expressions contain numbers and/or variables under a radical sign,. A radical sign tells you to take the square root of the value

### 2014 Summer Review for Students Entering Algebra 2. TI-84 Plus Graphing Calculator is required for this course.

1. Solving Linear Equations 2. Solving Linear Systems of Equations 3. Multiplying Polynomials and Solving Quadratics 4. Writing the Equation of a Line 5. Laws of Exponents and Scientific Notation 6. Solving

### Name Period Date. Use mathematical reasoning to create polynomial expressions that generalize patterns. Practice polynomial arithmetic.

Name Period Date POLYNOMIALS Student Packet 4: Polynomial Arithmetic Applications POLY4.1 Hundred Chart Patterns Gather empirical data to form conjectures about number patterns. Write algebraic expressions.

# %

### Summer Review Packet. for students entering. AP Calculus BC

Summer Review Packet for students entering AP Calculus BC The problems in this packet are designed to help you review topics that are important to your success in AP Calculus. Please attempt the problems

### Algebra II Notes Unit One. Syllabus Objective 1.1 The student will differentiate among subsets of the real number system.

Syllabus Objective 1.1 The student will differentiate among subsets of the real number system. Real Numbers: Numbers that can be graphed on the number line Ex:,!10, 2, 8,4.2," Put the numbers in order

### Intermediate Algebra 100A Final Exam Review Fall 2007

1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,

### How do you write and evaluate algebraic expressions? How can algebraic expressions and equations represent actual situations?

Topic: Expressions, Equations and Functions Days: 13 Key Learning: Expressions, equations, tables and graphs are used to model realworld situations. Unit Essential Question(s): How do you write and evaluate

### STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 2 nd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 2 nd Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

### Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website.

BTW Math Packet Advanced Math Name Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website. Go to the BTW website

### Remember, you may not use a calculator when you take the assessment test.

Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

### Prealgebra and Elementary Algebra

Prealgebra and Elementary Algebra 978-1-63545-035-4 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek,

### Solving Equations Quick Reference

Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number

### Algebra I Study Topics

This Algebra I Study Guide contains clear, straight-forward problems that represent the topics covered in a complete Algebra I course. After completing the study guide without a calculator, correct it

### College Algebra with Trigonometry

College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (556 topics + 614 additional

### x and y, called the coordinates of the point.

P.1 The Cartesian Plane The Cartesian Plane The Cartesian Plane (also called the rectangular coordinate system) is the plane that allows you to represent ordered pairs of real numbers by points. It is

### Monroe Township High School Monroe Township, New Jersey

Monroe Township High School Monroe Township, New Jersey Geometry *SUMMER PREPARATION PACKET* Geometry is a fast- paced, rigorous course that will provide you with the fundamental tools of geometric understanding

### Math Review. for the Quantitative Reasoning measure of the GRE General Test

Math Review for the Quantitative Reasoning measure of the GRE General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important for solving

### A polynomial expression is the addition or subtraction of many algebraic terms with positive integer powers.

LEAVING CERT Honours Maths notes on Algebra. A polynomial expression is the addition or subtraction of many algebraic terms with positive integer powers. The degree is the highest power of x. 3x 2 + 2x

### Math 096--Quadratic Formula page 1

Math 096--Quadratic Formula page 1 A Quadratic Formula. Use the quadratic formula to solve quadratic equations ax + bx + c = 0 when the equations can t be factored. To use the quadratic formula, the equation

### Instructor Notes for Chapters 3 & 4

Algebra for Calculus Fall 0 Section 3. Complex Numbers Goal for students: Instructor Notes for Chapters 3 & 4 perform computations involving complex numbers You might want to review the quadratic formula

### Unit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions

CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.

### Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.

Polynomials Polynomials 1. P 1: Exponents 2. P 2: Factoring Polynomials 3. P 3: End Behavior 4. P 4: Fundamental Theorem of Algebra Writing real root x= 10 or (x+10) local maximum Exponents real root x=10

### Mathematics. Algebra I (PreAP, Pt. 1, Pt. 2) Curriculum Guide. Revised 2016

Mathematics Algebra I (PreAP, Pt. 1, Pt. ) Curriculum Guide Revised 016 Intentionally Left Blank Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction and

### Pre-Algebra Unit 2. Rational & Irrational Numbers. Name

Pre-Algebra Unit 2 Rational & Irrational Numbers Name Core Table 2 Pre-Algebra Name: Unit 2 Rational & Irrational Numbers Core: Table: 2.1.1 Define Rational Numbers Vocabulary: Real Numbers the set of

### Exploring Graphs of Polynomial Functions

Name Period Exploring Graphs of Polynomial Functions Instructions: You will be responsible for completing this packet by the end of the period. You will have to read instructions for this activity. Please

### PreCalculus Summer Packet

PreCalculus Summer Packet Entering into PreCalculus means entering into your first year of college preparatory mathematics. There is a major shift in epectation for students to be able to recall many skills

### POWER ALGEBRA NOTES: QUICK & EASY

POWER ALGEBRA NOTES: QUICK & EASY 1 Table of Contents Basic Algebra Terms and Concepts... 5 Number Operations... 5 Variables... 5 Order of Operation... 6 Translating Verbal and Algebraic Phrases... 7 Definition

Classical Academy High School Algebra 2 Readiness Assessment REVIEW PACKET - Spring 2012 Student Name: _ Algebra 2 Readiness Assessment REVIEW PACKET Math Success is the Goal! In working with our Classical

### Algebra 1 Math Year at a Glance

Real Operations Equations/Inequalities Relations/Graphing Systems Exponents/Polynomials Quadratics ISTEP+ Radicals Algebra 1 Math Year at a Glance KEY According to the Indiana Department of Education +

### Solving Equations. A: Solving One-Variable Equations. One Step x + 6 = 9-3y = 15. Two Step 2a 3 6. Algebra 2 Chapter 1 Notes 1.4 Solving Equations

Algebra 2 Chapter 1 Notes 1.4 Solving Equations 1.4 Solving Equations Topics: Solving Equations Translating Words into Algebra Solving Word Problems A: Solving One-Variable Equations The equations below

Equations in Quadratic Form MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this lesson we will learn to: make substitutions that allow equations to be written

### 1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = -2x 2 4x + 2 x y.

1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = -2x 2 4x + 2 x y y = x 2 + 6x -3 x y domain= range= -4-3 -2-1 0 1 2 3 4 domain= range=

### Solving Quadratic & Higher Degree Equations

Chapter 9 Solving Quadratic & Higher Degree Equations Sec 1. Zero Product Property Back in the third grade students were taught when they multiplied a number by zero, the product would be zero. In algebra,

### Chapter 2 Polynomial and Rational Functions

SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear

### ALGEBRA 1B GOALS. 1. The student should be able to use mathematical properties to simplify algebraic expressions.

GOALS 1. The student should be able to use mathematical properties to simplify algebraic expressions. 2. The student should be able to add, subtract, multiply, divide, and compare real numbers. 3. The

### Algebra III. Mathematics Curriculum Framework. Revised 2004

Algebra III Mathematics Curriculum Framework Revised 2004 Title: Algebra III (Fourth-year Course) Course/Unit Credit: 1 Course Number: Teacher Licensure: Secondary Mathematics Pre-requisite: Algebra II

### Mathematics Tutorials. Arithmetic Tutorials Algebra I Tutorials Algebra II Tutorials Word Problems

Mathematics Tutorials These pages are intended to aide in the preparation for the Mathematics Placement test. They are not intended to be a substitute for any mathematics course. Arithmetic Tutorials Algebra

### AP Calculus AB Summer Review Packet

AP Calculus AB Summer Review Packet 016-017 Mr. Le jtle1@gmail.com Leuzinger High School Rm. G-0 The following packet is designed to help you review topics that are important to your SUCCESS in AP Calculus.

### Essential Learning Outcomes for Algebra 2

ALGEBRA 2 ELOs 1 Essential Learning Outcomes for Algebra 2 The following essential learning outcomes (ELOs) represent the 12 skills that students should be able to demonstrate knowledge of upon completion

### WEST COVENTRY SIXTH FORM

WEST COVENTRY SIXTH FORM West Coventry Academy SUBJECT TRANSITION BOOK Summer 2017 Mathematics STUDENT NAME: SCHOOL: This booklet has been prepared by maths staff for you to read and the work contained

### B.3 Solving Equations Algebraically and Graphically

B.3 Solving Equations Algebraically and Graphically 1 Equations and Solutions of Equations An equation in x is a statement that two algebraic expressions are equal. To solve an equation in x means to find

### Welcome to the most exciting math class in high school! There are three major tasks you have to accomplish over the summer:

Dear AP Calculus BC Students, Welcome to the most exciting math class in high school! There are three major tasks you have to accomplish over the summer:. Prepare psychologically: Each day repeat I love

### and Transitional Comprehensive Curriculum. Algebra II Unit 4: Radicals and the Complex Number System

01-1 and 01-14 Transitional Comprehensive Curriculum Algebra II Unit 4: Radicals and the Complex Number System Time Frame: Approximately three weeks Unit Description This unit expands student understanding

### Math 70 and 95 Master Syllabus Beginning and Intermediate Algebra, 5th ed., Miller, O Neill, Hyde with ALEKS.

Math 70 and 95 Master Syllabus 2017-2018 Course Coordinator: Tammy Nezol (tnezol@uoregon.edu) Textbook and ALEKS: Beginning and Intermediate Algebra, 5th ed., Miller, O Neill, Hyde with ALEKS. We have

### Review: Expressions and Equations

Review: Expressions and Equations Expressions Order of Operations Combine Like Terms Distributive Property Equations & Inequalities Graphs and Tables Independent/Dependent Variables Constant: a number

### Successful completion of the core function transformations unit. Algebra manipulation skills with squares and square roots.

Extension A: Circles and Ellipses Algebra ; Pre-Calculus Time required: 35 50 min. Learning Objectives Math Objectives Students will write the general forms of Cartesian equations for circles and ellipses,

### AP Calculus AB SUMMER ASSIGNMENT. Dear future Calculus AB student

AP Calculus AB SUMMER ASSIGNMENT Dear future Calculus AB student We are ecited to work with you net year in Calculus AB. In order to help you be prepared for this class, please complete the summer assignment.

### AP CALCULUS AB - Name: Summer Work requirement due on the first day of class SHOW YOUR BEST WORK. Requirements

AP CALCULUS AB - Name: Summer Work For students to successfully complete the objectives of the AP Calculus curriculum, the student must demonstrate a high level of independence, capability, dedication,

### Copy Material. Grade 8 Unit 7. Introduction to Irrational Numbers Using Geometry. Eureka Math. Eureka Math

Copy Material Grade 8 Unit 7 Introduction to Irrational Numbers Using Geometry Eureka Math Eureka Math Lesson 1 Name Date Lesson 1: The Pythagorean Theorem Exit Ticket 1. Determine the length of the unknown

### Alta Loma Junior High 8 th Grade Math

Alta Loma Junior High 8 th Grade Math Dear Parent(s): The following outline is being provided to better help you and your student to understand the current Common Core concepts of this trimester. Trimester

### 3.3 Real Zeros of Polynomial Functions

71_00.qxp 12/27/06 1:25 PM Page 276 276 Chapter Polynomial and Rational Functions. Real Zeros of Polynomial Functions Long Division of Polynomials Consider the graph of f x 6x 19x 2 16x 4. Notice in Figure.2

### Math 1320, Section 10 Quiz IV Solutions 20 Points

Math 1320, Section 10 Quiz IV Solutions 20 Points Please answer each question. To receive full credit you must show all work and give answers in simplest form. Cell phones and graphing calculators are

### Course Text. Course Description. Course Objectives. Course Prerequisites. Important Terms. StraighterLine Introductory Algebra

Introductory Algebra Course Text Dugopolski, Mark. Elementary Algebra, 6th edition. McGraw-Hill, 2009. ISBN 9780077224790 [This text is available as an etextbook at purchase or students may find used,

### Algebra 2 CP Final Exam Review

Algebra CP Final Exam Review Name: THIS PACKET IS INTENDED TO BE USED AS SUPPLEMENTAL REVIEW AND PRACTICE THAT REFLECT THE TOPICS WHICH WILL BE COVERED ON THE FINAL EXAM. IT SHOULD NOT BE USED AS YOUR

### Intermediate Algebra

Intermediate Algebra The purpose of this course is to strengthen students foundational conceptual and procedural skills in order to prepare students for college-and-career readiness. The course textbook,

### Introduction. So, why did I even bother to write this?

Introduction This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The review contains the occasional

### Solve by factoring and applying the Zero Product Property. Review Solving Quadratic Equations. Three methods to solve equations of the

Hartfield College Algebra (Version 2015b - Thomas Hartfield) Unit ONE Page - 1 - of 26 Topic 0: Review Solving Quadratic Equations Three methods to solve equations of the form ax 2 bx c 0. 1. Factoring

### Solve by factoring and applying the Zero Product Property. Review Solving Quadratic Equations. Three methods to solve equations of the

Topic 0: Review Solving Quadratic Equations Three methods to solve equations of the form ax 2 bx c 0. 1. Factoring the expression and applying the Zero Product Property 2. Completing the square and applying

### Algebra 2 with Trigonometry

Algebra 2 with Trigonometry This course covers the topics shown below; new topics have been highlighted. Students navigate learning paths based on their level of readiness. Institutional users may customize

### Chapter 2A - Solving Equations

- Chapter A Chapter A - Solving Equations Introduction and Review of Linear Equations An equation is a statement which relates two or more numbers or algebraic expressions. For example, the equation 6

### Fundamentals of Mathematics I

Fundamentals of Mathematics I Kent State Department of Mathematical Sciences Fall 2008 Available at: http://www.math.kent.edu/ebooks/10031/book.pdf August 4, 2008 Contents 1 Arithmetic 2 1.1 Real Numbers......................................................

### Algebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards

Algebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards Standard 2 : Number & Operations CLE 3103.2.1: CLE 3103.2.2: CLE 3103.2.3:

### Accuplacer College Level Math Study Guide

Testing Center Student Success Center Accuplacer Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these

### CHAPTER 1: Functions

CHAPTER 1: Functions 1.1: Functions 1.2: Graphs of Functions 1.3: Basic Graphs and Symmetry 1.4: Transformations 1.5: Piecewise-Defined Functions; Limits and Continuity in Calculus 1.6: Combining Functions

### Congratulations! You ve completed Practice Test 1! You re now ready to check your

Practice Test 1: Answers and Explanations Congratulations! You ve completed Practice Test 1! You re now ready to check your answers to see how you fared. In this chapter, I provide the answers, including

### Physics Motion Math. (Read objectives on screen.)

Physics 302 - Motion Math (Read objectives on screen.) Welcome back. When we ended the last program, your teacher gave you some motion graphs to interpret. For each section, you were to describe the motion

### AP CALCULUS BC Syllabus / Summer Assignment 2015

AP CALCULUS BC Syllabus / Summer Assignment 015 Name Congratulations! You made it to BC Calculus! In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work

A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Acute triangle A triangle in which all three angles are acute Addends The

### Unit 2 Notes Packet on Quadratic Functions and Factoring

Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a

### Westside Algebra 2 PreAP

Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for

### Square Roots and the Pythagorean Theorem Lesson Tutors with Vision Project. Spring 2008

The square root of a number, n, written below is the number that gives n when multiplied by itself. Square Roots and the Pythagorean Theorem Lesson Tutors with Vision Project Center for Teacher Certification

### Summer AP Assignment Coversheet Falls Church High School

Summer AP Assignment Coversheet Falls Church High School Course: AP Calculus AB Teacher Name/s: Veronica Moldoveanu, Ethan Batterman Assignment Title: AP Calculus AB Summer Packet Assignment Summary/Purpose:

### Shrine Catholic High School Required Summer Math Quiz. Designed for Students entering Algebra 2 & Honors Algebra 2

Shrine Catholic High School Required Summer Math Quiz Designed for Students entering Algebra & Honors Algebra Dear Parents and Students: Summer work, such as math packets and novel reading, can be useful

### Algebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA

Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully

### CALCULUS. Department of Mathematical Sciences Rensselaer Polytechnic Institute. May 8, 2013

Department of Mathematical Sciences Ready... Set... CALCULUS 3 y 2 1 0 3 2 1 0 1 x 2 3 1 2 3 May 8, 2013 ii iii Ready... Set... Calculus This document was prepared by the faculty of the Department of Mathematical

### Lesson 9: Radicals and Conjugates

Lesson 9: Radicals and Conjugates Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert

### Important Math 125 Definitions/Formulas/Properties

Exponent Rules (Chapter 3) Important Math 125 Definitions/Formulas/Properties Let m & n be integers and a & b real numbers. Product Property Quotient Property Power to a Power Product to a Power Quotient

### Algebra/Trigonometry Review Notes

Algebra/Trigonometry Review Notes MAC 41 Calculus for Life Sciences Instructor: Brooke Quinlan Hillsborough Community College ALGEBRA REVIEW FOR CALCULUS 1 TOPIC 1: POLYNOMIAL BASICS, POLYNOMIAL END BEHAVIOR,

### Define the word inequality

Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two

### Sail into Summer with Math! For Students Entering Algebra II

Sail into Summer with Math! For Students Entering Algebra II The Pyle Math Department requests that students review math skills over the summer. Reviewing core concepts helps students retain math knowledge