When solving application problems, you should have some procedure that you follow (draw a diagram, define unknown values, set-up equations, solve)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "When solving application problems, you should have some procedure that you follow (draw a diagram, define unknown values, set-up equations, solve)"

Transcription

1 When solving application problems, you should have some procedure that you follow (draw a diagram, define unknown values, set-up equations, solve) Once again when solving applied problems I will include questions in my notes to help set-up equations. Keep in mind that the questions below in red will not appear in the homework, or on quizzes and exams; these are simply questions that you should be asking yourself when you see problems like these in order to help get equations that you can solve. Also keep in mind the various method for solving quadratic equations: - solve by factoring o write the equation as a polynomial set equal to zero, factor, use Zero Factor Theorem - solve as a special quadratic equation (perfect squares) o isolate the perfect square and take the square root of both sides of the equation - solve by completing the square o divide by the leading coefficient, isolate the constant, add half the square of the coefficient of x to both sides of the equation, factor, solve as a special quadratic equation - solve using the quadratic formula o identify a, b, c, plug-in to the formula, simplify completely

2 Example 1: A rock is thrown directly upward with an initial velocity of 96 feet per second from a cliff 200 feet above a beach. The number of feet above the ground (f), after t seconds, is given by the equation f = 16t t a. When will the rock be 328 feet above the ground? Which variable will 328 replace in the equation f = 16t t + 200, feet above the ground f or time t? b. When will the rock hit the ground? (round to the nearest hundredth of a second). When the rock is on the ground, what is the value of f?

3 Example 2: A 12 x 15 inch picture is mounted on a wall and surrounded by a border of uniform width. The total area of the picture with the border around it is 304 in 2. What is the width of just the border? What is the width of the border? (if you don t know, assign a variable to represent this value) Draw a diagram of the picture with the border around it (a rectangle inside of another rectangle), and list the dimensions of the inner rectangle and the dimensions of the outer rectangle. Write an equation for the total area of the picture with the border around it, and use that equation to solve for your variable. total width total length = total area

4 Example 3: The blueprints for a new bathroom show a raised, rectangular bathtub with an area of 9 ft 2. The blueprints show that the raised tub will be surrounded by tile on all four sides; half a foot of tile on each side of the rectangle tub as well as at the bottom of the rectangle, and 1 foot of tile at the top of the rectangle. The total length of the raised tub including the tile will be twice the total width. Find the dimensions of the bathtub only. Draw a diagram of the bathtub and the surrounding tile (a rectangle inside of another rectangle), and list the dimensions of the inner rectangle and the dimensions of the outer rectangle. Write an equation for the area of the bathtub, and use that equation to solve for your variable. length of tub width of tub = area of tub

5 Example 4: A gardener plans to enclose a rectangular region using fencing on three sides and part of a shed on the fourth side. The side parallel to the shed needs to be twice the length of an adjacent side. If the area of the region is 6050 ft 2, how many feet of fencing should be purchased? Draw a diagram of the region, and list the length of each side. Write an equation for the area of the rectangular region. length of the region width of the region = area

6 Example 5: A family plans to have the hardwood floors in their square dining room re-finished, and new baseboards installed. The cost of refinishing the hardwood floors is $4.50 per square foot and the cost of purchasing and installing the new baseboard is $12.00 per linear foot. If the family paid $1,224, what are the dimensions their dining room (width and length)? Draw a diagram of the square dining room and labels the sides. (if you don t know the side length, assign a variable to represent this value) The floor represent the area of the room, so write an equation for the cost to re-finish the hardwood floors based on the area of the room. The baseboard represent the perimeter of the room, so write an equation for the cost to install new baseboards based on the perimeter of the room. Write an equation for the total cost of the job, and use that equation to solve for your variable. cost of floors + cost of baseboard = total cost

7 Example 6: A rectangular piece of cardboard is 2 inches longer than it is wide. From each corner, a 2 2 inch square is cut out and the flaps are then folded up to form an open box. If the volume of the box is 96 in 3, find the length and width of the original piece of cardboard. What is the width of the rectangular piece of cardboard? (if you don t know, assign a variable to represent this value) What is the length of the rectangular piece of cardboard? (remember that the length is 2 inches more than the width) Draw a diagram of the rectangular piece of cardboard and list its dimensions. Then draw the 2 2 inch squares in each corner and the flaps, and list the dimensions of the box. Keep in mind that the width and length of the box will be LESS than the width and length of the cardboard. Write an equation for the total volume of the box, and use that equation to solve for your variable. box width box length box height = box volume

8 Example 7: Two trains leave a station at 11:00am. One train travels north at a rate of 45 mph and another travels east at a rate of 60 mph. Assuming they do not stop, at what time will the trains be 200 miles apart? Draw a diagram of the distances traveled by each train, and the distance between them. This should produce a right triangle, which means we can use the Pythagorean Theorem to write an equation in terms of the length (distance) of each side. (distance traveled north ) 2 + (distance traveled east) 2 = (distance between them) 2

9 Answers to Exercises: 1a. t = 2, 4 seconds ; 1b. t = 7.64 seconds ; 2. 2 inches ; 3. 2 ft 4.5ft ; feet ; ft 12 ft ; ; 7. 1: 40pm ;

Sect 6.7 - Solving Equations Using the Zero Product Rule

Sect 6.7 - Solving Equations Using the Zero Product Rule Sect 6.7 - Solving Equations Using the Zero Product Rule 116 Concept #1: Definition of a Quadratic Equation A quadratic equation is an equation that can be written in the form ax 2 + bx + c = 0 (referred

More information

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square 9. Solving Quadratic Equations by Completing the Square 9. OBJECTIVES 1. Solve a quadratic equation by the square root method. Solve a quadratic equation by completing the square. Solve a geometric application

More information

12) 13) 14) (5x)2/3. 16) x5/8 x3/8. 19) (r1/7 s1/7) 2

12) 13) 14) (5x)2/3. 16) x5/8 x3/8. 19) (r1/7 s1/7) 2 DMA 080 WORKSHEET # (8.-8.2) Name Find the square root. Assume that all variables represent positive real numbers. ) 6 2) 8 / 2) 9x8 ) -00 ) 8 27 2/ Use a calculator to approximate the square root to decimal

More information

QUADRATIC WORD PROBLEMS

QUADRATIC WORD PROBLEMS MPM 2DI: 2010-2011 UNIT 6 QUADRATIC WORD PROBLEMS Date Pages Text Title Practice Day 3: Tue Feb 22 Day 4: Wed Feb 23 2-3 Quadratic Word Problems Handout Day 1: Thu Feb 24 Day 2: Fri Feb 25 4-5 4.6 Quadratic

More information

7.2 Quadratic Equations

7.2 Quadratic Equations 476 CHAPTER 7 Graphs, Equations, and Inequalities 7. Quadratic Equations Now Work the Are You Prepared? problems on page 48. OBJECTIVES 1 Solve Quadratic Equations by Factoring (p. 476) Solve Quadratic

More information

MAT 080-Algebra II Applications of Quadratic Equations

MAT 080-Algebra II Applications of Quadratic Equations MAT 080-Algebra II Applications of Quadratic Equations Objectives a Applications involving rectangles b Applications involving right triangles a Applications involving rectangles One of the common applications

More information

Tallahassee Community College PERIMETER

Tallahassee Community College PERIMETER Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

More information

Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the

More information

Many Word problems result in Quadratic equations that need to be solved. Some typical problems involve the following equations:

Many Word problems result in Quadratic equations that need to be solved. Some typical problems involve the following equations: Many Word problems result in Quadratic equations that need to be solved. Some typical problems involve the following equations: Quadratic Equations form Parabolas: Typically there are two types of problems:

More information

MATH 100 PRACTICE FINAL EXAM

MATH 100 PRACTICE FINAL EXAM MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number

More information

Review Exercise Set 3

Review Exercise Set 3 Review Eercise Set 3 Eercise 1: The larger of two positive numbers is greater than the smaller. Find the two numbers if their product is 63. Eercise : The length of a rectangle is 4 inches less than twice

More information

Rectangle Square Triangle

Rectangle Square Triangle HFCC Math Lab Beginning Algebra - 15 PERIMETER WORD PROBLEMS The perimeter of a plane geometric figure is the sum of the lengths of its sides. In this handout, we will deal with perimeter problems involving

More information

MATH 90 CHAPTER 6 Name:.

MATH 90 CHAPTER 6 Name:. MATH 90 CHAPTER 6 Name:. 6.1 GCF and Factoring by Groups Need To Know Definitions How to factor by GCF How to factor by groups The Greatest Common Factor Factoring means to write a number as product. a

More information

Solving Quadratic Equations

Solving Quadratic Equations 9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation

More information

Review Test 4. 1. Simplify: 6 7 2 7. 93 25y xy. 93 25y xy. C) y. D) xy E) None of the above. 2. Simplify: Page 1

Review Test 4. 1. Simplify: 6 7 2 7. 93 25y xy. 93 25y xy. C) y. D) xy E) None of the above. 2. Simplify: Page 1 Review Test 4. Simplify: 6 7 7 x xy 5xy 6x 9 5y xy 9 5y xy 9x 5y y 9y 5 xy. Simplify: 5 5 c c5 c 5 ( c)( c5) 0c 5 ( c)( c5) 0c 0 ( c)( c5) 0c 5 ( c)( c5) 0c 5 ( c)( c5) Page . Simplify: r r 9 r 4r 9 r

More information

2.3 Maximum and Minimum Applications

2.3 Maximum and Minimum Applications Section.3 155.3 Maximum and Minimum Applications Maximizing (or minimizing) is an important technique used in various fields of study. In business, it is important to know how to find the maximum profit

More information

Sect 9.5 - Perimeters and Areas of Polygons

Sect 9.5 - Perimeters and Areas of Polygons Sect 9.5 - Perimeters and Areas of Polygons Ojective a: Understanding Perimeters of Polygons. The Perimeter is the length around the outside of a closed two - dimensional figure. For a polygon, the perimeter

More information

SECTION 1-6 Quadratic Equations and Applications

SECTION 1-6 Quadratic Equations and Applications 58 Equations and Inequalities Supply the reasons in the proofs for the theorems stated in Problems 65 and 66. 65. Theorem: The complex numbers are commutative under addition. Proof: Let a bi and c di be

More information

LESSON 10 GEOMETRY I: PERIMETER & AREA

LESSON 10 GEOMETRY I: PERIMETER & AREA LESSON 10 GEOMETRY I: PERIMETER & AREA INTRODUCTION Geometry is the study of shapes and space. In this lesson, we will focus on shapes and measures of one-dimension and two-dimensions. In the next lesson,

More information

Characteristics of the Four Main Geometrical Figures

Characteristics of the Four Main Geometrical Figures Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

More information

Chapter 8. Quadratic Equations and Functions

Chapter 8. Quadratic Equations and Functions Chapter 8. Quadratic Equations and Functions 8.1. Solve Quadratic Equations KYOTE Standards: CR 0; CA 11 In this section, we discuss solving quadratic equations by factoring, by using the square root property

More information

Section 2-5 Quadratic Equations and Inequalities

Section 2-5 Quadratic Equations and Inequalities -5 Quadratic Equations and Inequalities 5 a bi 6. (a bi)(c di) 6. c di 63. Show that i k, k a natural number. 6. Show that i k i, k a natural number. 65. Show that i and i are square roots of 3 i. 66.

More information

Pizza! Pizza! Assessment

Pizza! Pizza! Assessment Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the

More information

Mathematical Modeling and Optimization Problems Answers

Mathematical Modeling and Optimization Problems Answers MATH& 141 Mathematical Modeling and Optimization Problems Answers 1. You are designing a rectangular poster which is to have 150 square inches of tet with -inch margins at the top and bottom of the poster

More information

A.G.1: Compositions of Poygons and Circles 2: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle

A.G.1: Compositions of Poygons and Circles 2: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle A.G.1: Compositions of Poygons and Circles 2: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle 1 In the accompanying figure, ACDH and BCEF are rectangles,

More information

Area Long-Term Memory Review Review 1

Area Long-Term Memory Review Review 1 Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter

More information

Applications of the Pythagorean Theorem

Applications of the Pythagorean Theorem 9.5 Applications of the Pythagorean Theorem 9.5 OBJECTIVE 1. Apply the Pythagorean theorem in solving problems Perhaps the most famous theorem in all of mathematics is the Pythagorean theorem. The theorem

More information

Covering and Surrounding: Homework Examples from ACE

Covering and Surrounding: Homework Examples from ACE Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:

More information

Sample Problems. Practice Problems

Sample Problems. Practice Problems Lecture Notes Quadratic Word Problems page 1 Sample Problems 1. The sum of two numbers is 31, their di erence is 41. Find these numbers.. The product of two numbers is 640. Their di erence is 1. Find these

More information

Solving Geometric Applications

Solving Geometric Applications 1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas

More information

POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

More information

Law of Cosines. If the included angle is a right angle then the Law of Cosines is the same as the Pythagorean Theorem.

Law of Cosines. If the included angle is a right angle then the Law of Cosines is the same as the Pythagorean Theorem. Law of Cosines In the previous section, we learned how the Law of Sines could be used to solve oblique triangles in three different situations () where a side and two angles (SAA) were known, () where

More information

Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

More information

6.4 Factoring Polynomials

6.4 Factoring Polynomials Name Class Date 6.4 Factoring Polynomials Essential Question: What are some ways to factor a polynomial, and how is factoring useful? Resource Locker Explore Analyzing a Visual Model for Polynomial Factorization

More information

Formulas for Area Area of Trapezoid

Formulas for Area Area of Trapezoid Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet

More information

Solving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form

Solving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving

More information

Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.

Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. 42. The sum of the measures of the angles of a triangle is 180. Therefore, The sine of an angle

More information

Measure the side of the figure to the nearest centimeter. Then find the perimeter. 1.

Measure the side of the figure to the nearest centimeter. Then find the perimeter. 1. Measure the side of the figure to the nearest centimeter. Then find the perimeter. 1. a. 3 cm b. 6 cm c. 8 cm d. 9 cm 2. a. 4 cm b. 6 cm c. 8 cm d. 10 cm Powered by Cognero Page 1 Find the perimeter of

More information

COMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh

COMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure.

CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. CALCULATING PERIMETER WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. HOW DO WE CALCULATE PERIMETER? The formula one can use to calculate perimeter depends on the type of

More information

Applications for Triangles

Applications for Triangles Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given

More information

Imperial Length Measurements

Imperial Length Measurements Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading

More information

1.1 Practice Worksheet

1.1 Practice Worksheet Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)

More information

A Resource for Free-standing Mathematics Qualifications

A Resource for Free-standing Mathematics Qualifications To find a maximum or minimum: Find an expression for the quantity you are trying to maximise/minimise (y say) in terms of one other variable (x). dy Find an expression for and put it equal to 0. Solve

More information

Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

More information

1 Math 116 Supplemental Textbook (Pythagorean Theorem)

1 Math 116 Supplemental Textbook (Pythagorean Theorem) 1 Math 116 Supplemental Textbook (Pythagorean Theorem) 1.1 Pythagorean Theorem 1.1.1 Right Triangles Before we begin to study the Pythagorean Theorem, let s discuss some facts about right triangles. The

More information

a) x 2 8x = 25 x 2 8x + 16 = (x 4) 2 = 41 x = 4 ± 41 x + 1 = ± 6 e) x 2 = 5 c) 2x 2 + 2x 7 = 0 2x 2 + 2x = 7 x 2 + x = 7 2

a) x 2 8x = 25 x 2 8x + 16 = (x 4) 2 = 41 x = 4 ± 41 x + 1 = ± 6 e) x 2 = 5 c) 2x 2 + 2x 7 = 0 2x 2 + 2x = 7 x 2 + x = 7 2 Solving Quadratic Equations By Square Root Method Solving Quadratic Equations By Completing The Square Consider the equation x = a, which we now solve: x = a x a = 0 (x a)(x + a) = 0 x a = 0 x + a = 0

More information

Veterans Upward Bound Algebra I Concepts - Honors

Veterans Upward Bound Algebra I Concepts - Honors Veterans Upward Bound Algebra I Concepts - Honors Brenda Meery Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org Chapter 6. Factoring CHAPTER

More information

Hiker. A hiker sets off at 10am and walks at a steady speed for 2 hours due north, then turns and walks for a further 5 hours due west.

Hiker. A hiker sets off at 10am and walks at a steady speed for 2 hours due north, then turns and walks for a further 5 hours due west. Hiker A hiker sets off at 10am and walks at a steady speed for hours due north, then turns and walks for a further 5 hours due west. If he continues at the same speed, what s the earliest time he could

More information

Perimeter, Circumference, Area and Ratio Long-Term Memory Review

Perimeter, Circumference, Area and Ratio Long-Term Memory Review Review 1 1. Which procedure is used to find the perimeter of any polygon? A) Add all the lengths B) Multiply length times width ( l w ) C) Add only one length and one width D) Multiply all of the lengths

More information

Each pair of opposite sides of a parallelogram is congruent to each other.

Each pair of opposite sides of a parallelogram is congruent to each other. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

More information

Perimeter. 14ft. 5ft. 11ft.

Perimeter. 14ft. 5ft. 11ft. Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine

More information

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left. The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

More information

11-4 Areas of Regular Polygons and Composite Figures

11-4 Areas of Regular Polygons and Composite Figures 1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

More information

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial

More information

Factoring Polynomials

Factoring Polynomials UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

More information

Applications of Quadratic Functions Word Problems ISU. Part A: Revenue and Numeric Problems

Applications of Quadratic Functions Word Problems ISU. Part A: Revenue and Numeric Problems Mr. Gardner s MPMD Applications of Quadratic Functions Word Problems ISU Part A: Revenue and Numeric Problems When ou solve problems using equations, our solution must have four components: 1. A let statement,

More information

Quadratics - Rectangles

Quadratics - Rectangles 9.7 Quadratics - Rectangles Objective: Solve applications of quadratic equations using rectangles. An application of solving quadratic equations comes from the formula for the area of a rectangle. The

More information

Inv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.

Inv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units. Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE

More information

Homework from Section Find two positive numbers whose product is 100 and whose sum is a minimum.

Homework from Section Find two positive numbers whose product is 100 and whose sum is a minimum. Homework from Section 4.5 4.5.3. Find two positive numbers whose product is 100 and whose sum is a minimum. We want x and y so that xy = 100 and S = x + y is minimized. Since xy = 100, x = 0. Thus we have

More information

Park Forest Math Team. Meet #5. Algebra. Self-study Packet

Park Forest Math Team. Meet #5. Algebra. Self-study Packet Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number

More information

Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

More information

Tennessee Department of Education

Tennessee Department of Education Tennessee Department of Education Task: Pool Patio Problem Algebra I A hotel is remodeling their grounds and plans to improve the area around a 20 foot by 40 foot rectangular pool. The owner wants to use

More information

A Quick Algebra Review

A Quick Algebra Review 1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals

More information

called and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles?

called and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles? Factoring Reporting Category Topic Expressions and Operations Factoring polynomials Primary SOL A.2c The student will perform operations on polynomials, including factoring completely first- and second-degree

More information

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR! DETAILED SOLUTIONS AND CONCEPTS - SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST

More information

Algebra II A Final Exam

Algebra II A Final Exam Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.

More information

Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder).

Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder). Math 50, Chapter 8 (Page 1 of 20) 8.1 Common Factors Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder). Find all the factors of a. 44 b. 32

More information

10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED

10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations

More information

Calculus for Business Key- Optimization Word Problems Date:

Calculus for Business Key- Optimization Word Problems Date: Calculus for Business Key- Optimization Word Problems Name: Date: Mixed Problem Set- Optimization 1. A box with an open top and a square base is to have a surface area of 108 square inches. Determine the

More information

b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

More information

A.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it

A.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply

More information

Pre-Algebra Lesson 6-1 to 6-3 Quiz

Pre-Algebra Lesson 6-1 to 6-3 Quiz Pre-lgebra Lesson 6-1 to 6-3 Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the area of the triangle. 17 ft 74 ft Not drawn to scale a. 629 ft

More information

Area and Circumference

Area and Circumference 4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert

More information

Integrated Algebra: Geometry

Integrated Algebra: Geometry Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

More information

Factoring and Applications

Factoring and Applications Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the

More information

Area and Perimeter. Name: Class: Date: Short Answer

Area and Perimeter. Name: Class: Date: Short Answer Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and

More information

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice. Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite

More information

Square Roots and the Pythagorean Theorem

Square Roots and the Pythagorean Theorem 4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate

More information

17.2 Surface Area of Prisms and Cylinders

17.2 Surface Area of Prisms and Cylinders Name Class Date 17. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Explore G.11.C Apply the formulas for the total and lateral surface

More information

Florida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District

Florida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve

More information

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min. Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

More information

Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice. Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

More information

Answer Key for the Review Packet for Exam #3

Answer Key for the Review Packet for Exam #3 Answer Key for the Review Packet for Eam # Professor Danielle Benedetto Math Ma-Min Problems. Show that of all rectangles with a given area, the one with the smallest perimeter is a square. Diagram: y

More information

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object.

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a three-dimensional

More information

Perimeter is the length of the boundary of a two dimensional figure.

Perimeter is the length of the boundary of a two dimensional figure. Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose

More information

STUDENT NAME: GRADE 10 MATHEMATICS

STUDENT NAME: GRADE 10 MATHEMATICS STUENT NME: GRE 10 MTHEMTIS dministered October 2009 Name: lass: Multiple hoice Identify the choice that best completes the statement or answers the question. 1 The sides of squares can be used to form

More information

10 7, 8. 2. 6x + 30x + 36 SOLUTION: 8-9 Perfect Squares. The first term is not a perfect square. So, 6x + 30x + 36 is not a perfect square trinomial.

10 7, 8. 2. 6x + 30x + 36 SOLUTION: 8-9 Perfect Squares. The first term is not a perfect square. So, 6x + 30x + 36 is not a perfect square trinomial. Squares Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it. 1.5x + 60x + 36 SOLUTION: The first term is a perfect square. 5x = (5x) The last term is a perfect

More information

MATD 0390 - Intermediate Algebra Review for Pretest

MATD 0390 - Intermediate Algebra Review for Pretest MATD 090 - Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: - - + [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x +

More information

Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

More information

Math 10 - Unit 3 Final Review - Numbers

Math 10 - Unit 3 Final Review - Numbers Class: Date: Math 10 - Unit Final Review - Numbers Multiple Choice Identify the choice that best answers the question. 1. Write the prime factorization of 60. a. 2 7 9 b. 2 6 c. 2 2 7 d. 2 7 2. Write the

More information

Calculating Perimeter

Calculating Perimeter Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle

More information

Review Sheet for Third Midterm Mathematics 1300, Calculus 1

Review Sheet for Third Midterm Mathematics 1300, Calculus 1 Review Sheet for Third Midterm Mathematics 1300, Calculus 1 1. For f(x) = x 3 3x 2 on 1 x 3, find the critical points of f, the inflection points, the values of f at all these points and the endpoints,

More information

Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:

Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams: Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of

More information

1.3 Algebraic Expressions

1.3 Algebraic Expressions 1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,

More information

MA107 Precalculus Algebra Exam 2 Review Solutions

MA107 Precalculus Algebra Exam 2 Review Solutions MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

More information

Algebra 2 Chapter 5 Practice Test (Review)

Algebra 2 Chapter 5 Practice Test (Review) Name: Class: Date: Algebra 2 Chapter 5 Practice Test (Review) Multiple Choice Identify the choice that best completes the statement or answers the question. Determine whether the function is linear or

More information

Area of Parallelograms (pages 546 549)

Area of Parallelograms (pages 546 549) A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

More information