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 that will support you in all future advanced mathematics courses. Since you will be taking geometry after successful completion of Algebra I, the Geometry Preparation Packet contains review material of the algebraic concepts, skills, and procedures that should be mastered BEFORE entering Geometry in the fall. Essentially, this packet provides a review of the major algebra topics as well as a preview of geometric topics. The sections are based on the Achieve ADP Algebra I End- of- Course Exam Content Standards and the Common Core State Standards (CCSS). The textbooks, McDougal Littell Algebra I (2004) and Glencoe Geometry (2005) are available online and additional support material is available on the Monroe website. Both textbook links are provided below: http://cphs.dadeschools.net/departments/mathematics/ebooks/alg1mcd/source/ http://www.glencoe.com/sec/math/geometry/geo/geo_05/index.php/nj/2006 o USERNAME: GEOM05 *PASSWORD: N6despeZ Alternate online resources are available at: http://www.khanacademy.org/ http://www.wolframalpha.com/examples/ Math.html http://tinyurl.com/youtube- mthsgeometry The Monroe Township library also has copies of the algebra and geometry materials used in our courses. This practice problem packet is the only formal review of the concepts, procedures, and skills that you will have before beginning your geometry course. Your teacher will expect you to have mastered all topics included here. This collection of problems will identify those concepts that you have mastered as well as those you will need to practice and review. You are expected to seek extra help immediately on those concepts with which you have not demonstrated proficiency. Be resourceful use the online resources provided on the webpage! You are expected to seek extra help immediately on those concepts with which you have not demonstrated proficiency. Be resourceful use the online resources! Problems here are very representative of the types of items you will need to have mastered BEFORE geometry so we strongly encourage that you include it in your summer festivities! Good luck and enjoy! J Page 1
Achieve ADP Algebra 1 End- of- Course Exam Content Standards O: Operations on Numbers and Expressions N: Non- linear Relationships O1. Number Sense and Operations N1. Non- linear Functions O1.a Reasoning with real numbers N1.a Representing quadratic functions in multiple ways O1.b Using ratios, rates, and proportions N1.b Distinguishing between function types O1.c Using numerical exponential expressions N1.c Using quadratic models O1.d Using numerical radical expressions O2. Algebraic Expressions N2. Non- linear Equations O2.a Using algebraic exponential N2.a Solving literal equations expressions O2.b Operating with polynomial expressions N2.b Solivng quadratic equations O2.c Factoring polynomial expressions O2.d Using algebraic radical expressions L: Linear Relationships D: Data, Statistics, and Probability L1. Number Sense and Operations D1: Data and Statistical Analysis L1.a Representing linear functions in D1.a Interpreting linear trends in data multiple ways L1.b Analyzing linear function D1.b Comparing data using summary statistics L1.c Graphing linear functions (including absolute value) D1.c Evaluating data- based reports in the media L1.d Using linear models L2. Algebraic Expressions D2: Probability L2.a Solving linear equations and D2.a Using counting principles inequalities L2.b Solving equations involving absolute D2.b Determining probability value L2.c Graphing linear inequalities L2.d Solving systems of linear equations L2.e Modeling with single variable, linear equations, one- or two- variable inequalities or systems of equations Page 2
COMMON CORE STATE STANDARDS (CCSS): Geometry CONGRUENCE o Experiment with transformations in the plane o Understand congruence in terms of rigid motions o Prove geometric theorems o Make geometric constructions SIMILARITY, RIGHT TRIANGLES, & TRIGONOMETRY o Understand similarity in terms of similarity transformations o Prove theorems involving similarity o Define trigonometric ratios and solve problems involving right triangles o Apply trigonometry to general triangles CIRCLES o Understand and apply theorems about circles o Find arc length and areas of sectors of circles EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS o Translate between the geometric description and the equation for a conic section o Use coordinates to prove simple geometric theorems algebraically GEOMETRIC MEASUREMENT & DIMENSION o Explain volume formulas and use them to solve problems o Visualize relationships between two- dimensional and three- dimensional objects MODELING WITH GEOMETRY o Apply geometric concepts in modeling situations Page 3
**SHOW ALL WORK** Solve each equation given in #1-5. Write your answer in the blank provided. Leave answer as an improper fraction when necessary. 1. 3x 4 = 17 ANSWER: 2. 5(2x 8) = 80 ANSWER: 3. 1 ( 4x 16) = 84 ANSWER: 2 4. 7x 2 = 3x +14 ANSWER: 5. 6x 2 + 4x +14 = 180 ANSWER: Page 4
Determine the area and perimeter of each figure described in #6-7. Do not forget your units. 6. RECTANGLE with length 3.6 cm and width 4.2 cm AREA: PERIMETER: 7. SQUARE with sides of length 9 mm AREA: PERIMETER: Using the given information, determine area and circumference for #8-9. Leave your answer in terms of π. 8. Area and circumference of a circle with radius 9 inches. AREA: CIRCUMFERENCE: 9. Area and circumference of a circle with diameter 12 centimeters. AREA: CIRCUMFERENCE: Page 5
Use the Pythagorean Theorem to determine the missing side in questions 10-12. Leave in simplest radical form. 10. 15 x 20 x = 11. 21 x 13 x = 12. 9 5 10 x x = 13. Find the slope of the line containing (- 2, - 8) and (- 1, 0). SLOPE: 14. Find the slope of the line perpendicular to the line containing (- 3, 2) and (4, - 1). SLOPE: Page 6
15. The complement of a 60 angle is. 16. The supplement of a 100 angle is. 17. Find x and the measure of the missing angle. 40 20 3x x = Angle = 18. State the difference between a line and a line segment. You may write sentences or draw diagrams. Predict the next number in the sequence given in #19-20. 19. - 5, - 2, 4, 13, 20. 48, 16, 16 3, 16 9, Page 7
Use for #21-24: Quadrilateral FGHJ has vertices F(- 4, - 1), G(- 2, - 5), H(4, - 2), and J(2, 2). 21. Graph the quadrilateral below. A rectangle is a quadrilateral with four right angles and both pairs of opposite sides parallel and congruent to each other. You will determine whether FGHJ is a rectangle. 22. Find the slopes of all four sides and explain their significance in terms of the definition of rectangle. Slope FJ = Slope GH = Slope JH = Slope FG = 23. Find the lengths if all four sides and explain their significance. FJ = GH = JH = FG = 24. Do you think FGHJ is a rectangle? Explain why or why not. Page 8
25. Everyday, Michael goes for a run through the park. The park is shaped like a square. He follows the path shown by the points. About how far does Michael run? -------------200m------------- 26. Julia wants to paint two rectangular walls of her bedroom. One bedroom wall is 15 feet long and 8 feet high. The other wall is 12 feet long and 8 feet high. She wants to put two coats of paint on the walls. She knows 1 gallon of paint will cover about 350 square feet of a wall. Will one gallon of paint be enough? Show all of your work and explain your answer below. Page 9
27. Triangle ABC is shown in the xy- plane. The triangle will be rotated 180 degrees clockwise around the point (0, 0) to create triangle A B C. Draw the new triangle A B C on the coordinate plane. 28. Triangle ABC is show in the xy- plane. The triangle will be reflected over the y- axis. Draw the new triangle A B C on the coordinate plane. Page 10
29. Using the diagram below, describe the transformation that occurs from triangle ABC to triangle A B C by answering the questions below. a) What kind of transformation occurred? b) How do you know? c) Write a rule using arrow notation depicting the transformation. 30. Simplify the following radicals. Leave your answer in simplest radical form. a) 72 b) 40 c) 288 d) 800 Page 11