Geometry Summer Homework

Instructions

1. Summer homework is due on the first day of class by 1:20 pm. This is meant to start you off to learn to read the textbook, to familiarize yourself with it, and to brush up on skills you will need this coming semester.
2. All work and thinking must be clearly shown. Problems answered without work will receive at most half credit. The examples in the textbook are good models to follow.
3. Complete your assignment as such:
   1. You may use wide-ruled or college-ruled lined paper or graph paper only. Please do not do work on blank paper or paper with only dots.
   2. Write and underline each part number.
   3. Start each new problem by writing the problem number on the left of the margin before writing your worked solutions. Your solutions must be in order, with each step on a separate line. For part I, leave at least 2–3 blank lines of space before you begin the next problem in the set. For parts II–III you may leave just 1–2 blank lines between problems.

Homework
Part I: Worked Problems

Use a separate sheet of notebook paper showing the work for each problem. Document the process used while solving each exercise or problem. Box or highlight your final answer on the notebook paper. These problems should be completed independently and without the use of technology beyond a hand-held calculator. (This includes the use of any AI or image search ability such as google lens or photomath).

****Answer all the questions below and turn them in on THE FIRST DAY of geometry class. 

1. Solve 3 – (2t + 5) = -12. (Solving equations in one or more steps)
2. Solve 5a – 15 + 9a = 3a + 29.
3. Solve y – 7 > 3 + 2y. (Solving linear inequalities)
4. Solve 15 + 6n < -33.

5. The figures below are made from toothpicks. Use this pattern to determine how many toothpicks are in Figure 10. 

   
   
6. Find the slope of the line through (-4, 2) and (5, 8). (The slope of a linear function)
7. Draw a triangle that has sides of lengths 3.6 cm and 5.2 cm and a 42° angle between these two sides.
8. A fence along a schoolyard is 250 ft long. There is a fence post every 10ft. How many fence posts are there?
9. Simplify (-15)². (Power and exponents)

10. Simplify 

    

    . (Square root and real numbers)

11. Evaluate the expression –x(y – 8)² for x = -2 and y = 5. (Evaluate expressions)
12. Simplify 4x – (2 – 3x) + 5. (Solve equations and simplify expressions)
13. Complete by filling in the blank:               0.25 km = _______ m (How to safely convert between units)
14. Complete by filling in the blank:               180 in. = ________ yd

15. Solve the system of equations: 

    

     (Solving systems of equations in two variables)

16. Solve the system of equations: 

    
17. Solve A = 4πr² for r. (Solve equations and simplify expressions)
18. Simplify the ratio 0.6 : 2.4. (Rates and ratios)
19. Simplify the ratio 18b² to 45b.
20. An athletic club has 248 members. Of these, 164 lift weights and 208 perform cardiovascular exercises regularly. All members do at least one of those activities. How many members do both? (Principle of inclusion and exclusion)
21. Solve |x| - 7 = 6. (Solving absolute value equations and inequalities)
22. Draw graphs of y = x² and y = -2x in the same coordinate plane. (Graphing quadratic equations)
23. Draw graphs of y = x² and y = x² + 3 in the same coordinate plane.
24. Solve x² + 6x -7 = 0 for x. (Use graphing to solve quadratic equations)
25. Maria gave one-half of her jelly beans to Carl. Carl gave one-third of those to Austin. Austin gave one-fourth of those to Carmen. If Carmen received two jelly beans, how many did Maria start with?
26. Write 5.9% as a decimal. (Proportions and percent)
27. Simplify 18% of 300. (Solving problems with percent)

28. Simplify 

    

     (Simplify radical expressions)

29. Simplify 

    

    .

30. A bag contains 4 blue marbles, 6 green marbles, and 2 red marbles. What is the probability of selecting a red marble? (Probability of events)
31. A bag contains 4 blue marbles, 6 green marbles, and 2 red marbles. A green marble is removed from the bag. What is the probability that the next marble selected will be blue?

Part II: Textbook Search Tool Practice
The aim of this exercise is to help you look up the meaning of the many new vocabulary words or properties that you will encounter throughout the course. The following properties or definitions can be found at the back of the book from pages 779 through 815.
State the page number on which the word or phrase can be located as well as the property or definition of each of the following:
Example: Contrapositive: The contrapositive of the conditional “if p, then q” is the conditional “if not q, then not p.” A conditional and its contrapositive always have the same truth value, p.786

1. Altitude
2. Centroid
3. Construction
4. Hexagon
5. Indirect Reasoning
6. Counterexample
7. Skew Lines
8. Theorem
9. Similar Solids
10. Conditional

Part III: Learning about your textbook

1. Every lesson begins with a section titled: “Check Skills You’ll Need”. In addition, after each new topic is presented within the lesson and example given, there is a “Quick Check” section that allows you to check if you understood the concept. Answers to both sections can be found in the back of your book under “Instant Check System Answers”(p. 816 – 829). To make sure you can find them in your book when you need them, find the answers to the following questions and write the page number where you find the answer: Example: Lesson 6–1 “Check Skills You’ll Need” #6: 1, p.822
   1. Lesson 10–4 Check Skills You’ll Need #5
   2. Lesson 8–6 Quick Check #2b
   3. Lesson 12–5 Check Skills You’ll Need #3
   4. Lesson 11–5 Quick Check #3a
2. Most of your homework will be even-numbered problems. Many odd-numbered problems have answers or even solutions in the back of the book under “Selected Answers”(p. 831 – 852). If you find yourself stuck on a problem or are unsure you got it right, you could find a similar, odd-numbered problem, solve it, and check if you got the right answer. This will help you to know if you are on the right track. To make sure you can find these in your book when you need them, find the answers to the following questions.
   Example: Lesson 6–1 #29: A, p. 839
   1. Lesson 2–3 #27
   2. Lesson 8–5 #9
   3. Lesson 12–3 #29
   4. Chapter 4 Review #38
3. As we have limited time in class, it is important to understand what each chapter and section will be discussing. You should be able to locate the chapter and section topics whether in the table of contents or, more importantly, within the pages of the chapter itself.
   Please locate the title or topic for the following chapters or sections. Include the page number:
   Example: Lesson 6–1: Classifying Quadrilaterals, p. 306 (or 306 – 311)
   1. Lesson 2–3
   2. Lesson 8–5
   3. Lesson 12–3
   4. Chapter 4
4. Additionally to locating the chapter and section titles and topics, you should also be able to locate within the textbook what the outcome of understanding (objectives) for each chapter and section should be. These objectives are a good checklist to think through as you are preparing for exams and checking you are ready (especially when turned into “I can” statements). Objectives can be found on the chapter title page, as well as the first page of each new section. For example, Chapter 1’s title page can be found on page 3 of the textbook.
   Please locate the objectives for each of the following chapters or sections. Include the page number:
   Example: Lesson 6–1: To define and classify special types of quadrilaterals, p. 306
   1. Lesson 2–3
   2. Lesson 8–5
   3. Chapter 4

Tips to be successful in ATYP Geometry!

ALWAYS prepare for your next class! When reading new sections to be discussed in class ~

• Pay attention to what the book calls “New Vocabulary.” Some words or concepts may be familiar (highlighted in yellow). The definition or usage in Geometry may be a little different than areas outside of mathematics or in science. For each new vocabulary word, think about how the concepts can be demonstrated in an shape or an example.
• Read through the introduction of each new section. Study the processes in each example. Come to class with questions about what you’ve read or about specific problems in homework (can also email during week before class). After the school year starts, you will want to exchange phone numbers so you can also ask classmates to study groups or to work together over the phone.
• ALWAYS …Bring completed homework to class along with any work done (show your work!), stapled together, in order by section, put your name and due date on top of the first page, initials thereafter. If it took more than one step in your head, then SHOW YOUR WORK and circle the answer reached. Remember: neatness counts!