Galena Park ISD. Friday, September 9, 2016 (Due Date) Summer Assignment. Pre-AP Geometry. (Name)

Transcription

1 Summer Assignment (Name) Friday, September 9, 2016 (Due Date) Pre-AP Geometry

2 Summer Assignment: Pre-AP Geometry This assignment should serve as a review of the skills necessary for success in Pre-AP Geometry. Our expectation is that this review will keep you mathematically active during the summer; allowing you to identify possible Algebra weaknesses, and preparing you for the fun and challenging year ahead. Assignment Format The completed assignment should: Contain a cover page including: Name, Title, Algebra I Teacher s Name & Middle School Attended, and Date. Organize work using a separate page for each section. Be neat. Show your work on lined paper, numbering each problem. Box all answers. Tutorials will be available after school for extra help during the first two weeks of school. A quiz will be given over the included material during the third week of school. Help You may work with a classmate, peer, adult, or use other resources; however, each student must submit their own packet and each student is responsible for understanding the material contained therein. All work must be shown and directions must be followed. Part of the assignment requires access to the internet. If you do not have internet access at home, the City of Houston and Harris County public library provides access at no cost. Packet includes: 1. Algebra Review 2. Basic Geometry Review a. Shapes b. Internet component. Suggested Pacing: June: Parts 1, 2, 3; July: Parts 4, 5, 6; August: Parts 7 & 8 A copy of this assignment will be made available to students on the website: 1

3 1. Algebra Review: The Coordinate Plane Use this graph to answer the following questions. Name the coordinates of each point. 1. M 6. T 2. N 7. U 3. K 8. V 4. R 9. W 5. S 10. Q 11. Name all the points shown that lie on the x-axis. 12. Name all the points shown on the y-axis. 13. What is the x-coordinate of every point that lies on a vertical line through P? 14. Identify which of the following point(s) lie on a horizontal line through W? ( 2, 1), (2, 3), (1, 3), ( 2, 0), (0, 3), (2, 0) 15. Name the two points that both have a y-coordinate value of Name the points that are in more than one quadrant and identify which quadrants they are in. For each of the conditions below, create a point on the graph. Name that point with a capital printed letter and write the coordinate pair representing its location. 17. x < 3 y x > 4 y < x 1 y x 3 y < 6 2

4 2. Algebra Review: Solving Linear Equations and Inequalities Example: 4x 2(1 x) = 38 Example: 3(x + 1) > 12 4x 2 + 2x = 38 3x 3 > 12 6x 2 = 38 3x > 12 6x = 36 x < 4 x = 6 Solve each equation or inequality. Show all steps. Simplify and leave any fractional answer in improper format. Linear Equations 1. 2p + 5 = b = 2 + 5b 3. 4x x + 40 = (4x + 4) = x (x + 5) = 3(x 2) Linear Inequalities x 3(90 x) y > 2(90 y) 8. 6x 3(6 5x) 4(2 x) (8x 12) < 2 1 (2x 4) 10. (3x 1) + 7 > 3(x 5) + 4 3

5 3. Algebra Review: Solving Literal Equations Example: Given the perimeter of a rectangle, solve for w. P = 2l + 2w P 2l = 2l 2l + 2w P 2l = 2w P 2l = 2w 2 2 P 2l = w 2 Solve each equation for the given variable. 1. Perimeter of rectangle: P = 2w + 2l. Solve for l. 2. Volume of prism: V = lwh. Solve for w. 3. Surface area of sphere: S = 4πr 2. Solve for r. 4. Lateral area of cylinder: A = 2πrh. Solve for r. 5. Area of regular polygon: A = 2 1 ap. Solve for a. 6. Volume of cylinder: V = πr 2 h. Solve for h. 7. Area of triangle: A = 2 1 bh. Solve for h. 8. Circumference of circle: C = 2πr. Solve for r. 9. Volume of cone: V = 3 1 πr 2 h. Solve for r. 10. Area of trapezoid: A = 2 1 (b1 + b 2 )h. Solve for b 1. 4

6 4. Algebra Review: Quadratic Equations Factor the GCF: 1. 21x x x 3. 6x 4 + 8x x 2 Factor each expression completely into two binomials: 4. x x 2 + 6x x 2 5x + 6 Simplify the following expressions: 7. (x + 5) (x + 3) 8. (x 7) (2x + 1) 9. (x 9) (3x 1) Solve using the Quadratic Formula: The Quadratic Formula uses the a, b, and c from ax 2 + bx + c = 0, where a, b, and c are just numbers; they are the numerical coefficients. The formula is derived from the process of completing the square, and is formally stated as: For ax 2 + bx + c = 0, the value of x is given by: ± 2a 2 b b 4ac Leave your answers in simplest radical form x 2 3x 1 = x 2 3x 15 = x 2 = 5x 1 5

7 5. Algebra Review: Graphing Graph each system of linear equations on the graph provided. 1. y = 1 2x 2. y = 2x + 7 y = 5 + 4x x = x + 3y = 3 4. y = 5x y = 4 1 x 10x + 2y = 6 Use the slope formula to find the slope of the line containing each set of points. Find the y-intercept of each and write the equation of each line in slope intercept form. 5. (3, 6), ( 6, 0) 6. ( 7, 2), ( 1, 4) 7. (5, 1), (5, 4) 6

8 6. Algebra Review: Radical Expressions Simplifying Radicals - Radicals are in the simplest form when there are no perfect square factors inside the radical. (Simplified radicals cannot have a radical in the denominator or a fraction inside of the radical.) Simplify the following completely using perfect squares or factor trees. Do NOT use a calculator to find the decimal approximations for these square roots. Show all work. 1) 36 3) 400 2) 27 4) ) 9 6) Use the Pythagorean Theorem to find the missing side. Leave answers in simplest radical form. Do NOT give answers in decimal form. 7) 8) ) 10)

9 7. Geometry Review: Basic Figures For each geometric solid below, identify the following (if applicable): name of solid, number of vertices, number of edges, number of faces, how many bases it has, and the 2 dimensional shape of the base. 8

10 8. Internet Components Internet Component: In Pre-AP Geometry class, you will be expected to answer questions about geometry using complete sentences. Students need to be able to write about the math they are learning as well as completing problems. This exercise will allow you to practice this. Write each question and answer each thoroughly. Use your own words. Watch the video Mathematics - Investigating Geometry I: Geometry Around the World (link below) and answer the questions below using complete sentences. Source: 1. What is the meaning of the word geometry? 2. What was measured with the earliest use of geometry? 3. What Egyptian monuments still stand today after 4,000 years and are considered as masterpieces of straight-line geometry? What geometric shape led them to develop the calculations needed to create the monuments? 4. Identify the 3 most common types of geometry taught in schools today. 5. How many books did Euclid write and what were they called? 6. What two things did Euclid focus on using to make mathematical statements? 7. What do mathematicians call statements that have been proven to be true? 8. What is another name for coordinate geometry and who was it named after? 9. Identify the three types of transformations demonstrated in the video. Also, determine what a possible fourth transformation could be such that it would create similar figures instead of congruent figures like the three already named types. 10. Define the meaning of a conjecture. 9