Welcome to Pre-AP Geometry Summer Homework Congratulations, you have qualified to be enrolled in Pre-AP Geometry. This class is a rigorous, 10 th grade level mathematics class. This class requires summer homework. The summer homework consists of problems covering 6 th, 7 th, 8 th, and Algebra concepts. You are expected to organize your time and complete the questions over the span of your summer vacation, not at the last minute. Take time to factor in vacations and other activities you have planned. We do not want to interfere with your vacation, but to keep you up to date with your current level of mathematics. You may look up examples on the internet, phone a friend, or even ask me. Simply giving up is not an option. You must be willing to dig a little bit and stretch your abilities as far as possible in order to be successful in an advanced mathematics class. The following guidelines will be followed: 1) SHOW ALL work, in a neat and organized manner. 2) Guess and Check is not considered showing your work. 3) Calculators should NOT be used on this assignment. All answers must be exact. 4) On the first day of class you will have the opportunity to ask questions. 5) The problems will be due the following class. 6) A summer homework assessment will be given on the second day of class. 7) There will be NO EXTENSIONS! This assignment can also be accessed through the Moore Home Page. Thank you and happy calculating! Moore MST Geometry Teacher Tamara Bowers Tamara.Bowers@tylerisd.org
PreAP/IB Geometry-Summer Math Name_ Block The following is a list of terms and definitions that you should know. Match the term on the right with the definition on the left by placing the letter in the blank. None will be used more than once. 1. Two points and all the points between them that lie on the line containing A. scalene triangle the two points. 2. Part of a line with an endpoint that extends endlessly in one direction. B. perpendicular lines 3. Two noncollinear rays with a common endpoint. C. line segment 4. The common endpoint of two rays that form an angle. D. obtuse angle 5. A segment from the center of a circle to any point on the circle. E. quadrilateral 6. An angle whose measure is 90º. F. acute angle 7. The point that divides a segment into two congruent segments. G. parallel lines 8. Lines that intersect to form right angles. H. octagon 9. An angle whose measure is between 0º and 90º. I. obtuse triangle 10. A ray that divides an angle into two congruent angles. J. vertex 11. A chord that is drawn through the center of a circle. K. pentagon 12. An angle whose measure is between 90º and 180º. L. right angle 13. Lines in the same plane that never intersect. M. ray 14. A pair of angles whose sum is 90º. N. decagon 15. A polygon with exactly four sides. O. angle bisector 16. A triangle in which all three angles measure less than 90º. P. regular polygon 17. A polygon with exactly ten sides. Q. right triangle 18. A triangle with no congruent sides. R. midpoint of a segment 19. A polygon with exactly eight sides. S. isosceles triangle 20. A triangle in which one angle measures greater than 90º. T. supplementary angles 21. A polygon with exactly five sides. U. radius of a circle 22. A pair of angles whose sum is 180º. V. acute triangle 23. A triangle that contains an angle whose measure is equal to 90º. W. diameter of a circle 24. A polygon with exactly six sides. X. complementary angles 25. A triangle with at least two congruent sides. Y. hexagon 26. A polygon in which all sides are congruent and all angles are congruent. Z. angle
General instructions: All work must be neat and readable to receive credit. Guess and check is not considered showing your work! Formulas can be found at www.tea.state.tx.us. All answers must be exact. ie : 15, 12, 3 5 7 Solve each of the following problems in the space provided. 1. 5x + 7x = 9x 40 2. 1 2 x + x = 28 3. 5 (3 + x) = 75 2 3 4. x = 4 5. 5x + 6 = 4x - 8 6. x - 4 = x - 8 16 x 10 6 x + 6 x - 3 Solve each of the following by factoring. 7. x 2 9x + 18 = 0 8. x 2 + 12 = 7x 9. 2x 2 + 5x + 2 = 0
Solve each system of equations by substitution or elimination. Verify your solution by graphing each set of lines. Be sure to use a straight edge. 10. x + y = 12 x y = 4 11. 2x 6y = 22 4x + 6y = 8 12. x = 3y - 12 4x + 30 = 6y
13. Plot points A (-12, 5) and B (-2, 1) and draw AB.. a) Use the formula to find the slope of AB. b) Use the formula to find the length of AB. c) Use the formula to find the coordinates of the midpoint of AB. d) Write the equation of AB in slope-intercept form. 14. Graph the set of lines and answer the following questions. a) x = - 4 b) x = 2 c) y = 3 d) y = 1 x 2 1. Identify any parallel or perpendicular lines. 2. Accurately describe the figure formed by the intersecting lines. 3. Find the area of the figure formed by the intersecting lines. 4. Find the perimeter of the figure formed by the intersecting lines.
15. Suppose the cost in dollars of a taxi ride is represented by the function: c = 0.42d + 3.50 where c is the cost of the taxi and d is the number of tenths of miles traveled. a) Name the dependent variable and state the range of the function. b) Name the independent variable and state the domain of the function. c) What is the rate of change? d) What is the cost if the taxi travels 5 miles? e) What is the cost if the taxi travels 120 miles? f) Draw a graph of this function. Solve for the indicated variable. You will not have real number answers on 16-19. 16. a 2 + b 2 = c 2 Solve for a. 17. A = ( b 1+ b 2 2 )h Solve for b2. 18. S = πrl + πr 2 Solve for l. 19. V = 4πr3 3 Solve for r.