Precollege Programming

Office of Precollege Programming
Western Michigan University
Kalamazoo MI 49008-5288 USA
(269) 387-2773

Geometry Summer Homework

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.

****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. 
    Figure 1 is one block, Figure 2 is one block centered on top of 3 blocks
    Figure 3 has 3 rows of blocks centered on each other. The top row has 1 block, the middle row has 3 blocks and the bottom row has 5 blocks
  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 of 256
    . (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: 
    Equation 1 is 4x - y = 8, Equation 2 is 2x - 4 = 3y.
     (Solving systems of equations in two variables)
  16. Solve the system of equations: 
    Equation 1 is 4x - 2y = 9, equation 2 is y=2x + 5.
  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 
    Square root of the fraction 3 fifths
     (Simplify radical expressions)
  29. Simplify
    square root of 6 times square root of 12
    .
  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?

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!