Name: ______________________________________________________ Per: ________ HW #: ________ CC7/8A Sem 2 Final Exam Review Worksheet #5: CC3 Chapters 6-­‐8 •
•
•
Chap 6: Transformations, Similarity, LESS+ with Systems of Equations Chap 7: Slope, Scatterplots, Association, Line of Best Fit, Prediction Equation Chap 8: Compound Interest, Exponential vs Linear Growth, Exponent Rules, Scientific Notation Note: This is a sample of the types of problems that might be on the Semester 2 Final Exam. 1) Solve the equation by clearing decimals first: 0.75x − 0.5 = x + 1.5 2) Graph the points X(−3, 5), Y(−2, 3), and Z(−1,4). Connect them to make a triangle. a) Reflect the triangle across the y-­‐axis. Write the ordered pair rule for this transformation. What are the new coordinates of point Z? b) Translate the original triangle down 6 units and right 3 units. Write the ordered pair rule for this transformation. What are the new coordinates of point Y? c) Dilate the original triangle by a scale factor of two. Write the ordered pair rule for this transformation. Describe the new shape you create. d) Which of the above transformations were rigid transformations? 3) What must be true for two figures to be congruent? Similar? Be complete! 4) The triangles below right are similar. All measures are in inches. a)
What is the scale factor, from little to big triangle? b)
Find x using your scale factor. c) Find y using a proportion. d) What is the ratio of the smaller perimeter to the larger perimeter? 5) Matt moved Triangle A on the graph at right to match up with Triangle B in three moves. Follow the steps Matt wrote below. What was his final move? 1. Slide the triangle up 3 units. 2. Reflect the triangle across the line y = 4. 3. ? 6) The school library has 6500 titles in its collection of books, magazines, and reference materials. The librarian is presenting information about the library to the parent association, and she made the graph at right. a) According to the graph, what percent of the collection are nonfiction books? b) Could the librarian have presented this information in a histogram? Why or why not? c) How many of the books in the library are fiction? d) Calculate the measure of the central angle for the movies sector of the circle. Do not use a protractor. 7) Ruthie did a survey among her classmates comparing the time spent playing video games to the time spent studying. The scatterplot of her data is shown below. a) What association, if any, can you make from her data? That is, how are the variables related? b) Describe the association in terms of form, direction, and strength. c) Use an ordered pair (x, y) to identify any outliers. d) Draw a line of best fit on the graph above. Select two points close to your line to calculate the slope of your trend line. What is the slope of your line? The y-­‐intercept? e) Using the slope and y-­‐intercept you estimated, write a prediction equation. f) Use your prediction equation to estimate how much time you expect a student in Ruthie’s class to spend studying if he or she spends 1 hour playing video games. 8) Compute each product or quotient. Convert the final answer to scientific notation if necessary. 9) Put these numbers in order from least to greatest. No calculator allowed. 10) In the year 2000, Los Angeles, CA had a population of about 3,700,000 people. What is this number in scientific notation? 11) The moon is about 2.26 x 105 miles from Earth. What is this distance in standard form? 12) Simplify the following expressions. Remember your exponent rules, expanding only if absolutely necessary. Your final answer should not have any negative exponents. 0
a) b) c) (xy3)(x2y) d) ⎛ x 2 y −3z 14 ⎞
e) !(4x y z) f) ⎜ 6 −7 −3 ⎟ ⎝x y z ⎠
!
3
4
3
13) You will need to do this problem in your graph comp book: You have $5,000 to invest in a savings account for 20 years and you have two account options to choose from. You can invest in an account that offers 9% annual simple interest or you can invest in an account that offers 7% interest compounded once a year. Use multiple representations (table, graph and rule) to analyze each option. How much money would you have under each option after 20 years? Which one will you choose? Why? Before you start, write the equations for simple and compound interest here: 14) Mariela graphed all of the equations below, but forgot which equation went with which graph. Help her match each equation with the appropriate graph. y = x – 3 y = –2x + 1 y = 2x – 3