Foundations of Math 1 Review

Transcription

1 Foundations of Math 1 Review Due Wednesday 1/6/16. For each of the 23 questions you get COMPLETELY correct, you will receive a point on an extra assessment grade. **All regular credit must be completed first!!** Unit 1 Questions 1. Simplifying vs. Solving. Below are expressions and equations. For each expression, write simplify and for each equation, write solve. a. 3x 4x + 10x d. 5! + 3 = 10 b. 5x 10 = x e c.!! x f. 10x = 3 2. Subsets of Real Numbers. State ALL subsets that each number belongs to: Natural Whole Integer Rational Irrational Real a. -5 b. π c d.!! e Function Representation. Fill out the table about the function. In words: Penny makes $4.00 an hour plus $23 in tips at a. Write an Equation aka Function Rule: Let The Cheesecake Factory. p=her pay and h=hours worked. b. Fill in the Table: Hours Pay c. Set of Ordered Pairs: { d. Domain: { e. Range: { f. Draw a Mapping Diagram: g. Graph and LABEL the data from your table: 1

2 4. Functions and Relations. Is each a Function? EXPLAIN YOUR REASONING. a. b. c. d. e. 3,0, 2,4, 3,1, (0,2) f. g. 5. Independent vs. Dependent. State the independent or dependent variables in each situation. a. y = 4x 3 b. c. independent= dependent= independent= dependent= independent= dependent= d. Jenny goes biking every morning. The farther she bikes, the more calories she burns during the bike ride. Let d = the distance Jenny bikes and c = the number of calories Jenny burns during the bike ride independent= dependent= e. At a coffee shop, the amount of tax due is calculated based on the cost of the customer's order. Let t = the amount of tax due and c = the cost of the order independent= dependent= 2

3 6. Recursive Functions. a. Make a table of values for each recursive function: Next = Now 2, Starting at -3 Next = 3(Now), Starting at 1/3 x x y y b. Write a recursive rule for each sequence, table, or function. i. -5, -6, -7, -8, -9. ii. x y iii. Carla has 32 stuffed animals. Each year, she purchases 3 more. iv. The population of 30 aardvarks is growing by 3% each year in a certain area. v. Johnny s bank account has 1,400. Each year, the balance grows by 0.6% 7. Translating. a. Write an algebraic phrase to represent each expression. i. 4x 7 ii. x iii.! x = 10! b. Write an algebraic expression to represent each phrase. i. Seven less than a number ii. A number is at least 8 iii. The quotient of a number and 8 iv. The product of a number and half the number v. 10 more than twice the number vi. The sum of a number and 5 of the number 3

4 Unit 2 Questions 8. Measures of Center. Use the data 11, 5, 7, 8, 4, 9, 9 to calculate: a. Mean b. Median c. Mode d. What value would need to be added to the data for the mean to be 7? e. What value would need to be added to the data for the mean to be 9? 9. Histograms and Dot Plots. Answer the questions about the histograms or dot plots. a. Use the histogram to answer. i. How many data points were at least 35 mpg? ii. How many data points were less than 15 mpg? iii. Which intervals had the largest frequency? b. Use the dot plot to answer. i. State the mode of the data. ii. State the median of the data. iii. State the mean of the data. iv. State the range of the data. 10. Shapes of Data and Effects of Outliers a. List the three measures of central tendency. b. Which of the measures of central tendency is most affected by outliers? c. List the three measures of spread. 4

5 d. Which of the measures of spread is the least affected by outliers? e. Draw an example of a histogram that has each shape: Skewed Right Skewed Left Approximately Normal: f. Which shape of distribution above is most likely to have a mean larger than median? Explain. g. You are planning to take on a part time job as a waiter at a local restaurant. During your interview, the boss told you that their best waitress, Jenni, made an average of $70 a night in tips last week. However, when you asked Jenni about this, she said that she made an average of only $50 per night last week. She provides you with a copy of her nightly tip amounts from last week. Calculate the mean and the median tip amount. i. Which value is Jenni s boss using to describe the average tip? ii.which value is Jenni using? iii. Which value best describes the typical amount of tips per night? Why? 11. Box-and-Whisker Plots and Percentiles. Use the data: 4, 7, 7, 8, 10, 11, 14, 22, 23. a. State the 5 number summary b. State the IQR c. State Q2 d. State the 50 th percentile. e. State the 75 th percentile f. What percentile rank is an 8? g. State the range. 5

6 12. Interpreting Box-and-Whisker Plots. Use the box plots below to answer. a. Which student has a larger IQR, and by how many points? b. Which student has a larger 75 th percentile? c. If each box plot represents 24 data points, how many of Ray s scores were between 82 and 87? d. If each box plot represents 24 data points, how many of Ken s scores were at least 78? e. Explain what it means that Ray s right box-plot whisker is longer than the left. 13. Interpreting Two-Way Frequency Tables. Use the two-way table below to answer each. a. What is the marginal frequency of students who can bike? bike? b. What is the joint relative frequency of boys who can bike? c. Out of all boys, what percent can t bike? d. Out of all students who can bike, what percent are girls? 14. Interpreting Two-Way Relative Frequency Tables. Use the two-way relative frequency table below to answer each about a survey of 400 participants. a. How many females chose yellow? b. How many more males than females were surveyed? c. How many people chose green? 6

7 Unit 3 Questions 15. Slope-Intercept Form of Lines. Write the equation of a line in slope intercept form for the line represented in each situation. a. b. The line that passes through (4, -2) and (3, -3) c. The line that passes through (0, 2) and (8, -1) d. e. f. g. Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. Write the equation pounds, P, of aluminum cans after w weeks. h. The water level of a river is 34 feet and that it is receding (going down) at a rate of 0.5 foot per day. Write an equation for the water level, L, after d days. i. The sequence below shows the number of j. Next = Now 7, Starting at -3 apps Carol downloads on her new phone after owning it 1, 2, 3, 4,. days 20, 23, 26, 29,. 7

8 16. Interpreting Slope and Y-intercept a. How to put slope into words: b. What do we always remember for x-intercept? c. What do we always remember for y-intercept? d. i. What is the slope in the graph to the left? ii. What does the slope represent in the context of the problem? iii. What is the y-intercept? (, ) iv. What does it represent in the context? e. e. i. What is the slope in the table to the left? ii. What does the slope represent in the context of the problem? iii. What is the y-intercept? (, ) iv. What does it represent in the context of the problem? 8

9 17. Correlation. Match each of the correlation coefficients in the box with their graph: 18. Linear Regression. The following data chart shows the world record times for the 200 m race for flying start machines (a kind of bicycle). Round all answers to 3 decimal places. a. Write the linear regression model of the data where x is the number of years since 1974 b. State the value of R and what it means about the data c. Predict the record time in d. Predict the year the record time would be 8 sec. 19. Solving Equations. Solve each equation, showing all steps. a. 13 = 5(1 + 4m) 2m b. 8 = 8v 4(v + 8) c. 30 = 5(6n + 6) 9

10 20. Solving Literal Equations. Solve for the variable indicated in parenthesis. Show all work. a. 2x 3y = 8 (for y) b. A =!!!! (for x) c. P =!!!! (for R) d. x = 8 2y (for y) e. m =! (x + y) (for x) f. r =! k 2 (for k)!! 21. Solving Inequalities in 1-variable. Solve and graph. Show all work. a. 6x x < 14 b. 28 7x 4( 7x 7) c. x x 22. Inequalities in 2-variables. a. Graph b. Graph 10

11 c. Write the inequality that is graphed. d. Write the inequality that is graphed. 23. Parallel and Perpendicular Lines. Show all work. a. Write the equation of a line that is parallel to 4x 3y = 9 that passes through (0, 5). b. Write the equation of a line that is perpendicular to x 3y = 6 that passes through (3, 4). c. Write the equation of a line that is perpendicular to x + y = 8 that passes through (1, -1). 11