Great Mills High School Math Department Summer Review. Intermediate Algebra. 2. Reinforce the expectation that you are prepared to take this course

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1 Great Mills High School Math Department Summer Review Intermediate Algebra Name This packet contains review material. You have been taught and tested on this material in prior math courses. However, math is a cumulative study; it builds upon itself. Recalling these prerequisite mathematical concepts and processes is critical to your success in this course. The purpose of this review packet is three-fold: 1. Review/refresh prerequisite skills. Reinforce the expectation that you are prepared to take this course 3. Provide a smooth transition into a higher-level math course This material will be graded as follows: 1. Completion of this packet is a process grade for the class.. This packet will be returned to you and each problem will be reviewed. Following review, you will take a process-grade group quiz. 3. Lastly, there will be a product-grade individual quiz on this material. For each topic addressed, there are examples, explanations, and/or references, followed by a short set of practice problems. You are expected to complete this packet on your own. Be sure to show your work. If you need additional space, use lined notebook paper and This packet is due on August 1, 013, the first day of school. Topics: 1. Patterns Linear, Quadratic, Cubic and Geometric. Linear Equations and Graphs 3. Linear Inequalities. Graphs of Non-Linear Functions 5. Systems of Equations in Two Variables 6. Probability, Simulations and Making Predictions 7. Measures of Central Tendency 8. Misleading Data Representations

2 1. Patterns Linear, Quadratic, Cubic and Geometric This unit has corresponding practice on under Algebra, topics P.1 P.7. Linear Patterns Given: 8, 15,, 9, a. Write an equation which represents this linear pattern. b. What is the 1 th term? c. What term has a value of 50? Quadratic Patterns Given: 3,, 7, 1, 19. a. Write an equation which represents this quadratic pattern. b. What is the value of the 15 th term? c. What term has a value of 10? Cubic Patterns Given: -9, -, 17, 5, 115, 06, a. Write an equation which represents this cubic pattern. b. What is the value of the next term? c. What term has a value of 719?

3 Geometric Patterns Given: 3, -15, 75, -375, 1875, a. What is the value of the next term?. Linear Equations and Graphs This unit has corresponding practice on under Algebra, topics S.1 S.18 a. What is the slope-intercept form of the equation of the line in the graph below? y x b. Screen-printing a batch of shirts requires minutes per shirt in addition to minutes of initial set-up time. Write an equation that shows the relationship between the number of shirts s and the time t. c. Bonita has already prepared kilograms of dough and will continue preparing 1 kilogram of dough every hour. How much dough did Bonita prepare if she worked for 5 hours? Write and solve an equation to find the answer.

4 d. A corporate team-building event costs $, plus an additional $ per attendee. How many attendees can there be, at most, if the budget for the corporate team-building event is $10? Write and solve an equation to find the answer. e. Graph this function using intercepts: x + y = y x f. Line r has a slope of 5/3. Line s is parallel to line r. What is the slope of line s? g. Line d has a slope of 9/7. Line e is perpendicular to d. What is the slope of line e? h. Line k has an equation of. Line l which is parallel to line k, passes through the point (-6, -3). What is the equation of line i?

5 3. Linear Inequalities This unit has corresponding practice on under Algebra, topics K.1 S.15 and T.1 T.5 a. Solve the inequality and draw the graph on a number line. i. 5 r > 1 iii. ii. iv. b. Does the point (3, 7) satisfy the inequality y < x +1 c. Graph the inequality y < x y x

6 d. Graph the inequality 3x y y x. Graphs of Non-Linear Functions This unit has corresponding practice on under Algebra, topics Q.1 Q.1. a. For the graph below find the range, domain, maximum, minimum, determine if it is a function or not a function, determine if it is continuous or not continuous, and find all the zeros. i. range ii. domain iii. maximum iv. minimum v. function yes or no vi. continuous yes or no vii. zeros y x

7 5. Systems of Equations in Two Variables This unit has corresponding practice on under Algebra, topics U.1 U.15. a. Solve each system of equations using an appropriate method: i. ii. iii. b. Lucia is training for a triathlon and needs to swim a certain distance for today's workout. If she swims at the rec center pool, she will complete a 157-yard warmup and then swim laps in a lane that is yards long. If Lucia swims at the indoor pool at her gym, she will complete a 113- yard warmup, plus a main set that consists of yards per lap. If Lucia swims the correct number of laps, she can complete the same distance in either pool. How long will Lucia's workout be in total? How many laps will that take? c. The drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 3 regular gift baskets and 5 deluxe gift baskets, earning a total of $80. During the spring musical, they sold 16 regular gift baskets and 0 deluxe gift baskets, earning a total of $1,00. How much are they charging for the different sized gift baskets?

8 Rows d. Two groups of volunteers are cleaning up the football stadium after the Homecoming game. Volunteers from the Band Booster Club have already cleaned 10 rows of bleachers and will continue to clean at a rate of 1 row per minute. The leadership class has completed 5 rows and will continue working at rows per minute. Once the two groups get to the point where they have cleaned the same number of rows, they will take a break and decide how to split up the remaining work. How many minutes will each group have cleaned by then? Write a system of equations, graph them, and write the solution as an ordered pair. 30 Cleaning Bleachers Minutes

9 Probability, Simulations and Making Predictions This unit has corresponding practice on under Algebra, topics II.1 II.7 a. You roll a 6-sided die. What is P(1)? Simplify your answer and write it as a fraction or whole number. b. During 1 spins, a spinner landed on red times. If you spin the spinner once, what is the experimental probability that it will land on red? c. You flip a coin and spin the spinner. How many outcomes are possible? d. Eric is packing a lunch. He has three different choices for sandwiches and five different choices for fruits. How many different lunches are possible for Eric to pack?

10 6. Measures of Central Tendency a. Find the mean, median and mode of the data set below: b. Use the data below to draw a box-and-whisker graph: c. A pottery factory kept track of the number of broken plates per shipment last week. Use the data to complete the histogram below. Broken plates per shipment d. Students were surveyed as to how many stuffed animals they had at home. This box-andwhisker plot shows the results What percent of the students own 50 or more stuffed animals?

11 7. Misleading Data Representations a. Megan polled the 1 customers who had been going to a particular barbershop the longest. Is this sample of the customers at the barbershop likely to be biased? Explain your reasoning. b. Based on the graphs below, Dylan claims that the number of students who earned a B in math last year is the same as the number of students who earned a B in math this year. Is Dylan correct? Explain your answer. What characteristic of the graph may have led Dylan to believe his statement is correct? 1 Grades This Year by Subject Area Number of A's Number of B's Number of C's Number of D's Number of F's 0 English Science Social Studies Art Math P.E. Grades Last Year by Subject Area Number of A's Number of B's Number of C's Number of D's Number of F's 10 English Science Social Studies Art Math P.E.