Name: ALGEBRA I HUNDERSMARCK UNIT 2 TEST REVIEW Date: VOCABULARY equation consecutive integers set interval notation infinite solutions consecutive even/odd integers roster form set-builder notation no solutions inequality compound inequality solution set at least// at most (AND/OR) Topics: Solving Linear Equations (includes use of PEMDAS, infinite solutions, no solutions) Linear Word Problems (includes work with Consecutive Integers) 1. Solve the following equations. If an equation has no solutions, state NO SOLUTIONS and if it has infinite solutions state INFINITE SOLUTIONS. (a) 2 3 x -5 = - 1 4 x +6 (d) 4( b 1) 2 b 6( b 3) 8 b (b) 1 (16-2x) = -2(x + 4) (e) x 2 5x 2x 3 3x 10 (c) 3(x + 2) 4 = (x - 3) (f) 2 3 (12x -6) +3x =10(1 5 x - 2 5 ) +9x
1. (Continued from front) (g) 4 3m 4 2 6m 8 2. Rachael and Sabine belong to different local gyms. Rachael pays $35 per month and a one-time registration fee of $15. Sabine pays only $25 per month but had to pay a $75 registration fee. After how many months will Rachael and Sabine have spent the same amount on their gym memberships? 3. The Admiral Players are going to raise money by printing calendars that feature photos from its shows this year. The cost of printing the calendars is $5.50 per calendar. The photographer charges $200 for taking the photos. The Admiral Players have $1500 to cover the initial costs of the calendars. How many calendars will they be able to order? 4. The fare for a cab ride is $5 per trip plus $0.50 per mile. The fare for the trip from the airport to the convention center was $11.50. Write and solve an equation to find how many miles the trip is from the airport to the convention center. 5. If x 4 represents an odd integer, then the next consecutive odd integer in terms of x is 5. (1) x 6 (2) x 4 (3) x 3 (4) x 2 6. Find three consecutive even integers such that the sum of twice the first and three times the third is fourteen more than four times the second.
Topic: Literal Equations 7. Solve the following equations for the given variable. 3 x 2y 5x for x (b) (a) k 2 2 n 1 for k Topic: Solving Inequalities (includes no solutions, graphing solution set) 8. Determine whether each number is a solution of the given inequality. Show substitutions. 3y 5 20 2 0 5 9. Solve each inequality and graph the solution set. If the inequality has no solutions, write NO SOLUTIONS. (a) 2 p 4 3p 10 (b) x 6 1 (c) 3 w 21 3 (d) 4 3x 1 2 x 3 (e) 9 2x 7 2 x 3 10. A student must earn at least 24 credits in high school in order to graduate. 10. Which inequality or graph does NOT describe this situation? (1) c 24 (3) (2) (4) 24 c -18-12 -6 0 6 12 18 24 30 36 42-18 -12-6 0 6 12 18 24 30 36 42
Topics: Set-Builder Notation, Interval Notation 11. Each number line below shows the graph of a set of points. Write each set using set builder notation and interval notation. (a) set-builder: (b) set-builder: (c) set-builder: (d) set-builder: 12. Solve each inequality. Graph your solutions and write each solution set in set-builder and interval notation. (a) 2 5 21 2 x 7 10 6x x (b) 13. At a hydroelectric plant, Pump 1 is on for all times on the interval 0,8 and Pump 2 is on 13. 4,18. Which of the following represents all times, t, when both for all times in the interval pumps are on? (1) 4 t 8 (2) 0 t 18 (3) 4 t 8 (4) 8 t 18
Topic: Compound Inequalities 14. Solve each compound inequality. Graph your solutions and write each solution set in set-builder and interval notation. (a) 5 x 2 and x 2 11 (b) 9 x 2 or 3x 15 Topic: Modeling with Inequalities 15. The goal of a toy drive is to donate more than 1000 toys. The toy drive already has collected 300 toys. How many more toys does the toy drive need to meet its goal? Write and solve an inequality to find the number of toys needed. 16. An oil refinery aims to process 900,000 barrels of oil per day. The daily production varies up to 50,000 barrels from this goal, inclusive. What are the minimum and maximum numbers of barrels of oil processed each day? 17. A maple syrup producer would like to increase production by 500 gallons per year with a goal of producing at least 20,000 gallons of syrup over the first five year period of production. (a) If the first year s production, in gallons, is given by x, write expressions for each of the other years productions. Year 1 x Year 2 = Year 3 = Year 4 = Year 5 = (b) Find all possible values of syrup that could be produced in the first year to meet the goal of at least 20,000 gallons total over the five-year period.