Review Packet For Math III Student Name: The problems in this packet are designed to help ou review topics from previous mathematics courses that are important to our success this coming ear. I hope that this review will keep our mind mathematicall active, identif weaknesses if the exist, and prepare ou for a fun and challenging ear ahead. You will be tested on this material the first week of school. You should not struggle with these concepts and MUST be able to work through the problems with ver little issue. These topics are expected to have alread been mastered. You have an opportunit to earn up to 10 points extra credit on the first test. To earn an points, the packet must be completed full, showing all the work on a separate sheet of paper and posting the answers on the lines provided. This packet is due Wednesda, August 26th. Use the following guidelines below when completing this packet. 1) NO WORK, NO CREDIT. Do not tr to cram all of ou work on this page. Use notebook paper to show work, along with keeping our work organized. Show the corresponding problem numbers on our work papers and write down the problem being worked on. 2) Show all steps when working out problems. An overall expectation of this course is that ou are able to PROVE our work, no matter how simple the problem. 3) Put all answers on the answer spaces provided. All answers should be written as whole numbers, or fractions (no decimals or mixed numbers). 4) If the problem involves drawing a graph, it must be exact and on the graph paper provided on the answer sheet. NO ROUGH SKETCHES ALLOWED! 5) If an answer is a fraction, it should be reduced to lowest terms. All factoring should be complete, remember GCF goes first. All exponents left in an answer should be positive, and all radicals should be reduced to lowest radical form. 6) If the question is a word problem interpret our answer using a complete sentence (in other words what does our answer MEAN?) 7) If a set of directions indicates NOT to use a calculator, then that is the expectation.
Student Name DUE Wednesda, AUGUST 26, 2015 Show all work for all problems. You ma need a separate sheet of paper. Write our final answer on the line provided. 1. Solve the following equations for x. Show our work and check our answers. a. (x 1) 2(4x + 6) = 8 b. 2x 7x + 4 = 7 4x 3 2 3 x 2 5 c. = x + 3 6 d. 2x 1 = 9 2. Solve the following formulas for the given variables. a. 4x 7 = 63; solve for b. a 2 + b 2 = c 2 ; solve for a 3. State the form of each linear equation and graph each on the coordinate plane. No calculator. Identif the coordinate point for the -intercept. Show the coordinates b the point. a. = 2x 3 b. 2x 3 = -6 2 c. 6 = ( x + 1) 5 Form: Form: Form: 1
4. a. Solve the inequalit 6 + 3 < 4(3 x) for. b. Is (0, -5) a solution to the inequalit? 5. Solve the sstem of equations algebraicall: 2x + 6 = 12 - x + 3 = 0 6. Perform each operation with fractions. Show value as a fraction if not an Integer. a. 2½ + 3¾ b. 5/8 2/3 c. 4/7 3/8 d. 5¼ 1¼ 7. Simplif the expressions a. (x 3 + 3x 2 2) + (5x 3 + x + 8) (9x 3 x 2 + 4) b. (4x 3)(x + 5) c. (3x 2 + x + 1)(2x 3) 4 5 5 3 16x 12x d. 3 2 2x e. (5x 2) 2 f. 2(x 3 5x 2 + 6x) (x 2 + 3x) 8. Factor completel. a. 9x 2 3 3x 3 2-15x b. 2x 2 4x 30 c. x 3 + 4x 2 + 3x 2
9. Solve the quadratic equations b factoring, extracting square roots, completing the square, or using the quadratic formula. a. 4x 2 81= 0 b. x 2 + 5x 9 = 0 c. 2x 2 3x = -1 d. 3(x + 4) 2 = 12 10. Simplif using the properties of exponents. 4 3 a. x 3 x 2 x b. (m 3 ) 5 c. ( 2 ) 3 a 2 d. e. 7 a 3 5 3x f. 2 0 12x 3 2 g. (-3x 2 ) 2 h. (8a 3 b 2 ) (2a 4 b 5 3x ) i. 2 1 6x 11. Simplifing Radicals radicals are in simplest form when there are no perfect square factors inside the radical. Simplif the following completel! DO NOT find the decimal approximations for these square roots! a. 12 b. 72 c. 2 18 d. 75 27 12. Graph the following sstem of inequalities: 2x + 5 < 10 > 3x 2 Is (-2, 1) a solution to the sstem? Is (-5, 4) a solution to the sstem? 3
13. Find the values of x and/or. Use our knowledge of special right triangles, the Pthagorean Theorem, the Distance and Midpoint Formulas. Leave answers as simplified radicals. a. b. c. A line segment has endpoints located at (4, 6) and (-2, 5). Find 1) the midpoint of the segment and 2) the length of the segment. Leave answer for 2 as a simplified radical 1) 2) _ Real World Applications 14. The length of a rectangle is 2 feet more than its width. If its perimeter is 40 feet, what is the measure of the length and the width? L: W: 15. The second angle in a triangle is 3 0 less than twice the first angle. The third angle measure 8 o more than twice the first angle. What is the measure of each angle? 16. Jeffer has grades of 93 and 81 on the first two tests of the quarter. Progress reports will go home after the third test. If Jeffer does not have an A average (90 or higher) on his progress report, he cannot go to the football game that week. Jeffer will have to make at least what grade on the third test to be allowed to go to the football game? 17. The profits of Mr. Unluck's compan can be represented b the equation = -3x 2 + 18x 4, where is the amount of profit in hundreds of thousands of dollars and x is the number of ears of operation. He realizes his compan is on the downturn and wishes to sell before he ends up in debt. Round to the nearest tenth if not a whole number. a) When will Unluck's business show the maximum profit? b) What is the maximum profit? c) How long will it take Mr Unluck to have no profit? 4