advertisement

MAT 1033 REVIEW FOR EXAM #3 This review has been designed to give you more practice before the exam. It is not meant to be the only thing that you study. Be sure to look at your notes, homework, your book, etc. Sections 4.1 and 4.3 1. Solve by graphing: a) x + y = 2 b) 2x + 3y = 6 2 y x 1 3 x–y=4 y c) x = 6 y =–2 y 6 y 6 6 x -6 6 x -6 -6 2. Solve by addition: a) 6x – 6y = -5 10x – 2y = 1 3. a) Solve by substitution: 5x + 2y = 15 x=6–y 6 x -6 6 -6 b) 6x – 4y = 3 3x – 2y = 9 b) 3x + 4y = 14 2x + y = 1 -6 c) 3 5 x + y = 11 4 2 1 3 x - y = -1 16 4 c) –6x + 3y = 3 y = 2x + 1 4. A science museum charges $10 regular admission and $5 student admission. Last Saturday, 750 tickets were sold for a total of $5400. How many of each type were sold? 5. One number is three times a second number, and twice the sum of the numbers is168. Find the numbers. 6. A pharmacist needs 500 milliliters of a 20% phenobarbital solution but has only 5% and 25% phenobarbital solutions available. Find how many milliliters of each she should mix to get the desired solution. Sections 5.1 – 5.7 1. Add: a) 3 x 2 2 x 2 5 x 3 Divide: a) 2. Multiply: a) 2a 52 3. b) 3 x 2 2x x 2 5 x 3 Subtract: b) 3x 2 x2 4x 3 32a3b2c 24a2b5 40a 4b3 2 2 8a b 5(x2 + 1) + 3x(x2 + 1) 6. x2 + xy – 3x – 3y 7. 12a2b – 2ac – 42ab + 7c 8. x2 + 8x + 12 c) (4mn – 7)(4mn + 7) b) x3 5x 14 x 3 Factor each of the following: 4. 21a5b4c – 3a7b3c – 6a3b6c3 5. Check: 9. x2 – x – 12 Check: 10. 2x2 + 3x – 5 Check: 11. 2x2 – 15x + 18 Check: 12. 2x2 – 7x – 30 Check: 13. 3x2 + 7x + 1 Check: 14. 6x2 + 16xy + 8y2 Check: 15. 25x2 – 10x + 1 Check: 16. 49x2 – 100y2 Check: 17. 27a3 – 125 18. 8x3 + 1 Solve each equation. 19. x2 – 9 = 0 21. 3x2 – 10x = 8 23. – 18 = 2x2 – 15x 20. 10x2 + 7x + 1 = 0 22. 4x2 + 12 = – 14x ANSWER KEY – MAT 1033 Review for Exam #3 Sections 4.1 and 4.3 1. a) (3, -1) b) No Solution, lines are parallel c) (6, -2) 2. a) (1/3, 7/6) b) No Solution, lines are parallel c) (8, 2) 3. a) (1, 5) 4. $330 regular, $420 students 5. 21 and 63 b) (-2,5) c) {(x, y) | y= 2x +1} 6. 125 ml of 5%; 375 ml of 25% Sections 5.1 – 5.7 1. a) 4 x 2 5 x 5 b) 2 x 2 7 x 3 2. a) 4a2 20a 25 b) 3x3 14x2 17x 6 3. a) 4ac 3b3 5a2b b) x 2 3x 4 4. 3a3b3c(7a2b – a4 – 2b3c2) 5. (x2 + 1)(5 + 3x) 6. (x + y)(x – 3) 7. (6ab – c)(2a – 7) 8. (x + 6)(x + 2) 9. (x – 4)(x + 3) 10. (2x + 5)(x – 1) 11. (2x – 3)(x – 6) 12. (2x + 5)(x – 6) 13. not factorable 14. 2(3x + 2y)(x + 2y) 15. (5x – 1)2 16. (7x + 10y)(7x – 10y) 17. (3a – 5)(9a2 + 15a + 25) 18. (2x + 1)(2x2 – 2x + 1) 19. x = 3, – 3 20. 1 1 x= , 5 2 21. x = 2 ,4 3 c) 16m2n2 49 2 x3 22. x = 3 , –2 2 23. x = 6, 3 2