Math 99 Project 1 (60 points) Due Thursday 28 th September
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1 Math 99 Project 1 (60 points) Due Thursday 28 th September Students Name: This Project is to help you to review some of the concepts from Math 94 that you will use in this class. These questions need to be done by hand but you may ask the Tutors and your fellow students to help you solve any of these problems, but it is important that you are able to do all of these types of questions on your own as we will be using all of them at some point during the course. Section I- Multiple Choice 1. The expression 3x 2 10x + 3 when factored fully is:- A. (3x 1)(x 3) B. (3x 1)(x + 3) C. (3x + 1)(x 3) D. (3x + 1)(x + 3) E some other answer 2. The expression 100y 2 400x 2 when factored fully is:- A. 100(y 2 4x 2 ) B. 100(y + 2x)(y 2x) C. (2y + 20x)(2y 20x) D. Can t be factored 3. The expression 4a 2 b 3 8a 3 b 3 when factored fully is:- A. 4a 2 b 3 (1 2a) B. 4a 2 b 3 ( 2a) C. a 2 b 3 (4 8a) D. 4ab(ab 2 2a 2 b 2 ) E some other answer 4. The expression 3x x 8 when factored fully is:- A. (3x + 8)(x + 2) B. (3x 2)(x + 4) C. (3x 4)(x 2) D. (3x + 2)(x + 4) E some other answer 5. FOIL the following expression. (2x 5)(x + 6) A. 2x 2 x 30 B. 2x 2 + x 30 C. 2x 2 7x 30 D. 2x x 30 E some other answer
2 6. Simplify the following expression 4(x 6) 2(x 5) A. 2x + 14 B. 2x 34 C. 2x + 34 D. 2x 14 E some other answer 7. Solve the following Equation 2x 7 = 14 5x A. x = 3 B. x = 1 3 C. x = 1 3 D. x = 3 E some other answer 8. Solve the following Equation (x 8)(2x 1) = x(2x + 6) 15 A. x = 1 B. x = 1 C. x = 1 2 and x = 8 D. x = 3 E some other answer 9. Solve the following equation 2x+1 5 = 3+x 2 A. x = 1 B. x = 13 C. x = 1 2 D. x = 13 E some other answer 10. Solve the following equation 1 2 x = x A. x = 9 B. x = 1 9 C. x = 1 9 D. x = 9 E some other answer 11. Evaluate the following [23 8( 2 + 5)] 2 A. 1 B. 1 C.5625 D E. Some other answer.
3 12. Evaluate 4x + 4(x 3) 2 when x = 1 A. 2 B.4 C.6 D.8 E.. Some other answer. 13. When you combine like terms in the expression 5x + 6 2x + 4 you get which of the following. A. 13x B. 7x +10 C. 3x + 10 D. 3x 10 E. Some other answer. 14. Simply the following expression 3 (x 3) + x A. 0 B. 6 C. 2x 6 D. 2x + 9 E. Some other answer. 15. The solution to the equation 3x 2 = x 8 is A. x = 3 B. x = 3 C. x = 2.5 D. x = 2.5 E. Some other answer. 16. The solution to the equation 4 x = 8 3 is A. x = B. x = 3 C. x = D. x = 8 E. Some other answer.
4 Section II Answer each of the following questions it is important to show your working as credit will be given for partially correct answers. 1. Simplify the expression 3x + 2y x 2y + 4 show all your working. 2. Solve the equation 3x + 7 = 28 show all your working. 3. Solve the equation 5x + 7 = 2x + 35 show all your working. 4. Solve the equation 3(2x 2) = 4x 4 show all your working.
5 5. Solve the equation 5 24 = 10 x show all your working. 6. Solve the equation x 2 4 = 1 x 2 3 show all your working. 7. Combine like terms where possible and simplify the result. (a) 4x x + 5x x = (b) 2x 5 + 5x 1 = (c) 2(2x 3y + 5) + 5y 4x 10 =
6 8. Solve the equations (a) 2 + 4(x 3) = 2x + 6 (b) 5(x 5) 5 = 2x + 3( x 2) 9. The length of a rectangular swimming pool is 8 meters more than twice its width. If its perimeter is 136 meters, find its dimensions.
7 10. Mark weighs 50 pounds less than twice as much as Laura. The sum of their weights is 250 pounds. How much do they each weigh? 11. Factor each of the following expressions as much as possible. (a) x 3 5x 2 + 6x = (b) 4x 2 9 = (b) x 4 8x =
8 12. Find the products: (a) (x + 6)(x 5) (b) (3a 3b)(2a + 2b) (c) 3x 3 (x 2 2x + 3) (d) (2x 9)(9 2x)
9 Section I- Multiple Choice Solutions 1. The expression 3x 2 10x + 3 when factored fully is:- A. (3x 1)(x 3) B. (3x 1)(x + 3) C. (3x + 1)(x 3) D. (3x + 1)(x + 3) E some other answer 2. The expression 100y 2 400x 2 when factored fully is:- A. 100(y 2 4x 2 ) B. 100(y + 2x)(y 2x) C. (2y + 20x)(2y 20x) D. Can t be factored 3. The expression 4a 2 b 3 8a 3 b 3 when factored fully is:- A. 4a 2 b 3 (1 2a) B. 4a 2 b 3 ( 2a) C. a 2 b 3 (4 8a) D. 4ab(ab 2 2a 2 b 2 ) E some other answer 4. The expression 3x x 8 when factored fully is:- A. (3x + 8)(x + 2) B. (3x 2)(x + 4) C. (3x 4)(x 2) D. (3x + 2)(x + 4) E some other answer 5. FOIL the following expression. (2x 5)(x + 6) A. 2x 2 x 30 B. 2x 2 + x 30 C. 2x 2 7x 30 D. 2x x 30 E some other answer 6. Simplify the following expression 4(x 6) 2(x 5) A. 2x + 14 B. 2x 34 C. 2x + 34 D. 2x 14 E some other answer 7. Solve the following Equation 2x 7 = 14 5x A. x = 3 B. x = 1 3 C. x = 1 3 D. x = 3 E some other answer
10 8. Solve the following Equation (x 8)(2x 1) = x(2x + 6) 15 A. x = 1 B. x = 1 C. x = 1 2 and x = 8 D. x = 3 E some other answer 9. Solve the following equation 2x+1 5 = 3+x 2 A. x = 1 B. x = 13 C. x = 1 2 D. x = 13 E some other answer 10. Solve the following equation 1 2 x = x A. x = 9 B. x = 1 9 C. x = 1 9 D. x = 9 E some other answer 11. Evaluate the following [23 8( 2 + 5)] 2 A. 1 B. 1 C.5625 D E. Some other answer. 12. Evaluate 4x + 4(x 3) 2 when x = 1 B. 2 B.4 C.6 D.8 E. Some other answer = When you combine like terms in the expression 5x + 6 2x + 4 you get which of the following. A. 13x B. 7x +10 C. 3x + 10 D. 3x 10 E. Some other answer. 14. Simply the following expression 3 (x 3) + x A. 0 B. 6 C. 2x 6 D. 2x + 9 E. Some other answer. 15. The solution to the equation 3x 2 = x 8 is A. x = 3 B. x = 3 C. x = 2.5 D. x = 2.5 E. Some other answer. 16. The solution to the equation 4 x = 8 3 is A. x = B. x = 3 C. x = D. x = = 8 2 E. Some other answer.
11 Section II - Solutions Answer each of the following questions it is important to show your working as credit will be given for partially correct answers. 1. Simplify the expression 3x + 2y x 2y + 4 show all your working. 3x + 2y x 2y + 4 = 3x 2x + 2y 2y = x Solve the equation 3x + 7 = 28 show all your working. 3x = 21 x = 7 3. Solve the equation 5x + 7 = 2x + 35 show all your working. 7x = 28 x = 4 4. Solve the equation 3(2x 2) = 4x 4 show all your working. 6x 6 = 4x 4 2x = 2 x = 1 5. Solve the equation 5 24 = 10 x 5x = 240 x = 48 show all your working. x 6. Solve the equation = x 2 show all your working. 3 3x + 24 = 2x 12 x = Combine like terms where possible and simplify the result. (a) 4x x + 5x x = 7x (b) 2x 5 + 5x 1 = 2x + 5x 5 1 = 7x 6 (c) 2(2x 3y + 5) + 5y 4x 10 = 4x 6y y 4x 10 = 4x 4x 6y + 5y = y
12 8. Solve the equations (a) 2 + 4(x 3) = 2x + 6 (b) 5(x 5) 5 = 2x + 3(x 2) 2 + 4x 12 = 2x + 6 5x 25 5 = 2x + 3x 6 4x 10 = 2x + 6 5x 30 = 5x 6 2x = = 6 x = 8 No solution possible 9. The length of a rectangular swimming pool is 8 meters more than twice its width. If its perimeter is 136 meters, find its dimensions. Perimeter = 2 Length + 2 Width Perimeter = 2(2x + 8) + 2x Perimeter = 4x x Width = x Perimeter = 6x = 6x = 6x 20 = x Length = 2x + 8 Width = x = 20 m Length = 2x + 8 = 2(20) + 8 = 48m 10. Mark weighs 50 pounds less than twice as much as Laura. The sum of their weights is 250 pounds. How much do they each weigh? Lauras Weight = x Sum = Lauras Weight + Marks Weight Marks Weight = 2x 50 Sum = x + 2x = 3x = 3x 100 = x Lauras Weight = x = 100 pounds Marks Weight = 2x 50 = 2(100) 50 = = 150 pounds 11. Factor each of the following expressions as much as possible. (a) x 3 5x 2 + 6x = x(x 2 5x + 6) = x(x 2)(x 3) (b) 4x 2 9 = (2x 3)(2x + 3) (c) x 4 8x = (x 2 4)(x 2 4) = (x 2)(x + 2)(x 2)(x + 2) = (x 2) 2 (x + 2) Find the products: (a) (x + 6)(x 5) = x 2 5x + 6x 30 = x 2 x 30 (b) (3a 3b)(2a + 2b) = 6a 2 + 6ab 6ab 6b 2 = 6a 2 6b 2 (c) 3x 3 (x 2 2x + 3) = 3x 5 6x 4 + 9x 3 (d) (2x 9)(9 2x) = 18x 4x x = 4x x 81
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