MAT 0020 / MAT Final Review. A. Acosta. 1. What is the equation of the graph? Choose the answer from the following: x = 2. y = 2 x.

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1 1. What is the equation of the graph? Choose the answer from the following: x = 2 y = 2 x y = 2 y = x 2

2 2. A replica of the Declaration of Independence is to be mounted on cardboard, as shown in the illustration. If the border around the document has a uniform width of x inches, the total area of the display is given by 24x x + 6 in 2 Factor this expression to find the expressions that represent its length and width.then determine the length of the document. e. f. 8x 2 4x 2 4x + 2 8x + 2 6x + 2 6x 2 3. Evaluate the expression b 2 4 a if a = 43.75, and b = 16. Do the operations within the radical first, and then simplify the radical The largest ocean in the world is the Pacific Ocean, which covers approximately square miles. Express this number in standard notation miles miles miles 5. Build up the whole number 8 to an equivalent fraction having the denominator

3 6. Use the associative property of addition to complete the statement: 87 + ( ) [ 87 + ( 4) ] [ 87 ( 4) ] 255 [ 87 ( 4) ] [ 87 + ( 4) ] Write the quotient as the quotient of two radicals and simplify: To the nearest tenth, find the circumference and the area of the target. a = 4 in in., 50.3 in in., in in., 50.3 in in., in Find the product. ( 6 t 5 z 6 ) ( 2 t 2 z 2 ) 12 t 7 z 8 12 t 10 z 12 8 t 7 z 8 12 t 3 z What is the correct classification of the following polynomial? 10s 2 2 monomial binomial trinomial

4 11. Write in scientific notation Find the pairs that satisfy the equation y = x ( 6, 212 ) ( 0, 4 ) ( 9, 725 ) ( 2, 8 ) e. ( 4, 60 ) f. ( 5, 121 ) 13. Write the fraction in lowest terms. If the fraction is already in lowest terms, so indicate in lowest terms Solve the inequality. 2x (, 0.5 ] [ 2.2, ) (, 2.2 ] [ 0.5, ) 15. One angstrom is millimeter. Express this number in standard notation millimeter millimeter millimeter 16. Factor the polynomials: (z + 8) 2 (z 8)(z + 8) (z 8) 2 z 2 16z + 64

5 17. Find the sum: ( 3.974) Equal amounts are invested in each of three accounts paying 7%, 8%, and 10.5% annually. The one year's combined interest income is $ How much is invested in each account? $4900 $3800 $6000 $ Do the operation 0.4( 8 ) Complete the following property. If z = s and c is any number, then z + c =. s + c s c z s e. s z 21. What numbers are a distance of 12 away from 8 on the number line? 20, 4 5, 3 5, 20 20, Consider the equation y = 2 x + 4. How many solutions does this equation have? none of these choices one solutions infinitely many solutions no solutions

23. Find the area of the stamp shown in the figure below. a = 3, b = 5, c = 9, d = 6 e. 27 x 2 + 27 x 30 27 x 2 27 x 30 12 x 2 + 27 x 11 27 x 2 + 27 x + 30 12 x + 27 24. Find the product.

6 23. Find the area of the stamp shown in the figure below. a = 3, b = 5, c = 9, d = 6 e. 27 x x x 2 27 x x x x x x Find the product. ( t + 4 ) ( t + 4 ) t t + 16 t t 2 8 t + 16 t Do the operation 0( 12 ) On the Scholastic Aptitude Test, or SAT, a high school senior scored 550 on the mathematics portion and 700 on the verbal portion. What percent of the maximum 1600 points did this student receive? Draw a diagram to help organize the facts of the problem % % % %

7 27. Factor the trinomial: 6t 4 150t e. 6(t 4)(3 t)(t + 4)(t + 3) 6(t 4)(t 4)(t + 3)(t + 3) 6(t 3)(t 3)(t + 4)(t + 4) 6(4 t)(t 3)(t + 4)(t + 3) 6(t 4)(t 3)(t + 4)(t + 3) 28. Factor the trinomial: 6 u u 84 Factor out any common monomials first (including 1 if necessary). 6 (u + 2) (u 7) 6 (u 2) (u 7) 6 (u 2) (u + 7) 29. Write the expression in simpler form. ( 15 ) Use the distributive property to remove parentheses. a ( a + 3 ) a + 3a a 2 + 3a a + a + 3a a 2 + 3

31. Leonardo davinci's drawing relating a human figure to a square and a circle is shown in the following illustration. Find the area of the square if the man's height is 5a feet. Simplify.

8 31. Leonardo davinci's drawing relating a human figure to a square and a circle is shown in the following illustration. Find the area of the square if the man's height is 5a feet. Simplify. 25 a 2 5 a 2 5 a 32. One month before a stock car race, the sale of ads for the official race program was slow. Only 12 pages, or just 60% of the available pages, had been sol What was the total number of pages devoted to advertising in the program? Draw a diagram to help organize the facts of the problem Factor the trinomial: 28ty 2 23ty + 15t e. f. t(3 7y)(4y 5) t(7y 3)(4y + 5) t(7y 3)(5y + 4) t(7y 3)(4y 5) t(3 7y)(5y + 4) t(3 7y)(4y + 5) 34. Complete factorization: y 2 10 y + 24 = (y? )(? 4). (y 6) (y 4) (y + 6) (y 4) (y 10) (y 4) (y 6) (24 y 4) e. (y 10) (y + 4)

9 35. If a house is purchased for $ and is expected to appreciate $700 per year, find a polynomial function that will give the value y of the house in x years. y = 700 x y = 700 x none of these y = 1400 x e. y = 1050 x f. y = 700 x The seawater Orthlieb Pool in Casablanca, Morocco is the largest swimming pool in the worl With a perimeter of 1066 meters, this rectangular shaped pool has a length that is 29 meters more than 6 times its width. Find its dimensions. 71 meters and 455 meters 73 meters and 467 meters 75 meters and 479 meters 72 meters and 461 meters 37. Find the area of the figure below. a = 10, b = 6, c = 10, d = 4. e. 100 x x x x 2 2 x x x x x Solve the equation: 7 x 2 4 x = 0 x = 4 7, x = 0 x = 7 4, x = 0 x = 4, x = 7 x = 4 7, x = 7 4

10 39. If the perimeter in inches of the checkerboard, shown in the illustration is 68m 2 72m + 40, what is the length of one side? e. f. 17m 2 18m m 2 20m m 2 18m m 2 19m m 2 19m m 2 18m Solve the formula for the given variable. 4y 20 = h for y h y = h y = 4 5 y = h 5 4 y = h Simplify the following expression. 4 z 5 2 z z 2 2 z Factor out 1 from the polynomial 10 x + 4 y. ( 1 ) ( 10 x + 4 y ) ( 1 ) ( 10 x 4 y )

11 43. Given z 2 17 z + 72, what is the coefficient of the middle term? Write the answer as the sum of two numbers whose product equals the last term. 17 = = = = Factor the polynomial: 5x (x 2)(x 2 + 2x + 4) (5x 2)(x 2 + 2x + 4) 5(x 2)(x 2 2x + 4) 45. A 9 foot pipe has been cut into two sections, one 2 times as long as the other. How long is each section? 2 ft and 7 ft 4 ft and 5 ft 3 ft and 6 ft 1 ft and 8 ft is 15% of what number? How many solutions does the following quadratic equation have? 6 a a = 4 two solutions one solution no solutions 48. Find the square root using a calculator and round the result to the nearest thousandth: e f

12 49. Complete the table of values. Input Output x x 5 + x 3 15? 45? Input Output x x 5 + x Input Output x x 5 + x Input Output x x 5 + x ANATOMY Use the measurements in the illustration to determine the length of the patient's arm if he lets it fall to his side, if a = and b = Select the correct answer:

13 51. Identify the coefficient of the term. 3 x 8 x 3 x Factor the trinomial: 6m 2 + 5m 6 e. f. (2m 3)(3m 2) (3 2m)(3m + 2) (2m 3)(3m + 2) (2m + 3)(3m + 2) (2m + 3)(3m 2) (2m + 3)(2 3m) 53. What numbers must appear in place of A, B and C, in order to make the following solution correct? 7 n n 560 = A (n n 80) = 7 (n B ) (n + C ). A = 7, B = 8, C = 10 A = 8, B = 10, C = 8 A = 7, B = 8, C = Write the expression without using a multiplication symbol. 3 a w 3aw 3ag aw 3a e. 3 + a + w 55. Evaluate the expression for the given values of the variables. a 2 + 2ab + b 2 for a = 5 and b =

56. For the finale of a musical, 45 dancers are to assemble in a triangular shaped series of rows, where each successive row has one more dancer than the previous row.

14 56. For the finale of a musical, 45 dancers are to assemble in a triangular shaped series of rows, where each successive row has one more dancer than the previous row. The illustration shows the beginning of such a formation. The relationship between the number of rows r and the number of dancers d is given by d = 1 2 r ( r + 1 ) Determine the number of rows in the formation Simplify the radical: a 7. a 3 a 4 a 6 a a a a 3 a Write the equation in quadratic form: 5 a a = 3 5 a a 3 = 0 5 a 2 = 8 a a a = Use the distributive property to remove parentheses. 10( a 2 ) 10a 12 10a 20 10a a + 2

15 60. The dimensions of a family portrait and the frame in which it is mounted are given in the illustration below, where a = 6, b = 5, c = 20, d = 20. Write an algebraic expression that describes the area of the portrait. 25 x 2 20 x 2 ( 6 x 5 ) 100 x x 3

16 ANSWER KEY 1. b 2. c 3. d 4. a 5. c 6. a 7. a 8. c 9. a 10. b 11. a 12. a,c,e 13. c 14. c 15. c 16. c 17. d 18. a 19. a 20. a 21. a 22. c 23. a 24. a 25. d 26. b 27. e 28. b 29. a 30. b 31. a 32. c 33. f 34. a 35. b 36. d 37. a 38. a 39. a 40. d 41. c 42. b 43. a 44. a 45. c 46. c 47. a 48. f 49. c 50. b 51. b 52. e 53. c 54. a 55. d 56. a 57. a 58. a 59. c 60. b

My Math Plan Assessment #1 Study Guide

My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.