Advanced Algebra/Trigonometry SUMMER PACKET Introduction (12 2)

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1 NAME Advanced Algebra/Trigonometry SUMMER PACKET Introduction (12 2) This packet is due on the first day of school in September. You are responsible to do and show work for any 50 problems that you decide to do. You must show work on these 50 problems to receive credit. If you choose a problem that only requires a calculator, you must write down the key strokes that you used. This assignment will count as a quiz grade so this is a great opportunity to start your senior year with an A in math. There will be a separate file on the CHS math department website that will contain some notes, hints, and worked out solutions that will help you complete this packet successfully. There are roughly 10 weeks in the summer before your senior year begins and we suggest that you try to do 5 problems a week so you will not feel overwhelmed if you wait until summer is almost over. This packet will help you review what you have already learned and give you a head start to having a great year in this course. HAVE A GREAT SUMMER AND WE LOOK FORWARD TO HAVING YOU AS A STUDENT WHEN SCHOOL STARTS IN SEPTEMBER!!!!

2 1. If a + 3b= 13 and a + b = 5, the value of b is A) 1 B) 7 C) 4.5 D) 4 2. If a = 3 and b = 1, what is the value of ab b 2? A) 2 B) 2 C) 4 D) 4 3. The expression (2x 2 + 6x + 5) (6x 2 + 3x + 5) is A) 4x 2 + 3x B) 4x 2 3x C) 4x 2 3x + 10 D) 4x 2 + 3x If r = 2 and s = 7, what is the value of r s A) 5 B) 5 C) 9 D) 9 5. On February 18, from 9 a.m. until 2 p.m., the temperature rose from 14 F to 36 F. What was the total increase in temperature during this time period? A) 50 B) 36 C) 32 D) Which expression is x 1 y 2? A) xy B) y 2 x C) x 2 y D) xy 2 7. The expression y 3 + y 3 is A) 2y 6 B) 2y 3 C) y 9 D) y 6 8. The expression ( 2a 2 b 3 )(4ab 5 )(6a 3 b 2 ) is A) 8a 6 b 30 B) 48a 5 b 10 C) 48a 6 b 10 D) 48a 5 b What is the product of 10x 4 y 2 and 3xy 3? A) 30x 4 y 5 B) 30x 4 y 6 C) 30x 5 y 5 D) 30x 5 y Expressed in simplest form, (3x 3 )(2y) 2 (4x 4 ) is A) 24x 12 y 2 B) 24x 7 y 2 C) 48x 12 y 2 D) 48x 7 y When 9x 5 is divided by 3x 3, x 0, the quotient is A) 3x 2 B) 3x 2 C) 27x 15 D) 27x The product of 3x 5 and 2x 4 is A) 5x 9 B) 5x 20 C) 6x 9 D) 6x The expression is A) 27 9 B) C) 3 9 D) The length of a rectangle is 3a 2 b 4 ft and the width is 5a 3 b 2 ft. What is the area in ft 2? A) 15a 5 b 6 B) 15a 6 b 8 C) 15b 7 a 4 D) 15b 12 a What is the product of 2x 2 y 3 and 5x 3 y? A) 10x 6 y 4 B) -10x 3 y 3 C) -10x 5 y 4 D) -10x 6 y The expression (ab 4 c 2 )(a 2 c 3 ) is A) a 2 b 5 c 6 B) a 3 b 4 c 5 C) a 3 c 5 D) a 2 b 3 c The expression ( 4a 3 b) 2 is A) 16a 6 b 2 B) 16a 6 b 2 C) 16a 5 b 2 D) 8a 6 b The expression (6x 3 y 6 ) 2 is A) 36x 6 y 12 B) 36x 5 y 8 C) 12x 6 y 12 D) 6x 6 y What is the value of ? A) 0 B) C) 1 D) The expression is A) 8 24 B) 8 2 C) 8 2 D) The video of the movie Star Wars earned $193,500,000 in rental fees during its first year. Expressed in scientific notation, the number of dollars earned is A) B) C) D) According to the 2000 census, the population of New York State was approximately 18,900,000. How is this number expressed in scientific notation? A) 1890 x 10 4 B) 18.9 x 10 6 C) 1.89 x 10 7 D) 189 x The expression is A) B) 62,000 C) 6.2 x 10 4 D) 6.2 x In a year, there are approximately 530,000 minutes. When this number is written in scientific notation, the numerical value of the exponent is A) 5 B) 5 C) 4 D) 4

3 25. The distance from Earth to the Sun is approximately 93 million miles. A scientist would write that number as A) B) C) D) What is the value of n if the number is written in the form n? A) 6 B) 5 C) 5 D) A micron is a unit used to measure specimens viewed with a microscope. One micron is inch. How is this number expressed in scientific notation? A) B) C) D) What is the sum of 2m 2 + 3m 4 and m 2 3m 2? A) m 2 6 B) 3m 2 6 C) 3m 2 + 6m 6 D) m 2 + 6m What is the sum of x 2 3x + 7 and 3x 2 + 5x 9? A) 4x 2 8x + 2 B) 4x 2 + 2x + 16 C) 4x 2 2x 2 D) 4x 2 + 2x The sum of 8x 2 x + 4 and x 5 is A) 8x B) 8x 2 1 C) 8x 2 2x + 9 D) 8x 2 2x When 3a 2 7a + 6 is subtracted from 4a 2 3a + 4, the result is A) a 2 + 4a 2 B) a 2 10a 2 C) a 2 4a + 2 D) 7a 2 10a The expression (x 2 5x 2) ( 6x 2 7x 3) is A) 7x 2 12x 5 B) 7x 2 2x + 1 C) 7x 2 + 2x + 1 D) 7x 2 + 2x When 3x 2 8x is subtracted from 2x 2 + 3x, the difference is A) x x B) x 2 11x C) x 2 5x D) x 2 5x 34. The expression (3x 2 + 2xy + 7) (6x 2 4xy + 3) is A) 3x 2 2xy + 4 B) 3x 2 2xy + 4 C) 3x 2 + 6xy + 4 D) 3x 2 6xy Kaylie's rectangular backyard is fenced in on three sides. The sum of the length of the fencing on these three sides is 2x 2 + 6x + 7. Tomorrow, she will add a fourth side to the fence, with a length of 2x 5. What will be the total length of the four sides? A) 4x 3 + 6x + 2 B) 2x 2 + 8x + 7 C) 2x 2 + 8x + 2 D) 2x 2 + 6x What is the product of 2r 2 5 and 3r? A) 6r 3 15r B) 6r 3 5 C) 6r 2 15r D) 6r Base your answer to the following question on the following information: The width of a rectangle is 4 less than its length. If x represents the length, which expression represents the area of the rectangle? A) x 2 4x B) x 2 4 C) 4x 2 D) 2x 2 8x 38. The width of a rectangle is represented by 2x and the length is represented by x 2 - x + 3. Which expression represents the area of the rectangle? A) 2x 3 - x + 3 B) x 2 + x + 3 C) 2x 2 + 2x + 6 D) 2x 3-2x 2 + 6x 39. What is the product of (c + 8) and (c - 5)? A) c 2 + 3c 40 B) c 2 + 3c 40 C) c c 40 D) c What is the product of x 2 y and xy 3? A) x 2 y 3 B) x 3 y 4 C) x 2 D) x 3 y 3 y The expression (x 3) 2 is A) x 2 9 B) x C) x 2 6x + 9 D) x 2 + 6x Which trinomial is (3x 1)(x + 4)? A) 3x x 4 B) 3x x 4 C) 3x 2 11x + 4 D) 3x x What is 6x 3 + 4x 2 + 2x divided by 2x? A) 3x 2 + 2x B) 3x 2 + 2x + 1 C) 4x 2 + 2x D) 4x 2 + 2x The expression (50x 3 60x x) 10x is equivalent to A) 5x 2 6x +1 B) 5x 3 6x 2 + x C) 5x 2 60x x D) 5x 2 6x

4 45. When 3x 2 6x is divided by 3x, the result is A) 2x B) 2x C) x + 2 D) x Expressed in factored form, the binominal 4a 2 9b 2 is A) (2a 3b)(2a 3b) B) (2a + 3b)(2a 3b) C) (4a 3b)(a + 3b) D) (2a 9b)(2a + b) 47. Which expression is a factor of x 2 81? A) (x 81) B) (x 18) C) (x + 9) D) (x + 18) 48. Which is a factor of x 2 + 5x 24? A) (x + 4) B) (x 4) C) (x + 3) D) (x 3) 49. What are the factors of x 2 + 3x 4? A) (x + 1) and (x 4) B) (x 1) and (x + 4) C) (x + 3) and (x 4) D) (x + 2) and (x + 2) 50. When Albert flips open his mathematics textbook, he notices that the product of the page numbers of the two facing pages that he sees is 156. Which equation could be used to find the page numbers that Albert is looking at? A) x + (x + 1) = 156 B) (x + 1) + (x + 2) = 156 C) (x + 1)(x + 3) = 156 D) x(x + 1) = Factor completely: 2x 2-50 A) 2(x - 5) 2 B) 2(x - 50) 2 C) 2(x + 5)(x - 5) D) (2x + 5)(2x - 5) 52. The greatest common factor of 12x 2 y 3 and 24xy 2 is A) 6xy B) 24xy 2 C) 12xy 2 D) 2xy 53. For which value of x is the expression undefined? A) 1 B) 1 C) 5 D) Jamie is 5 years older than her sister Amy. If the sum of their ages is 19, how old is Jamie? A) 5 B) 7 C) 12 D) Which expression is 7? A) 16 B) 21 C) 70 D) 56. Which number is irrational? A) B) C) D) 57. If the area of a square garden is 48 square feet, what is the length, in feet, of one side of the garden? A) 12 B) 4 C) 16 D) The expression can be simplified to A) 5 B) 5 C) 2 D) The expression is A) 2 B) 10 C) 100 D) The expression is equal to A) 2 B) 3 C) 5 D) Robin spent $17 at an amusement park for admission and rides. If she paid $5 for admission, and rides cost $3 each, what is the total number of rides that she went on? A) 12 B) 2 C) 9 D) What is the value of x in the equation 13x 2(x + 4) = 8x + 1? A) 1 B) 2 C) 3 D) What is the value of x in the equation 5(2x 7) = 15x 10? A) 1 B) 0.6 C) 5 D) Kevin and Hunter have $273 in total. If Kevin has $27 more than Hunter has, how much money does Kevin have? A) $27 B) $123 C) $150 D) $ What is the solution of the equation 3y 5y + 10 = 36? A) 13 B) 2 C) 4.5 D) Three times as many robins as cardinals visited a bird feeder. If a total of 20 robins and cardinals visited the feeder, how many were robins? A) 5 B) 10 C) 15 D) If 6x + 2y = 3x + 8y, which of the following must be true? A) x = 2y B) y = 2x C) y = x + 2 D) y = x 2

5 68. What is the value of n in the equation 0.6(n + 10) = 3.6? A) 0.4 B) 5 C) 4 D) A girl can ski down a hill five times as fast as she can climb up the same hill. If she can climb up the hill and ski down in a total of 9 minutes, how many minutes does it take her to climb up the hill? A) 1.8 B) 4.5 C) 7.2 D) What is the value of p in the equation 8p + 2 = 4p 10? A) 1 B) 1 C) 3 D) What is the value of n in the equation 3n 8 = 32 n? A) 10 B) 6 C) 6 D) If c = 2m + d, then m is equal to A) B) C) D) d 2c 73. Which equation represents the line whose slope is 2 and whose y-intercept is 6? A) y = 2x +6 B) y = 6x +2 C) 2y + 6x = 0 D) y + 2x = If a line is horizontal, its slope is A) 1 B) 0 C) undefined D) negative 75. What is the y-intercept of the graph of the line whose equation is y = x + 4? A) B) C) 0 D) 4