Int Math 2 Midterm Review Handout (Modules 1-4)

Transcription

1 Int Math 2 Midterm Review Handout (Modules -) Write y y as a radical expression. 9 y 8 8 y 9 36 y 5 5 y 36 2 Write the expression 6 6 in radical form, and simplify. Round to the nearest whole number if necessary. ; 2 6 ; 2 ( 6 ) ; ; Short nswer: (Put all work and answers in the boxes below). a.) Write a function to match the graph. b.) Write the range in set notation..

2 Simplify the expression biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years. White-sided jackrabbits: 7.2x x lack-tailed jackrabbits: 0.3x x +. What polynomial models the total number of white-sided and black-tailed jackrabbits? 7.5x 2 9.x x x.3 7.5x x x 2 9.x.3 6 How many factors does the algebraic expression 5xy have? 7 escribe the error Tamba made when simplifying the expression shown. 7(3x ) = 2x 3 5 The expression was changed from one term into two. The factor was not multiplied by both terms. The common terms were not collected. The coefficient in the simplified expression is not 2. 8 Simplify. ll variables represent nonnegative numbers. Ê ËÁ a 2 b 2 ˆ 2 b 2 a 8 b 3 a 2 b 3 a 6 b 2 a 8 b 2 2

3 9 Short nswer: (Put all work and answer in the box below. Solve 2 6 3x = 6. Must show LL work necessary. 0 Write y y 9 9 y 9 y 9 as a radical expression. The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30 meters. round the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Which expression represents the area of the tiled floor? (2w w) m 2 9 y (2w w + 75) m 2 (w w + 200) m 2 (w w) m 2 2 Which pair of functions are inverses of each other? 3 Is the following representation of the interval shown on the number line? (, 6] Yes No 3

4 oes the graph below increase on the following interval? [-6,2) 5 Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 6g g 3 + 0g g + 0g 2 g 3 ; cubic binomial 0g 3 g 2 + 6g 2; quadratic binomial g 3 0g 2 + 6g 2; cubic trinomial g 3 + 0g 2 + 6g 2; cubic polynomial Yes No 6 Short nswer: (Put all work and answers in the box below). Use the Power of a Power Property to show that taking the square root of a number is the same as raising a number to the power. (Hint: Start with the fact that the square of the square root of a number is equal to Ê ˆ 2 that number, x ËÁ = x. Then write x in a second way using the Power of a Power Property and set the two expressions equal to each other.)

5 7 Find the inverse of f(x) = x + 2. f (x) = x 2 f (x) = 2x f (x) = (x 2) f (x) = x 2 8 Jennifer is a car saleswoman. She is paid a salary of $2000 per month plus $500 for each car that she sells. Her salary can be modeled by the equation f(x) = 500x where x is the number of cars sold. Graph this equation and give its reasonable domain and range in this context. : {$500, $2500, $500, $6500,...} R: {0,, 2, 3,...} : {0,, 2, 3,...} R: {$2000, $2500, $3000, $3500,...} : {0,, 2, 3,...} R: {$500, $2500, $500, 6500,...} : {$2000, $2500, $3000, $3500,...} R: {0,, 2, 3,...} 5

6 9 dd. ( 8r 2 s + 8rs) + ( 2r 2 s 5rs 6) + ( 7rs 2) 0r 2 s + 6rs 8 3r 2 s rs + 2 5r 2 s + rs 8 0r 2 s rs 8 20 Given f(x) = x + 2 and g(x) = x + 2, choose True or False for the following statement. g(x) is f(x) translated up 2 units and left units True False 2 Short nswer: (Put all work and answers in the boxes below). Use the figure below to answer the following questions. a.) Write the domain nd the range of the function in interval notation. b.) escribe the end behavior of the function. 6

7 3 22 Simplify the expression 27x 9. ssume that all variables are positive. 3x 5 3x x x 5 23 How many terms are in the algebraic expression 7x 5xy + 3y? What are the solutions to x + 7 = 5? -3-2,2-3,- No Solutions 25 Short nswer: (Put all work and answers in the box below). Graph the solutions to 2 x 3 = Which of the following polynomials is a binomial with a degree of 3? 7x 3 y 3x 2x 3 7x 9y 2xy x 3 y + 5x 8 7

8 27 The length of a rectangle is (2x + ). The width of the rectangle is (x 2 + 2x ). Which expression represents the perimeter of the rectangle? x 2 + x + 3 2x 2 + 8x 2x 2 + 2x + 6 x 3 + 2x 2 + x Solve 3x + = 7. x = 2 or x = 8 3 x = 2 or x = 8 3 x = 2 only 29 Evaluate the algebraic expression 9(x + y) 2 when x = 5 and y = x = 8 3 only 30 Short nswer: (Put all work and answers in the box below). 3 Use the power of a power property to show that 32 6 Ê 3 = 32 ËÁ ˆ 6. 3 Solve to find the inverse of f(x) = 3x 7. g(x) = 3 x + 7 g(x) = 3x + 7 g(x) = 3 x g(x) = 3 x 7 3 8

9 32 arlita has a rectangular swimming pool in her back yard that has a length of 22 feet and a width of 6 feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood deck c + 2w 38 + c + w c + 8w 6 + 8c + 8w 33 Which of the following best describes the end behavior of f(x) = x 2 2? 3 Short nswer: (Put all work and answers in the boxes below). Graph the function with the given domain. lassify the function as discrete or continuous. Then identify the range of the function for the given domain as an inequality, set notation, and interval notation. y = 5 x + 6; domain x 2 6 a.) b.) 9

10 35 Last year, a large trucking company delivered tons of goods with an average value of $23,000 per ton. What was the total value of the goods delivered? Write the answer in scientific notation dollars dollars dollars dollars 36 Simplify the expression. (5m 3 5n 3 )(m 50m / 9 n / 32 50m 5 / 3 n 3 / 8 50mn / 72 9 / 2 50mn 2n 8 ) 37 What is the simplified form of each expression? ( 5g h 6 ) 2 (g 5 h 5 ) 5 25g 33 h 37 25g 6 h 8 g 33 h g 33 h Simplify the expression. Ê x + 5y 3 ˆ + 6 ËÁ Ê 3x ËÁ 2 + 5xy ˆ Ê y 3 ËÁ + + 6xy ˆ 2x + 6y 3 + xy 2x + 6y 3 xy + x + y 3 + xy + 8 2x 6y 3 39 Simplify the expression. Ê x 2 ˆ ËÁ Ê x 2 ËÁ 2x + ˆ 2x 2x 2 2x 288 2x 2 + 2x x 288 0

11 0 escribe the end behavior of the following function. f(x) = x 2 x + Short nswer: (Put work and answers in the boxes below). etermine the domain and the range of the following graphs. a.) b.)