Algebra II Benchmark 3. 4) Simplify. 1) Simplify. 5) What is the simplified form of the following expression? 2) Simplify the expression.

Transcription

1 lgebra II enchmark 3 Please choose the best answer choice for each of the following questions. 1) Simplify. 4) Simplify. 1 x ItemI 2K orrect Standard: II 7.0 ItemI 2K orrect Standard: II 7.0 5) What is the simplified form of the following expression? 2) Simplify the expression. ItemI 2K orrect Standard: II 7.0 3) Simplify the expression below. Then evaluate for. 1 2 ItemI 2K orrect Standard: II 7.0 ItemI 2K orrect Standard: II 4.0 6) gnes would like to factor into a perfect square. For which integer(s) b can her expression be factored into a perfect square? 12 only 24 only ItemI 2K orrect lgebra II enchmark 3 Page 1

2 Standard: II 4.0 7) Francis oversees the financial data for a retail store. The store s total daily profit is represented by. The number of customers who enter the store in a day is represented by. Which expression represents the profit-percustomer ratio? ItemI 2K orrect Standard: II 4.0 8) ngela and Hugo have found two factors of. These factors are and. If they factor completely, what are the remaining factors? and and and ItemI 2K orrect Standard: II 3.0 and 9) Find the product. ItemI 2K orrect Standard: II ) The volume of a cardboard box is given by the function. Which of the following can also be used to represent this volume? ItemI 2K orrect Standard: II ) Simplify. (x 2 + 2x 4) (4x 2 + 2x 7) 3x 2 + 4x 11 3x 2 + 4x + 3 3x x ItemI 2K orrect Standard: II ) If and, what is? ItemI 2K orrect Standard: II 24.0 lgebra II enchmark 3 Page 2

3 13) Which of the following functions is the inverse of f(x) = 5x 3? 14) Which of the following is the graph of? ItemI 2K orrect Standard: II 24.0 ItemI 2K orrect Standard: II 17.0 lgebra II enchmark 3 Page 3

4 15) Given the equation of a circle,, write the equation in standard form. ItemI 2K orrect Standard: II ) The Millers are using a coordinate grid to plan the layout of flower beds in their backyard. Which equation represents the elliptical rose garden they sketched? 16) Which of these is a possible equation for the graph below? ItemI 2K orrect Standard: II 16.0 ItemI 2K orrect Standard: II ) What is the minimum value of the function y = x 2 4? ItemI 2K orrect Standard: II 10.0 lgebra II enchmark 3 Page 4

5 19) Mr. Henderson asked four students to graph the function. Which student graph is correct? ItemI 2K orrect Standard: II ) Sammy plotted a parabola on this coordinate grid. Which equation represents Sammy s parabola? ItemI 2K orrect Standard: II 10.0 lgebra II enchmark 3 Page 5

6 21) Mr. Thomas showed the graph of to his class. 23) Ms. Evans asked her class to consider the following statement. If is a real number, then is a real number. For which value of is this statement false? One of the zeros of this function is. What is the other zero? 1 2 ItemI 2K orrect Standard: II ) For which of these values will the inequality ItemI 2K orrect Standard: II 15.0 NEVER be true? ItemI 2K orrect Standard: II ) Which statement about the functions and is NOT TRUE? They both have the same range. They both have the same domain. They both have the same end behavior. They both have the same horizontal asymptote. ItemI 2K orrect Standard: II 15.0 lgebra II enchmark 3 Page 6

7 25) Which ordered pair is the solution to the system of equations below? 27) Ethan wrote this matrix equation. ItemI 2K orrect Standard: II ) Laura has an electrical problem at her home. She has called both ce Electric ompany and oone Electric ompany to find out how much they charge for repairs. ce Electric ompany charges a flat fee of $50.00 plus $15.00 per hour. oone Electric ompany charges $10.00 per hour plus a flat fee of $ If x represents the number of hours worked and y is the total amount charged, which system of equations models this situation? What is the solution to Ethan s equation? ItemI 2K orrect Standard: II ) nutrition specialist planned a lowcalorie, low-fat diet for a patient. The patient s daily calorie intake from 540 grams of food will be 2410 calories with 40% of the calories from protein. There are 4 calories per gram of protein, 4 calories per gram of carbohydrate, and 9 calories per gram of fat. How many daily grams of protein (p ), carbohydrates ( c ), and fat ( f ) will this diet include? (Hint: Use ramer s rule to solve.) p = 241, c = 249, f = 50 p = 200, c = 290, f = 50 p = 241, c = 255, f = 44 p = 200, c = 296, f = 44 ItemI 2K orrect Standard: II 2.0 ItemI 2K orrect Standard: II 2.0 lgebra II enchmark 3 Page 7

8 29) If and, which of these represents? ItemI 2K orrect Standard: II ) evon is finding the sum of and. Part of his work is shown below. Step 1: Step 2: Which property did he use in step 2 of his work? addition property transitive property associative property commutative property ItemI 2K orrect Standard: II ) Mr. costa plans to build a deck. He wants the length of the deck to be 7 feet longer than the width (w) and the total area of the deck to be 120 square feet. To determine the width of his deck, he wrote the equation shown below. w(w + 7) = 120 Which quadratic formula setup can Mr. costa use to find an exact value of w? ItemI 2K orrect Standard: II ) Which equation describes the function graphed below? ItemI 2K orrect Standard: II 8.0 lgebra II enchmark 3 Page 8

9 33) Which of these is the set of all solutions to this equation? ItemI 2K orrect Standard: II ) new convertible sports car costs approximately $39,670. The car drops in value (depreciates) 5% each year. Estimate, to the nearest $1,000, what the car is worth two years after it has been sold. $32,000 $34,000 $36,000 $38,000 ItemI 2K orrect Standard: II ) Sandra found the answerto her problem to be. What was her final answer? 32i 128i ItemI 2K orrect Standard: II ) If i =, which of these expressions is the difference of ( 8 5i) and (2 3i), in standard form? 37) Simplify: ItemI 2K orrect Standard: II i i 10 2i 10 8i ItemI 2K orrect Standard: II 6.0 lgebra II enchmark 3 Page 9

10 38) Jeremy graphed two functions on this coordinate plane. 40) Jared deposited $150 into a savings account. The interest rate on the account is 2.5% compounded continuously. To determine how long it will take to double his money, Jared wrote this equation where t represents time, in years. Which equation represents Jeremy s graph? ItemI 2K orrect Standard: II 12.0 on 300 = 150e 0.025t Which equation is equivalent to the one above? ln 2 = t ln 300 = 3.75 t ln 2 = ln t ln 300 = ln 3.75 t ItemI 2K orrect Standard: II ) hoose the equivalent form for the equation below. 39) Jasper plans to use logarithms to solve the equation. Which of these equations can Jasper use to solve for? ItemI 2K orrect Standard: II 11.1 ItemI 2K orrect Standard: II ) What is the product of (2 5i) and (2 + 5i) in standard form? ItemI 2K orrect Standard: II 6.0 lgebra II enchmark 3 Page 10

11 43) Wade graphed the function. If a is negative and c is positive, which of the following could be Wade s graph? 44) Ms. Halperin s students have just graphed on the grid below. Ms. Halperin suggests that her students graph a second parabola. On a different coordinate grid, she would like her students to graph. Which graph represents their new parabola? ItemI 2K orrect Standard: II 9.0 ItemI 2K orrect lgebra II enchmark 3 Page 11

12 Standard: II ) my determined that equals the complex number. Which graph represents this complex number? 46) Erik knows that equals i. If he simplifies answer? 5 and 5 5 5i and 5i 5i ItemI 2K orrect Standard: II 5.0, what would be his 47) How can melia rewrite as a single logarithm? ItemI 2K orrect Standard: II 14.0 ItemI 2K orrect Standard: II 5.0 lgebra II enchmark 3 Page 12

13 48) alvin was asked to determine the approximate value of loga (15) 2 using the table below. If he uses the properties of logarithms to simplify his expression, which value should alvin obtain? ItemI 2K orrect Standard: II ) Erick is rearranging the letters in his name. How many different 5-letter combinations can be made with the letters E, R, I,, and K? ItemI 2K orrect Standard: II ) Mr. Pang has 8 types of flowers in his garden. He wants to put 3 types of flowers in a vase. How many groups of 3 different types of flowers can Mr. Pang create? ItemI 2K orrect Standard: II ) 4-person committee is formed from a group of 5 men and 3 women. What is the probability that the committee will be composed of 2 men and 2 women? ItemI 2K orrect Standard: II ) Kelley is picking out invitations for her birthday party. She can choose the paper color to be tan, gray, or white. She can pick bold or normal print. She can also pick a flower, a rainbow, a ballerina, or a heart for the front picture. What is the probability that Kelley will pick the invitations on gray paper with bold print and a heart? lgebra II enchmark 3 Page 13

14 ItemI 2K orrect Standard: II ) Maria graphs the function. Jake s graph is identical to Maria s. Which polynomial represents Jake s function? ItemI 2K orrect Standard: II ) What is the fourth term in the expansion of? -15,124x 4 22,680 x 3 ItemI 2K orrect Standard: II ) Look at the pattern below. 1, 5, 9, 13, 17, 21,... Which expression represents the value of the nth term in the pattern? ItemI 2K orrect Standard: II ) What is the limit of the series ? infinity ItemI 2K orrect Standard: II ) box contains 10 light bulbs. Of these, 7 bulbs work and 3 are defective. Michael randomly takes 3 bulbs out of the box. What is the probability that exactly 2 of the light bulbs Michael chooses will work? ItemI 2K orrect Standard: PS ) Shelly has 2 quarters, 10 dimes, 6 nickels, and 4 pennies in her pocket. She reaches into her pocket andpulls out a dime. Without putting back the dime, she pulls out another coin. What is the probability that the second coin is a quarter? lgebra II enchmark 3 Page 14

15 ItemI 2K orrect Standard: PS ) Three coins are tossed. What is the probability that all 3 land showing heads, given that at least 1 shows heads? 61) ngela rolls a pair of number cubes. What is the probability that their sum is 11, given that their sum is greater than 8? ItemI 2K orrect Standard: PS 2.0 ItemI 2K orrect Standard: PS ) This spinner is divided into 5 equal sections. 60) In Rebecca s neighborhood, 68% of the houses have garages, and 54% have a garage and a pool. What is the probability that a house in her neighborhood has a pool given that it has a garage? 14% 37% 54% 79% ItemI 2K orrect Standard: PS.2.0 If the arrow is spun 100 times, which of these is the EST prediction of the number of times it will land on an even number? ItemI 2K orrect Standard: PS 2.0 lgebra II enchmark 3 Page 15

16 63) If x is a real number, which best describes the values of x for which the inequality > 0 is true? all x >0 all x 0 all values of x no values of x ItemI kirstenwoo.1271 orrect Standard: II 15.0 lgebra II enchmark 3 Page 16