Putnam County School System Advanced Algebra Final Exam Fall 2024 PDF

Putnam County School System Test Booklet Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 Name Date Powered...

Putnam County School System Test Booklet Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 Name Date Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 1. Subjects are randomly assigned to a treatment group and a control group. What does this situation describe? A. a survey B. an observational study C. an event D. an experiment 2. A senator wants to find out the level of concern people in her state have about internet privacy issues. She conducted a poll by mailing surveys to 40% of registered voters whose names were randomly sampled. Survey participants were given the option of completing the survey online or returning the survey by mail. Over 20% of those who were mailed a survey completed it online or returned it by mail. The poll showed that 42% of respondents were “very concerned” about internet privacy. Which statement best explains why the sample is biased? A. The sample is biased because it only includes registered voters. B. The sample is biased because it is too small to represent the state population. C. The sample is biased because there were two methods to complete and return the poll. D. The sample is biased because they did not survey all registered voters, only those randomly chosen. 3. In a survey, a random selection of 2757 adults was asked whether they identified more strongly with political Party A, Party B, or Party C. The table shows the results of the survey broken down by gender. Based on the results from the survey, which conclusion is valid? A. Approximately 45% of adults identify most strongly with Party A. B. Approximately 42% of the males identify themselves with Party B. C. Approximately 50% of the males identify most strongly with Party C. D. Approximately 61% of the females identify most strongly with Party A. Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 4. Which graph shows a normal distribution of student heights with a mean of 170 cm and a standard deviation of 5 cm? A. B. C. D. Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 5. The results of a survey suggested that 64% of the voters will vote for a particular candidate in an election. The candidate wants to be 95% confident that she will receive the majority of the votes in the election. The results from 100 computer simulations of this situation are shown below. Based on the margin of error and these simulations, what is the range of the percentages of votes this candidate could receive? A. 0.43 to 0.63 B. 0.48 to 0.58 C. 0.54 to 0.74 D. 0.59 to 0.69 6. The owner of three bicycle shops records the number of bicycles sold by each store each week. The data for 10 weeks is summarized in the box-and-whisker plot below. The owner wrote a report based on the data in the box-and-whisker plot. Which of the sentences from the report are justified by the data in the plot? Choose all that are correct. A. The weekly sales for Store 1 and Store 3 do not show a statistically significant difference. B. Store 2 sold the fewest bicycles per hour opened. C. Store 3 has the greatest mean weekly bicycle sales. D. The weekly sales for Store 2 are skewed, while the weekly sales for Stores 1 and 3 appear to be more normally distributed. E. For each of the 10 weeks, Store 2 sold fewer bicycles than either Store 1 or Store 3. Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 7. Which function represents the graph below? A. f(x) = 1 + 2 log(3 − x) B. f(x) = 1 + 2 log(3 + x) C. f(x) = 1 − 2 log(3 − x) D. f(x) = 1 − 2 log(3 + x) 8. Solve for x. log8 4 = x A. 2 3 B. 3 2 C. 32 D. 4,096 9. Which expression represents the solution of e4x = 10 ? A. log1 010 4 B. log1 04 10 C. ln 4 10 D. ln 10 4 Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 10. Through conservation efforts, a previously endangered species of penguin is making a comeback. When the conversation effort began, there were 75 penguins of this species in the wild, and since then, the number of penguins in the wild has been doubling every 5 years. If y is the number of years since the conservation effort began and p is the number of penguins in the wild, which of these equations represents this situation? A. p = 75 (2y− 5 ) B. p = 75 (2y+ 5 ) C. p = 75 (25y) ⎛ ⎞ D. y p = 75 2 5 ⎝ ⎠ 11. What is the logarithmic transformation of the equation given below? y = 20x8 A. y = log 20 + 8 log x B. log y = log 20 + 8 log x C. log y = 20 + 8 log x D. log y = log 20 + x8 12. √ Select all expressions equivalent to 2 24. A. 2√16 B. 4 22 C. 2 4 2 D. √22 13. In the equation shown, x represents a real number. √x − 4 = 4 What is the solution to this equation? A. x = 4 B. x = 8 C. x = 12 D. x = 20 Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 14. Casey wants to write an equation to express that the square root of the sum of twice a number and 7 is equal to the same number increased by 2. Which of these gives the equation he can use as well as the solution? A. The equation is √2x + 7 = x + 2 and its solutions are x = 6 ± √11. B. The equation is √2x + 7 = x + 2 and its solutions are x = –3 and 1. C. The equation is √2x + 7 = x + 2 and its solution is x = 1. D. The equation is √2x + 7 = x + 2 and its solution is x = 6 + √11. 15. The graph below shows how the vibration frequency of a certain guitar string varies with tension when its length is held constant. Which function could describe f(x), the vibration frequency in hertz, of the guitar string when its tension is x pounds? A. f(x) = ax B. f(x) = a√x C. f(x) = ax3 D. f(x) = ax2 16. 1 Hakim throws a javelin as far as he can. His throw is described by the equation y =− (x − 30)2 + 20, 45 where y represents the height of the javelin when it has traveled a distance x. What are the coordinates of the point at the highest point of Hakim’s throw? A. (45, 30) B. (20, 30) C. (30, 45) D. (30, 20) Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 17. Look at the expression below. 4a2 − b2 Which of the following is equivalent to the expression? A. (2a − b) (2a − b) B. (4a − b) (a − b) C. (4a − b) (a + b) D. (2a − b) (2a + b) 18. The graph below shows how the temperature of a substance varies with time during a certain science experiment. Assume that there are no other x-intercepts besides those showing on the graph. Which equation best models the function f(x) , the Celsius temperature of the substance after x minutes, shown in the graph? A. f(x) = 2(x + 1)(x + 3)(x + 6) B. f(x) = 2(x − 1)2 (x − 3)(x − 6) C. 1 f(x) = (x + 1)(x + 3)(x + 6) 9 D. 1 f(x) = (x − 1)2 (x − 3)(x − 6) 9 19. What is the product of the complex numbers below? 2i(3 + 2i) A. 4 + 6i B. −4 + 6i C. 8i D. 10i Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 20. The owner of a hotdog stand wants to make the price of her hotdogs reasonable but also maximize her profits. In the equation below, x represents the extreme values for the possible prices of a hotdog. −200x2 +2,800x − 4,800 = 0 To solve for x, the owner first factors –200 out of the trinomial expression and then factors the result. Which of these is one of those factors? A. x + 12 B. x − 2 C. x + 24 D. x − 14 21. Which of these represents the solution to 3x2 + 14 = −37 ? A. x = ±17 + i B. x = ±17i C. x = ±17i2 D. x = ±i√17 22. Solve the following system of equations. { y = x2 − 4x − 5 y= x−9 A. (−2, −11) and (7, −2) B. (2, −7) and (−7, −16) C. (−1, −10) and (−4, −13) D. (1, −8) and (4, −5) 23. Miguel launches his model rocket. He times the rocket’s flight from launch to landing. Miguel believes the function representing the relationship between the time in seconds and the rocket’s height in feet is h(t) = −50t2 + 150t. Use the zeros of the polynomial to determine the flight time of Miguel’s rocket. A. 1.5 seconds B. 2.5 seconds C. 3.0 seconds D. 5.0 seconds 24. Which equation has exactly one real root? A. y = 4x2 − 12x + 9 B. y = 2x2 + 5x + 8 C. y = 2x2 + 7x − 15 D. y = 4x2 − 8x + 3 Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 25. How do you write the quotient in simplest form? 8y 2 32y 5 A. 1 4y 3 B. 1 24y 3 C. y7 4 D. 4y3 26. Simplify. x2 −9 x2 −x−6 A. −3 −x−2 B. x−3 x−2 C. x−3 x+2 D. x+3 x+2 27. Which expression is equivalent to the expression below? 5a 2a a−3 + a+3 A. 7 2 B. 7a2 +9a a2 −9 C. 7a2 a2 −9 D. 7a a2 −9 28. Simplify. 5 4 2a − 5a2 A. 25a−8 10a2 B. 25a−8 10a C. 1 10a2 D. 1 a(2−5a) Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 29. How do you write the quotient in the simplest form? x2 −9 ÷ (x − 3) 4x2 A. x+3 4x2 2 B. (x+3)(x−3) 4x2 C. 4x 2 x+3 D. 4x−3 x2 −9 30. Simplify. 3x6 b5 14 ⋅ 7 15x7 b3 A. 14b2 22x B. 2 5xb3 C. 2b2 5x D. 3b2 5x 2 31. Which of these represents the graph of f(x) = 3x −13x+4 ? 2x2 −9x+4 A. Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 B. C. D. Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 32. The graph below shows a rational function. Select the function that represents the graph. A. 3x+5 y = x+1 B. 3x+5 y = x+2 C. x2 y = x+3 D. x y = x−1 33. Solve for x: 5 3 = x+2 x+7 A. 5 2 B. 2 C. 3 D. 11 2 34. Which of the following is the solution to the equation below? 1 2 2x−3 + x−2 = 2 x−4 x −6x+8 A. x=3 B. x=7 C. x=9 D. x = 13 Powered by Illuminate Education. Advanced Algebra_FinalExam_Fall 2024 Assessment ID:2425001140 35. 2x 4 What is the solution to x−2 − 1 = x−2 ? A. 2 x= 3 B. x = 2 C. x = 6 D. There is no solution. Powered by Illuminate Education.