Quarter 3 Review - Honors 1. Amber conducted a survey to find the eye colors of her neighbors. Use the following information to complete the frequency table. (Hint: Extend the table to include a column total and Row total) She surveyed 30 children, 15 teenagers, and 5 adults. Ten adults had blue eyes, and ten adults had green eyes. No teenagers had green eyes. Six teenagers had hazel eyes. The same number of teenagers had brown eyes as hazel eyes. In all, 45 people had brown eyes Blue Green Hazel Brown Child 3 4 9 14 Teenager Adult Use the above frequency table and answer the following questions. a) What is the conditional relative frequency of a person being a child given that his/her eyes is blue in color? b) What is the conditional relative frequency of a person having blue eyes given that is a child? c) What is the joint relative frequency of a teenager having hazel eyes? d) What is the marginal frequency for a person having green eyes? e) What is the conditional relative frequency for a person having brown eyes given he/she is an adult?
. Solve each problem.. The number of calls per day to a fire and rescue service for three weeks is given below. Use the data to complete the frequency table. Calls for Service 5 17 1 0 6 3 8 15 1 4 19 16 8 11 13 18 3 10 6 Fire and Rescue Service Number of Calls Frequency 0 3 4 7 8 11 1 15 16 19 a. Use the frequency table to make a histogram with a title and axis labels. b. Which intervals have the same frequency? c. Is the distribution symmetrical? Explain. d. Use the histogram to estimate the mean. Then compare your answer with the actual mean, found by using the original data. e. Use the histogram to estimate the median. Then compare your answer with the actual median, found by using the original data. f. By examining the histogram, can you tell that the mode number of calls lies in the first interval? Explain your reasoning. 3. The data sets below show the ages of the members of two clubs. Use the data for Problems 5 9. Club A: 4, 38, 40, 34, 35, 48, 38, 45 Club B:, 44, 43, 63,, 7, 58, 65 a. Find the mean, median, range, and interquartile range for Club A. b. Find the mean, median, range, and interquartile range for Club B. c. Find the standard deviation for each club. Round to the nearest tenth. d. Use your statistics to compare the ages and the spread of ages on the two clubs. e. Members of Club A claim that they have the younger club. Members of Club B make the same claim. Explain how that could happen.
4. Make a box plot for this set of data. Be sure to mark the five key points. 10, 14, 18, 1, 0, 4, 9, 5, 14, 16 5. Find the degree of each monomial. a) b c b) 4d 4 e c) 1 d) 7y 5 6. Simplify. a) (g 4 4g + 11) + ( g 3 + 8g) b) 6j j + 5 + 3j + 4j 6 c) ( 1h 4 + h) ( 6h 4 + 3h 4h) d) 3d + 8d (d 7d + 6) 7. Simplify each product. a) (x 6)(x + 3) b) (4p + )(3p 1) c) (3a + a + 4)(a 6) d) (c + 8)(c 4c 1) 8. Factor each expression. Check your answer. a) n 1n + 35 b) x + 16 x + 63 c) z + 3z 40 d) a 7a 18 e) 6r 10r 4 f) c 3c + 11 g) 45k 0 h) 5x 144 i) 8b + 80b + 00
9. Factor each expression. a) 18r 3 1r + 1r 14 b) 45w 4 36w 3 + 15w 1w 10. Find the Zeros of each function. a) h(f) = (3f + )(f 5) b) f(d) = d(d 8) c) k(x) = (x 7)(4x + 10) 11. Solve each equation by completing the square. If necessary, round to the nearest hundredth. a) r + 8r + 13 = 0 b) y + 16y = 17 c) k + 4k = 5 1. The height of a triangle is 4x inches and the base is (5x + 1) inches. The area of the triangle is 500 square inches. What are the dimensions of the base and height of the triangle? 13. Use the quadratic formula to solve each equation. a) x 6x + 4 = 0 b) 7d + d + 9 = 0 c) j 3j = 1 14. Find the number of real-number solutions of each equation. a) 3x 4x 8 = 0 b) x + 4x + = 0 c) x 8x + 7 = 0 15. Simplify each radical using product property or quotient property whichever is applicable. a) 7 b) 3 c) 36 81 d) 0.0064 16. Solve the following quadratic equations by using square roots: a) z 56 = 0 b) d 14 = 50 c) 16x 49 = 0 17. Solve by Factoring: a) a 15a + 56 = 0 b) s + 1s = 3 c) 8x + 10x + 3 = 0 18. Use the function f ( x) x to write the equation in vertex form of each new function, g(x). Identify the vertex, Axis of Symmetry, Domain and Range of the function. a. The graph of f(x) is translated units up. b. The graph of f(x) is translated 5 units to the left and 3 units down.
c. The graph of f(x) is translated 8 units to the right. d. The graph of f(x) is translated 4 units down and 6 units to the right. 19. Order the functions from narrowest to widest. a) b) f(x) x ; g(x) 5x ; h(x) 4 5 x f(x) 9 x ; g(x) x ; h(x) 3 x 0. Solve each system algebraically. a) b) x 3 y x 3 x x 3 y x 5 1.Graph and solve the system x 8. 3x 4. The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.