ALGEBRA 2 HONORS MIDTERM EXAM

Transcription

1 Name: ALGEBRA 2 HONORS MIDTERM EXAM Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Evaluate the given expression if w = 41, x = 5, y = 15, and z = 2. a b c d The formula for the surface area A of a sphere with diameter d is c = 4. Write an expression to represent the surface area of the sphere. a. b. c. d. Write a verbal expression to represent the given equation. 3. a. A number minus 3 is equal to 21. b. Four times a number minus 3 is equal to 21. c. Four times a number is equal to 21. d. Four times a number minus 3 is equal to 2. Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line. 4. a. The solution set is. b. The solution set is.

2 c. The solution set is. d. The solution set is. 5. a. The solution set is. b. The solution set is. c. The solution set is. d. The solution set is. Mrs. Lobo earns a salary of $50,000 per year plus a 4% commission on her sales. The average price of a share she sells is $ How many shares should Mrs. Lobo sell to earn an annual income of at least $90,000? a. Mrs. Lobo must sell at least 20,000 shares to get the desired income. b. Mrs. Lobo must sell at the most 20,000 shares to get the desired income. c. Mrs. Lobo must sell exactly 20,000 shares to get the desired income. d. Mrs. Lobo must sell at least 2000 shares to get the desired income. Solve the given inequality. Graph the solution set on a number line. 7. a. The solution set is or.

3 b. The solution set is or. c. The solution set is or. d. The solution set is or. 8. Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (3.3, 5.3), ( 1.7, 5.3), ( 4.7, 3.3), ( 4.7, 2.7) a. c. b. Domain: { 4.7, 1.7, 3.3} Range: { 2.7, 3.3, 5.3} The equation is a function. d. Domain: { 4.7, 5.3, 3.3} Range: { 2.7, 3.3, 1.7} The equation is not a function. Domain: { 2.7, 3.3, 5.3} Domain: { 4.7, 1.7, 3.3}

4 Range: { 4.7, 1.7, 3.3} The equation is a function. Range: { 2.7, 3.3, 5.3} The equation is not a function. 9. Find the value of f( 9) and g(4) if and. a. f( 9) = 44 g(4) = b. f( 9) = 16 g(4) = c. f( 9) = 4 g(4) = d. f( 9) = 28 g(4) = State whether the given equation or function is linear. Write yes or no. Explain your reasoning. f(x) = 3x + 2 a. No, the equation is not linear. It is not of the form f(x) = mx + b. b. No, the equation is not linear. It is in the form x + y = c. c. Yes, the equation is linear. It is of the form f(x) = m + b d. Yes, the equation is linear. It is of the form f(x)= mx + b 11. Write the equation in standard form. Identify A, B, and C. a. where,, and. b. where,, and. c. where,, and. d. where,, and. 12. Find the x-intercept and the y-intercept of the graph of the equation x + 6y = 16. Then graph the equation. a. c. The x-intercept is. The y-intercept is. The x-intercept is. The y-intercept is 8.

5 b. d. The x-intercept is. The y-intercept is. The x-intercept is. The y-intercept is Find the slope of the line that passes through the pair of points ( 1, 3) and ( 8, 10). b. d. 14. Find the slope of the line that passes through the pair of points (5, 12) and ( 5.5, 7.5). a. 1.4 c b d Graph the line that passes through (1, 4), parallel to a line whose slope is 0.4.

6 16. Graph the line that is perpendicular to the graph of 8x + 4y = 3 and intersects that graph at its x-intercept. a. x-interceptc. x-intercept at (0.38, 2) at (0.75, 3) b. x-interceptd. x-intercept at (0.75, 1) at (0.38, 0) 17. Write an equation in slope-intercept form for the line that satisfies the following condition. slope 5 and passes through (2, 28) a. y = c. y = b. y = d. y =

7 18. Write an equation in slope-intercept form for the line that satisfies the following condition. slope and passes through (4, 17) a. y = c. y = b. y = d. y = 19. Write an equation in slope-intercept form for the line that satisfies the following condition. passes through (6, 11), parallel to the line that passes through (2, 4) and (23, 23) a. y = x c. y = x 6 b. y = x d. y = 19x Write an equation in slope-intercept form for the line that satisfies the following condition. passes through (10, 16), perpendicular to the graph of 9x + 12y = 15 a. y = x + c. y = 10x + b. y = x + d. y = 10x Identify the function below as S for step, C for constant, A for absolute value, I for identity, or P for piecewise. a. S c. I b. P d. A 22. Graph the given inequality.

8 23. Graph the given inequality.

9 Solve the following system of equations by graphing. 24. a. ( 1, 5) c. (5, 1) b. (1, 7) d. (1, 5) Graph each system of equations and describe it as consistent and independent, consistent and dependent, inconsistent, or none of these. 25. a. consistent and independent c. consistent and dependent b. inconsistent d. none of these Solve each system of equations by using substitution x + 7y = 18 3x 5y = 22 a. ( 2, 4) c. (4, 2) b. (3, 2) d. (4, 0) Solve the system of inequalities by graphing. 27. x > 2 y > 8

10 28. y > x 6

11 Find the coordinates of the vertices of the figure formed by each system of inequalities. 29. a. ( 1, 8), ( 30, 23), ( 34, 25) b. ( 1, 8), (10, 3), (34, 25) c. ( 1, 25), ( 34, 3), (10, 8) d. ( 1, 8), (10, 3), ( 34, 25) Given below are some inequalities. Plot the feasible region graphically. 30. a. vertices: c. vertices: (4, 5) max: f(4, 5) = 1 min: f(4, 5) = 1 (4, 5), (4, 0), ( 1, 5) max: f(4, 0) = 4 min: f( 1, 5) = 6

12 b. vertices: d. vertices: (4, 5), (4, 0), ( 1, 5) max: f(4, 0) = 4 min: f( 1, 5) = 6 (4, 5), (4, 0), ( 1, 5) max: f(4, 0) = 4 min: f( 1, 5) = 6 As a receptionist for a hospital, one of Elizabeth s tasks is to schedule appointments. She allots 60 minutes for the first visit and 30 minutes for a follow-up. The doctor cannot perform more than eight follow-ups per day. The hospital has eight hours available for appointments. The first visit costs $120 and the follow-up costs $70. Let x be the number of first visits and y be the number of follow-ups. 31. Write a system of inequalities to represent the number of first visits and the number of follow-ups that can be performed. 32. Graph the system of inequalities showing the feasible region to represent the number of first visits and the number of follow-ups that can be performed.

13 33. List the coordinates of the vertices of the feasible region to represent the number of first visits and the number of follow-ups that can be performed. a. (0, 0), (16, 0), (8, 8), (0, 8) c. (0, 0), (7, 0), (4.5, 8), (0, 8) b. (0, 0), (8, 0), (4, 8), (0, 8) d. (0, 0), (6, 0), (4, 8), (0, 8) 34. Determine the number of first visits and follow-ups to be scheduled to make the maximum income. a. 16 first visits and 0 follow-ups c. 8 first visits and 0 follow-ups b. 4 first visits and 7 follow-ups d. 4 first visits and 8 follow-ups 35. What is the maximum income that the doctor receives per day? a. $960 c. $970 b. $1040 d. $ Consider the quadratic function. Find the y-intercept and the equation of the axis of symmetry. a. The y-intercept is 2. The equation of the axis of symmetry is x =. b. The y-intercept is. The equation of the axis of symmetry is x = 2. c. The y-intercept is + 2. The equation of the axis of symmetry is x =. d. The y-intercept is. The equation of the axis of symmetry is x = 2. Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. 37. a. The function has a maximum value. The maximum value of the function is 1. b. The function has a maximum value. The maximum value of the function is 5. c. The function has a minimum value. The minimum value of the function is 1.

14 d. The function has a minimum value. The minimum value of the function is 5. Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. 38. a. The c. The b. solution set is. solution set is. d. The The solution set is. solution set is. Write a quadratic equation with the given roots. Write the equation in the form, where a, b, and c are integers and 2 Solve the equation by factoring. 40.

15 41. a. { 4, } c. { 4, 7} b. {, } d. {, 7} Simplify

16 49. Solve the equation by using the Square Root Property. 50. a. { } c. {, } b. {, 7} d. {, } 51. a. {, } c. { } b. {, } d. {, 3} Solve the equation by completing the square Find the exact solution of the following quadratic equation by using the Quadratic Formula

17 Short Answer 56. Name the sets of numbers to which all of the following numbers belong. Then arrange the numbers in order from least to greatest. 57. If what is the value of Which property is used for calculating 58. If 8 years are subtracted from the present age of Jessica and 3 is added to the remaining number, then Olivia s age can be found. If Olivia is two years older than Daniel who is 7 years old, then what is Jessica s present age? 59. In an experiment a piece of iron was weighed several times, and its average weight was found to be 45.6 grams. In the next step, the piece of iron was broken into several small pieces, and those pieces were weighed separately. At the end of the experiment it was noted that there is an absolute error of 0.09 milligrams in the experiment. Write an absolute equation to find the maximum and minimum possible weight of the piece of iron. 60. The results of a survey of a population of 50,000 shows that candidate A got an average of 58% votes, candidate B got an average of 30% votes, and the remaining votes went to candidate C. Further, it was noted that the actual percent of votes in favor of candidate C can vary 2% above or below the population. Write and solve an equation to find the maximum and minimum number of votes in favor of candidate C.

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