-5(1-5x) +5(-8x - 2) = -4x -8x. Name Date. 2. Find the product: x 3 x 2 x. 3. Solve the following equation for x.
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1 Name Date CC Algebra 2 Period Units 1-5 Review Due Tuesday, January 3, 2017 Answer all of the following questions. The number of each question corresponds to the lesson in which it was covered. Copying will not be tolerated. If multiple people have answers that obviously do not make sense, those students will split the points they earned on his assignment. You may use your notes to complete the assignment. It is worth one test grade. Question 1. Simplify the following epression: 5 3 y 5 2y 2 3 y 3y 4 2. Find the product: Solve the following equation for. -5(1-5) +5(-8-2) = The epression has an integer zero somewhere on the interval Use a TABLE to find the zero on this interval. Show the table. 1
2 5. Which of the following functions is one-to-one? (1) y = 4 (3) y = 3 (2) y = (4) y = Based on the graph of the function y g shown below, answer the following questions. ( scale counts by ones, y-ais counts by fives) (a) Evaluate g( -2), g( 0), and g( 3). (b) How many values of solve the equation, g()= 0? Estimate the values to the nearest tenth. 7. What is the range of the function represented in the graph? 8/9 The g( ) = is defined over the interval 0 5 y (a) Sketch the graph of g. (b) What are the maimum and minimum values of the function? (c) Over what interval is g decreasing? (d) Over what interval(s) is g 0? 2
3 10. Which has a greater average rate of change over the interval -1 3; the function g function f ( ) = 2. Provide justification for your answer. ( ) = or the 11. Write the equation of a line that is perpendicular to y = and has a y-intercept of 6? A factory produces pencils. The cost, C, in dollars to produce pencils is given by the equation, C = Each pencil sells for 30 cents. Thus, the revenue gained, R, from selling these pencils is given by R = (a) Use your graphing calculator to sketch and label each of these linear functions for the interval Be sure to label your window. Dollars (b) Use the graph to determine the number of pencils that must be produced for the revenue to equal the (c) If profit is defined as the revenue minus the cost, cost to the nearest whole number. create an equation in terms of for the profit, P. 3
4 13. What is the inverse of the function, y = 1 5-3? 14. Consider the function defined by: f ( ) = ì ï í ï î (a) Graph the function < 4 f. y (b) State the range of the function f. 15. Write an absolute value function, f(), to model the difference between the cost of any toy in the store,, and the average cost of a toy in the store which is $50. Grapg f() on the interval, (Use the table on the calculator to determine the appropriate window for viewing.) The costs of the majority of the toys in the store are within $20 of the average cost. Use the graph to find the cost interval for the majority of the toys in the store. 4
5 16. Solve the system of equations algebraically. -2y +3z = y + z = y -2z = Factor the following epression Factor the following epression Factor the following epression
6 20. Factor the following epression Solve the following system of equations algebraically using the zero product property. y = and y = y Solve the system graphically to verify your answer. 22. Solve the following quadratic equation by completing the square (Hint: Divide by 5 first) = An object is launched at 19.6 meters per second (m/s) from a 58.8 meter platform. The equation for the object s height s at time t seconds after launch is s(t)= -4.9t t +58.8, where s is in meters. When does the object strike the ground? 6
7 24. Use the discriminant to quickly determine if the following quadratic can be factored. If the equation can be factored, solve by factoring. If the equation cannot be factored, choose a different method to solve it Solve the following equation: Simplify the following comple epression. Write your answer in simplest a bi form. ( 2 + i) 2 - ( 5+ 2i) ( 4-3i) 27. Solve the following quadratic equation. Epress your solutions in simplest a bi form =
8 28. If the point (6, 3) lies on the graph of a power function what point must also lie on the graphs if each of the following power functions: a) A power function with an odd eponent: b) A power function with an even eponent: 29. Solve the following equation for : Given the cubic polynomial 3 2 f ( ) , answer the following, (a) Find the -intercepts of this function algebraically. (b) Eplain why the graph below could not represent f(). 31. Find the equation of the quadratic polynomial with zeroes at =3 and = -2 and passes through the point (6,12). Epress your answer in factored form and standard form. 8
9 32. Simplify the following rational epression using polynomial long division: answer in quotient-remainder form Epress your 33. What is the remainder when is divided by 5? Given p( ) and p(-5)=0, solve the equation Base on your answers, how many times will p() intersect the -ais. Eplain. 35. Mr. Farison gave his class the three mathematical rules shown below to either prove or disprove. Which rules can be proved for all real numbers? Show your work. I II III 1) I, only 2) I and II 3) II and III 4) I and III 9
10 36/37 The monthly profit, P, of a company in thousands of dollars, years after it opened, can be modeled by the 3 2 function, P If the company has been open for 8 years, what is the maimum monthly profit of the company, to the nearest thousand dollars. Eplain how you arrived at your answer. 36/37 The distance needed to stop a car after applying the brakes varies directly with the square of the car s speed. The table below shows stopping distances for various speeds. Determine the average rate of change in braking distance, in ft/mph, between one car traveling at 50 mph and one traveling at 70 mph. Eplain what this rate of change means as it relates to braking distance. 38. Completely factor: y y y 39. Simplify the following rational epression:
11 40. Epress the following in simplest form: Simplify the following epression: Write the following epression in simplest form: What is the solution of the following equation:
12 44. A pipe fills a barrel with water in 50 minutes. A drainage valve on the barrel, used for drainage, is used to empty the barrel when necessary. A new employee mistakenly left the drainage valve open when he turned on the pipe to fill a barrel. When the filling pipe was on and the drainage valve was open, the empty barrel was full in 90 minutes. How long would it take for the drainage valve to completely empty a full barrel on its own? 45. One pipe can fill a tank three hours faster than another pipe. Together, the pipes take two hours to fill the tank. How long does each pipe take to fill the tank when they work alone? 46. Solve the following equation algebraically: Algebraically prove that , where
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