Honors Algebra 2 Midterm Review Guide 2017

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1Honors Algebra 2Midterm Review Guide 2017The midterm will cover material from Chapter 1, 2, 3, and 5Chapter 1 (Solving Linear Equations)Solving Equations and InequalitiesAbsolute Value Equations and InequalitiesWord ProblemsChapter 2 (Functions)Function NotationPiecewise FunctionsDirect VariationLinear Modeling (Linear Regression)Properties of Absolute Value Functions (vertex, graph, intercepts, etc.)Chapter 3 (Systems)Solving Systems by Graphing, Substitution, and EliminationSolving/Graphing Systems of InequalitiesSolving System in three variablesSystems Word ProblemsChapter 5 (Quadratics)Modeling with Quadratic Functions (Quadratic Regressions)Properties of Parabolas (vertex, axis of symmetry, intercepts, domain, range)Translating ParabolasFactoring ExpressionsSolving Quadratic Equations by Factoring, Completing the Square, and Quadratic FormulaComplex Numbers and their propertiesWord Problems requiring Quadratic Equations to solve

2Practice ProblemsChapter 11. Solve for the variable indicated, simplify all solutions and list all restrictionsA. -7(8 – 4x) 3 – 2(x 4)B. 4 6(π‘šπ‘› 3π‘Ÿ) ;5𝑝(2𝑛 4π‘š)3π‘Ÿx ;restrictions:m restrictions:2. Solve the given inequities. Give answer in set notation and graph solution:23( 2π‘₯ 5) 355π‘₯ 113 143 π‘₯ 3 4 2 1053. Solve and determine if solutions are real or extraneous27 5π‘₯ 3 1 5122 π‘₯ 3 2 12π‘₯4. Evaluate the each expression for the given variable:-(a)2 – 7a 13 ; a -55(𝑠 7) 2(𝑠 6) 3𝑠 1; s -45. Simplify:𝟏 πŸ’ πŸ— πŸπŸ” 1.2.3.4.5. πŸπŸ— πŸ“ 𝟐𝟎True or False: A whole number is also an integerTrue or False: An whole number can be a negative numberTrue or False: An real number is a subset of the set of whole numbersTrue or False: 9/6 is a rational numberTrue or False: 3.14 is a irrational numberAnswer #6 with sometimes, always or never. If the answer is sometimes or never, provide an example thatsupports your position.6. If all variables are distinct non-zero integers (this means they are all different integers), thena 𝑏π‘₯ 𝑐 𝑑 𝑒 has two real solutions

37. Graph the solution and give the solution in interval notationA) 3x 15 x 2B) x 5 x 12C) x 5 x 28. Create an inequality that matches the solution shown:A) ( , 1) [3, )B)59. Given the equation m nx q r y , where m, n, q and r are integersSolve the equation for β€œx” and STATE ANY RESTRICTIONS10. Write an inequality and solve:A copper wire is to have a length of 12cm with a tolerance of 0.02cm. How much must be trimmed froma wire that is 15 cm long for it to meet specifications?11. The temperature T of a refrigerator is at least 37 degrees and at most 44 degrees. Write an absolutevalue inequality and a compound inequality for the temperature of the fridge. DO NOT SOLVE!!!!!YOU MUST SHOW EQUATION AND ALL WORK FOR FULL CREDIT!!!!12. A train leaves Boston traveling east at a rate of 160 mi/hr. Twenty minutes later another train leavesBoston traveling in the same direction at a rate of 175 miles per hour. When will the second trainovertake the first train?13. Mr. Smith wants to build a rectangular garden. He will use one side of his garage as the long side ofthe garden, so he only needs to fence in three sides. If he has 72 feet of fencing, and one side is 4times as long as it is wide, what are the dimensions of the garden?14. The sides of a triangle are in ratio 12:13:15. The perimeter is 120 cm. Find the lengths of the sides ofthe triangle.15. Find three consecutive even integers where the sum of the smallest and the largest integers are equalto 80.

416. A plane leaves San Juan traveling east at a rate of 450 mi/h. A half hour later another plane leaves SanJuan traveling in the OPPOSITE direction at a rate of 475 mi/h. When will the planes be 1500 milesapart?17. A contractor estimates that her expenses for her construction project would be between 700,000 and 750,000. She has already spent 496,000. Write and solve a COMPOUND INEQUALITY to show howmuch more can she spend and still be within her estimate.Chapter 2218. Given the function 𝑓(π‘₯) 3 3π‘₯ 3 4A. Create sketch of the graph and label the vertex.B. Give the piecewise definition and split domain that defines this functionC. Give the y-interceptD. Give x-intercept(s) if any19. Give the absolute value equation being described:A. Vertex at (3,-7) and a y intercept at -3B. Axis of symmetry at x -4, with a range of ,3 and goes through the point (-2,2)C. Axis of symmetry is at x 8, the range is negative infinity to -6 and the y intercept is at -1020. Find the value of β€œW” so that the point P lies on the line LP(3,1)L: -2x Wy 821. Find the value of β€œB” so that the line through the given points has a slope of β€œm”(B, B 1) and (6, -3) m 322. Find the area of the triangle that is bound by the x intercepts and vertex of the absolute value equation𝑦 π‘₯ 6 823. Given the following functions2𝑓(π‘₯) 5 π‘₯ 1 and 𝑔(π‘₯) π‘₯ 7A. g(-7)B. f(x) 2 g(x)C. f(x – 3)D. f(g(-3) 1)

524. Use the provided graph to answer the following questions:A. Is this a function? Explain your reasoning.B. What is the domain?C. What is the range?25. Match each inequality with a possible graph.A.)𝑦 π‘Ž π‘₯ β„Ž π‘˜C.) 𝑦 π‘Ž π‘₯ β„Ž π‘˜14.B.) 3𝑦 6π‘₯ 12D.) 2π‘₯ 2𝑦 142.3.5.6.

6Chapter 326. Classify and solve each system.a.7x y 6 14 x 2 y 12b.2 y 5x 6 10 x 4 y 827. Solve the system:3x y – z 14111x- y z 0248-2x 2y 1z 5228. Graph the system of inequalities: y 4 2 x 1y 3c.x 4 y 122x 8 y 4

729. If it takes an airplane 3 hours to fly 360 miles with the wind and 4 hours to make the return trip against thewind, find the speed of the wind and the speed of the airplane in miles per hour.30. John has a total of nine stamps, which consist of 25 cent and 2 cent stamps. His stamps have a value of 1.10. How many of each stamp does he have?31. Mrs. Mitchell put a total of 10,000 into two accounts. One account earns 6% simple annual interest. The otheraccount earns 6.5% simple annual interest. After 1 year, the two accounts earned 632.50 interest. How muchmoney was invested in each account?32. Davis Rent-A-Car charges a fixed amount per weekly rental plus a charge for each mile driven. A one-week trip of520 miles cost 250 and a two week trip of 800 miles cost 440. Find the weekly charge and the charge for eachmile driven.33. A fish was caught whose tail weighed 9 pounds. Its head weighed as much as its tail plus half its body. Its bodyweighed as much as its head and tail. How much did the fish weigh?34. Mrs. Bowe burns 4 cal/min walking and 10 cal/min running. She walks between 10 and 20 minutes a dayand runs between 30 and 45 minutes each day. She never spends more than an hour running and walkingtogether. How much time should she spend on each activity to maximize the number of calories that sheburns? Use x to represent walking and y to represent runningA.B.C.D.E.F.Write an objective function:Write the constraints:Draw graph and shade feasible region:List all vertices:Which vertices give a maximum number of calories burned?What is the maximum number of calories burned?

835. Refer to the system to answer the following questions: 12 x 9 y 21 4 x 3 y ?A.What value for? would make the system dependent?B.What value for? would make the system inconsistent?36. Create a system of inequalities that would match the graph show.(-4, 3)(-2, -6)(4, 3)(2, -6)Chapter 5 Test- Quadratics37. Factor and solve each equationA. x3 x2 – 30x 0B. 2x2 – 20x 50 0C. 3x2 11x 6 0D. -5x3 125x 038. Which statements are FALSE about the discriminant?IF FALSE, CORRECT THE STATEMENT TO BE TRUE.A)B)C)D)E)The discriminant is b2 4acIf the discriminant is positive there can be one or two real solutionsIf the discriminant is 0, there is one real solution and one imaginary solutionThe discriminant gives us the value of the solutions to a quadratic equationBecause the square roots of a negative are non-real numbers, the discriminant can never benegative

939. Which statements are TRUE about quadratic equationsI.II.III.40.The domain depends on the x value of the vertexThe axis of symmetry is the x value of the vertexIf there are two solutions they both fall the same distance from the axis of symmetryWhich statements are true about the quadratic equation: y ax2 bx cb2aI.The axis of symmetry is at x II.III.The a value determines if the graph has a minimum or maximumThe range would be c, )41. A student correctly solved the equation 0 ax2 bx c by using the quadratic formula. For her final3 5answer he got. The only simplifying he did was to simplify the radical. What were the values of a, b and4c for the equation?42. Evaluate and rewrite each expression as a complex numberA. 3 5i 2 4(2i 6)B.(5 6i )(8i 2)43. Graph the following complex number and find its absolute value: -2 – i

10What is the vertex form of the quadratic equation that has a range of 4, ,44.an axis of symmetry at x -2 and a y intercept at (0, 5)?45. Factor Completely:a.b.c.d.e.a2b6- c2m4n – n2n - 12(x2 – 1)2 – (x2 – 5x 4)2m2 – n2 – m – n(x – 2)3 – (x – 2)46. Given the function: y -2x2 8x – 3a.b.c.d.e.State vertex:Is the vertex a maximum or minimum?Find the y-intercept:Find the x-intercept(s)Draw a rough sketch using vertex and 2 corresponding points:47. Suppose that the profit, p for selling x number of cookies is given p(x) -0.1x2 8x – 50. Find themaximum profit for selling the cookies.48. A rectangular field is enclosed by a fence and divided into 2 parts by another fence. Find the maximumarea that can be enclosed and separated in this way with 1600 meters of fencing.49. There are currently ten students going on a trip to a museum. The cost is 16.00 per student. For eachadditional student going, the amount for all students will be reduced by twenty cents.a. How much would the cost be per person if there are a total of 20 students going on the trip?b. How much would the cost be per person if there are a total of β€œn” students going on the trip?c. What is the maximum amount of money that will be paid total for the trip and how many studentswould be going for that amount to occur?50.Solve for β€œx” in terms of β€œa” by completing the square.4x2 ax a2

1151. Find the value for β€œk” that would satisfy the following conditions:y x2 kx 4a. When solving for the roots, you would get one real solution:b. When solving for the roots, you would get two real solutions:52. Use the quadratic formula to solve for β€œx” in terms of β€œa”5a2x2 6ax 753. Find f(0), f(1), and f(2):f(x) -1 – x2 i54. Michelle was so excited over her last test score in Honors Algebra 2 that she jumped for joy. Whatmakes it strange is that she attached motion sensors to herself and derived the equation that modeled theheight and time of her jump. The equation that she came up with was:48h(t ) t 2 t , where h(t) is her height in inches and t is her time in seconds;93A) Write the equation in VERTEX FORM:B) What was Michelle’s height at 1 second?C) When was she 3 inches above the ground?D) What was her maximum height?E) How long did it take her to reach that height?F) What are the domain and range of the path of her jump?

Honors Algebra 2 Midterm Review Guide 2017 The midterm will cover material from Chapter 1, 2, 3, and 5 Chapter 1 (Solving Linear Equations) Solving Equations and Inequalities . For her final answer he got 35 4 r. The only simplifying he did was to simplify the radical. What were the values of a, b and

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