Algebra 2 Name Midterm Exam REVIEW 2014-15

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Algebra 2Midterm Exam REVIEW2014-1515 points – completionName25 points – accuracyThe exam review will be graded on completion (15 points) and randomly selected problemssolved and answered correctly (25 points). In order to earn full credit, you must show all workfor each problem!!The exam review is due no later than: Monday January 5, 2014 or Tuesday January 6, 2014 for a maximum of 4 bonus points. Wednesday, January 7, 2014 for a maximum of 3 bonus points. Thursday, January 8, 2014 for a maximum of 2 bonus points. Friday, January 9, 2014 for a maximum of 1 bonus point. Monday, January 12, 2014 is the final due date.(This is an “A” Day so “B” day classes will need to find me)The exam review is due no later than Monday January 12th by4:00 pm for completion and accuracy. You need to turn in thepacket directly to the teacher - NOT the teacher mailboxes inthe main office.The midterm exam will cover all material in Units 2 - 4 and the parts of Unit 5 that we have coveredin class by the end of first semester.Be sure to study your old tests and quizzes from all units.

NameCumulative ReviewDateCircle your final solutions!!UNIT 2: Investigating Functions1. Use your calculator to graph y 𝒙𝟑 𝟔𝒙𝟐 𝟗𝒙End behavior:As x à , f (x) à . As x à , f (x) à .Relative minimum/maximum?Absolute minimum/maximum?Zeros?Y-intercept?2. What type of discontinuity does this function have? Where does it occur?3. Sketch the inverse of the function shown below, using three points from the graph.

4.Use the graph to the right to answer the following:What is the Domain?Interval Notation:Inequality Notation:What is the Range?Interval Notation:Inequality Notation:What are the zeros?Is the INVERSE a function? ExplainIdentify:Relative Minimums Relative MaximumsAbsolute Minimums Absolute Maximums5. Use the graph to the right to answer the following:Number of turning points:Identify the Relative Minimums or MaximumsIdentify the Absolute Minimums or MaximumsIncreasing Interval (s)Decreasing Interval (s)End Behavior:As 𝑥   , 𝑓 𝑥 As 𝑥   , 𝑓 𝑥

6. Use the graph to the right to answer the following:What is the Domain?Interval Notation:Inequality Notation:What is the Range?Interval Notation:Inequality Notation:What is the type of discontinuity shown?# 7 & 8 Use the graph below to answer each question. EXPLAIN YOUR ANSWERS.7.Is this graph a function?Explain:8.Is its inverse a function?Explain:

UNIT 3: Absolute Value Functions1.Fill in the table based on each given absolute value equation. For vertex, domain, and range WRITE in your answer.For direction and dilation clearly CIRCLE your answer.Functiona.Vertexy x 2 3b.y 2 x 4c.1y 4d.y x pDownStretchShrinkStandardUpy x 6RangeStretchShrinkStandardUpx 3 1DomainDown2. Graph the following absolute value functions. You must include at least 5 points on your graph.(Be sure you can do this without a calculator!)y 2x 3 13y x 4y 2 x 4 etch/Shrink:10 y810 y866644422 10 8 6 4 210 y8 2x246810 10 8 6 4 2 22x246810 10 8 6 4 2 2 4 4 4 6 6 6 8 8 8 10 10 10x246810

3. Graphy x 2 5 using at least three distinct points. Then complete the information onthe right based on the graph.Domain:Range:10 y8Vertex:6Y-intercept:42 10 8 6 4 2 2 4 6x246810Zeros:Increasing:Decreasing:End Behavior: 8As x then f (x) 10As x then f (x) Solve the following equations for the indicated variable.4. q 3 16. 2x 12 4x5.2 5 2x - 7 157. x - 5 -8

Solve and graph the following inequalities.8. 2 3x 59.10. 5 2x 3 1111.12.2x 5 5313.-3x 8 x2 x 4 12x 5 12

UNIT 4: Quadratics – GRAPHING PART 11. Complete the table.FunctionFormDirectionDilationy ½ (x 1) - kf(x) x2 - 6x ky (x – 4) (x nk22y - 2x - 8x 5VertexDomainRange2. Graph each quadratic function. (Be sure you can do this without a calculator!)Y x2 – 2x - 810 y86644 212( x 2) 5210 y82 10 8 6 4 2y y ( x 4)( x 2)46810642x210 y8 10 8 6 4 2 2 4 4 6 6 8 8 10 10x24682x10 10 8 6 4 2 2 4 6 8 10246810

3. Graph the following using your calculator and fill in all blanks. Round values to 2 decimal places.f ( x) 1 2x x 3.2Vertex:10 y8x - Intercepts:Axis of Symmetry:6Y-intercept:4Domain:2 10 8 6 4 2 22468xRange:10Increasing: 4Decreasing: 6End Behavior:As x , f ( x) As x , f ( x) 8 10Maximum Value of function:Minimum Value of function:UNIT 4: Quadratics – REAL & COMPLEX NUMBERS PART 2Exponent Rules1.3 25a( 6a ) 24 x 4 y 52 64. 3x y2.13x x35.3354 x y 5xy 2 xy2y23.4x3y-5z6. 16 3 4 x y 4

Simplifying Square RootsSimplify using the product rule. Assume all variables are positive.7. 728. 24𝑎 ! 𝑏 ! 𝑐 !9.10. 144216𝑥 ! 𝑦 !11.6413.81012.14.315.17.19.16 24812 2410832 1216.7518. 1420.189Operations with Square Roots21.13 2 4 1824. 7 6 222.2 12 3 2725. 2 12 1823.26.2 50 32 3 223 7

Complex Numbers: Simplify the following.27. (3 2i) (4 – 3i)29.23i28. (3 4i) – (5 – 8i)30.3 2i5 iUNIT 4: Quadratics – Solving quadratics PART 3Solve using the square root method:1. x2 642.3. 4 (x – 1)2 – 3 254. -3 (x 1)2 815.(2x - 3)2 1216.5 (x – 2)2 – 6 24(x – 3)2 - 144

Solve using factoring (zero product property):7.9.4x2 24x 08.x2 - x – 12 010.x2 – 16 04x2 - 7x – 2 0Solve using the quadratic formula:11.x2 2x 7 012. x2 – 5x – 4 0Solve by completing the square:13.x2 – 6x – 7 014. x2 4x 8 0

Solve using any method:15.x2 – x 616.x2 8x – 13 017. If x2 – 10x c is a perfect square trinomial, what is the value of c? Then, write the trinomial infactored form, i.e, as a square binomial.18. How many real and imaginary solutions does the equation 5x2 – 3x 7 0 have? Explain.19. Find the solution set for the following system of equations using graphing.y ½x–3y x2 4x–1410 y8642 10 8 6 4 22 4 6 2 4 6 8 10Solutions:x810y x2 1y - ‐x2 910 y8642 10 8 6 4 22 4 2 4 6 8 10Solutions:x6810

20. Given the quadratic equationx2 – 4x – 12 0Solve by the Zero ProductProperty (Factoring)x2 – 4x – 12 0Solve by Completing theSquarex2 – 4x – 12 0Solutions:Solutions:Rewrite to Intercept Form Rewrite to Vertex Formy x2 – 4x – 12y x2 – 4x – 12Solve Using the QuadraticFormulax2 – 4x – 12 0Solutions:Describe the Rooty x2 – 4x – 12Find the Discriminant:Intercept form:Vertex Form:Identify the x-interceptsIdentify the Vertex:(,)and(,)Given y x2 – 4x – 12Identify the Number and Type ofSolutions:Graph y x2 – 4x – 12You must include 5 distinct points.10 y8Find the Vertex:64Axis of symmetry:Direction:2 10 8 6 4 2 2x246810 4Size (Vertical Stretch, Vertical Shrinkor Normal): 6 8 10Be sure to study all information regarding unit 5! The material will betaught prior to exams.

Algebra 2 Name _ Midterm Exam REVIEW 2014-15 15 points – completion 25 points – accuracy The exam review will be graded on completion (15 points) and randomly selected problems solved and answered correctly (25 points). In order to earn full credit, you must show all work for each problem!!

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