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Honors Algebra 2

Midterm Review Guide 2016

The midterm will cover material from Chapter 1, 2, 3, and 5

Chapter 1 (Solving Linear Equations)

Solving Equations and Inequalities

Absolute Value Equations and Inequalities

Word Problems

Chapter 2 (Functions)

Function Notation

Piecewise Functions

Direct Variation

Linear Modeling (Linear Regression)

Properties of Absolute Value Functions (vertex, graph, intercepts, etc.)

Chapter 3 (Systems)

Solving Systems by Graphing, Substitution, and Elimination

Solving/Graphing Systems of Inequalities

Solving System in three variables

Systems Word Problems

Chapter 5 (Quadratics)

Modeling with Quadratic Functions (Quadratic Regressions)

Properties of Parabolas (vertex, axis of symmetry, intercepts, domain, range)

Translating Parabolas

Factoring Expressions

Solving Quadratic Equations by Factoring, Completing the Square, and Quadratic Formula

Complex Numbers and their properties

Word Problems requiring Quadratic Equations to solve

Practice Problems

Chapter 1

1. Solve for the variable indicated, simplify all solutions and list all restrictions

  1. -7(8 – 4x) = 3 – 2(x + 4); x = restrictions:
  1. = ; m = restrictions:

2. Solve the given inequities. Give answer in set notation and graph solution:

3. Solve and determine if solutions are real or extraneous

4. Evaluate the each expression for the given variable:

-(a)2 – 7a + 13 ; a = -5 ; s = -4

5. Simplify:

  1. True or False: A whole number is also an integer ______
  2. True or False: An whole number can be a negative number______
  3. True or False: An real number is a subset of the set of whole numbers______
  4. True or False: 9/6 is a rational number______
  5. True or False: 3.14 is a irrational number______

Answer #6 with sometimes, always or never. If the answer is sometimes or never, provide an example that supports your position.

6.If all variables are distinct non-zero integers (this means they are all different integers), then a has two real solutions

7. Graph the solution and give the solution in interval notation

A) B) C)

8. Create an inequality that matches the solution shown:

A)B)

5

9. Given the equation , where m, n, q and r are integers

Solve the equation for “x” and STATE ANY RESTRICTIONS

10. 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 from a 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 absolute value inequality and a compound inequality for the temperature of the fridge. DO NOT SOLVE!!!!!

YOU MUST SHOW EQUATION AND ALL WORK FOR FULL CREDIT!!!!

  1. A train leaves Boston traveling east at a rate of 160 mi/hr. Twenty minutes later another train leaves Boston traveling in the same direction at a rate of 175 miles per hour. When will the second train overtake the first train?
  1. Mr. Smith wants to build a rectangular garden. He will use one side of his garage as the long side of the garden, so he only needs to fence in three sides. If he has 72 feet of fencing, and one side is 4 times as long as it is wide, what are the dimensions of the garden?
  1. The sides of a triangle are in ratio 12:13:15. The perimeter is 120 cm. Find the lengths of the sides of the triangle.
  1. Find three consecutive even integers where the sum of the smallest and the largest integers are equal to 80.
  1. A plane leaves San Juan traveling east at a rate of 450 mi/h. A half hour later another plane leaves San Juan traveling in the OPPOSITE direction at a rate of 475 mi/h. When will the planes be 1500 miles apart?
  1. 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 how much more can she spend and still be within her estimate.

Chapter 2

  1. Given the function
  1. Create sketch of the graph and label the vertex.
  2. Give the piecewise definition and split domain that defines this function
  3. Give the y-intercept
  4. Give x-intercept(s) if any
  1. Give the absolute value equation being described:
  1. Vertex at (3,-7) and a y intercept at -3
  1. Axis of symmetry at x = -4, with a range of and goes through the point (-2,2)
  1. Axis of symmetry is at x = 8, the range is negative infinity to -6 and the y intercept is at -10
  1. Find the value of “W” so that the point P lies on the line L

P(3,1)L: -2x + Wy = 8

  1. Find the value of “B” so that the line through the given points has a slope of “m”

(B, B+1) and (6, -3) m = 3

  1. Find the area of the triangle that is bound by the x intercepts and vertex of the absolute value equation
  1. Given the following functions

and

  1. g(-7)C. f(x – 3)
  2. f(x) = 2 g(x) D. f(g(-3) + 1)
  1. Use the provided graph to answer the following questions:
  1. Is this a function? Explain your reasoning.
  2. What is the domain?
  3. What is the range?
  1. Match each inequality with a possible graph.

A.) ______B.) ______

C.) ______D.) ______

12.3.

4. 5. 6.

Chapter 3

26. Classify and solve each system.

a. b. c.

27. Solve the system:

3x + y – z =

x - y + z = 0

-2x + 2y + z = 5

28. Graph the system of inequalities:

29. If it takes an airplane 3 hours to fly 360 miles with the wind and 4 hours to make the return trip against the wind, 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 other account earns 6.5% simple annual interest. After 1 year, the two accounts earned $632.50 interest. How much money 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 of 520 miles cost $250 and a two week trip of 800 miles cost $440. Find the weekly charge and the charge for each mile driven.

33. A fish was caught whose tail weighed 9 pounds. Its head weighed as much as its tail plus half its body. Its body weighed as much as its head and tail. How much did the fish weigh?

34. Mrs. Ginnetti burns 4 cal/min walking and 10 cal/min running. She walks between 10 and 20 minutes a day and runs between 30 and 45 minutes each day. She never spends more than an hour running and walking together. How much time should she spend on each activity to maximize the number of calories that she burns?Use x to represent walking and y to represent running

  1. Write an objective function:
  2. Write the constraints:
  3. Draw graph and shade feasible region:
  4. List all vertices:
  5. Which vertices give a maximum number of calories burned?
  6. What is the maximum number of calories burned?

35. Refer to the system to answer the following questions:

  1. What value for??? would make the system dependent?
  1. What value for??? would make the system inconsistent?

36. Create a system of inequalities that would match the graph show.

Chapter 5 Test- Quadratics

37. Factor and solve each equation

  1. x3 + x2 – 30x = 0B. 2x2 – 20x + 50 = 0

C. 3x2 + 11x + 6 = 0D. -5x3 + 125x = 0

  1. Which statements are FALSE about the discriminant?

IF FALSE, CORRECT THE STATEMENT TO BE TRUE!!!!

A)The discriminant is

B)If the discriminant is positive there can be one or two real solutions

C)If the discriminant is 0, there is one real solution and one imaginary solution

D)The discriminant gives us the value of the solutions to a quadratic equation

E)Because the square roots of a negative are non-real numbers, the discriminant can never be negative

  1. Which statements are TRUE about quadratic equations
  1. The domain depends on the x value of the vertex
  2. The axis of symmetry is the x value of the vertex
  3. If there are two solutions they both fall the same distance from the axis of symmetry

40.Which statements are true about the quadratic equation: y = ax2 + bx +c

I.The axis of symmetry is at

  1. The a value determines if the graph has a minimum or maximum
  2. The range would be

41. A student correctly solved the equation 0 = ax2 + bx + c by using the quadratic formula. For her final answer he got. The only simplifying he did was to simplify the radical. What were the values of a, b and c for the equation?

42. Evaluate and rewrite each expression as a complex number

A.B.

43.Graph the following complex number and find its absolute value: -2 – i

44. What is the vertex form of the quadratic equation that has a range of ,

an axis of symmetry at x = -2 and a y intercept at (0, 5)?

45. Factor Completely:

  1. a2b6- c2
  2. m4n – n2n - 12
  3. (x2 – 1)2 – (x2 – 5x + 4)2
  4. m2 – n2 – m – n
  5. (x – 2)3 – (x – 2)

46. Given the function: y = -2x2 + 8x – 3

  1. State vertex:
  2. Is the vertex a maximum or minimum?
  3. Find the y-intercept:
  4. Find the x-intercept(s)
  5. 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 the maximum profit for selling the cookies.

48. A rectangular field is enclosed by a fence and divided into 2 parts by another fence. Find the maximum area 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 each additional student going, the amount for all students will be reduced by twenty cents.

  1. How much would the cost be per person if there are a total of 20 students going on the trip?
  2. How much would the cost be per person if there are a total of “n” students going on the trip?
  3. What is the maximum amount of money that will be paid total for the trip and how many students would be going for that amount to occur?

50.Solve for “x” in terms of “a” by completing the square.

4x2 + ax = a2

  1. Find the value for “k” that would satisfy the following conditions:

y = x2 + kx + 4

a. When solving for the roots, you would get one real solution:

  1. When solving for the roots, you would get two real solutions:
  1. Use the quadratic formula to solve for “x” in terms of “a”

5a2x2 + 6ax = 7

  1. Find the first three output values for the following. Start with z = 0:(hint: find f(0), f(1), and f(2))

f(z) = -1 – z2 + i

  1. Michelle was so excited over her last test score in Honors Algebra 2 that she jumped for joy. What makes it strange is that she attached motion sensors to herself and derived the equation that modeled the height and time of her jump. The equation that she came up with was:

, where h(t) is her height in inches and t is her time in seconds;

A)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?