Alg 2 Semester Exam Prep

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Algebra 2 Honors Review

Review and Study Guide for Semester 1 Exam

One-to-One

• Discrete - set of unconnected points

• Continuous - infinite number of elements, graphed with a line or smooth curve

Discrete VS Continuous

• For a function to be one-to-one, it has to pass BOTH the vertical line test and the horizontal line test.

• Meaning: 1 x for every y, and 1 y for every x.

Onto

• Onto means that every element in the domain has a pair in the range and no-one is left out.

1.Which graphs are functions?

2. Which are continuous?

3. Give domain of each.

4. Give range of each.

Multiple Choice

Is this a function? Discrete or continuous? What is the range?

• $$\left[-4,\ 5\right)$$

  Function

  Continuous

• {-4,-3, 2, 3, 5}

  Not a function

  Discrete

• {-4,-3, 2, 3, 5}

  Function

  Discrete

• None of the answer choices

Multiple Select

Is this a function? What is the domain? What is the range? Select all that apply.

• Domain: [1,∞)

• Range: [1,∞)

• Range: (-∞,∞)

• Function

• Not a function

Multiple Select

Is this a function? Domain? Range

• Not a function

• D{-4,-2,1,3}

  R{-2,-1,2,3}

• D{-2,-1,2,3}

  R{-4,-2,1,3}

• Function

• D[-4,3]

  R:[-2,3]

C5L3 Solving Systems of Equations

Vocabulary

Intersecting Lines: Lines that meet or cross at one point are said to intersect​ and have One Solution. Intersecting lines have different slopes.

​

​Parallel Lines: Lines that have the same slope and different y-intercept, parallel lines have No Solution​ to the system of equations

Same Line: Lines that have the same slope and the same y-intercept are said to be the same. The Solution to a system with the same lines is said to have an Infinite number of Solutions​

Multiple Choice

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution

• (6, -2)

Multiple Choice

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

• Intersecting lines

• Same line

• Parallel lines

Multiple Choice

How many solutions will this system have?

• No solution

• One Solution

• Same Slopes

• Infinitely Many Solutions

Multiple Choice

What is the solution to the systems of equations?

• (-7, -9)

• (-10, 5)

• No Solution

• Infinitely Many Solutions

Multiple Choice

y = -3x + 4
2y = -2 - x

• (2,2)
• (-2,-2)
• (2,-2)
• (-2,2)

​The perimeter of a rectangle is 46m. The width is double the length plus five.

Find the Width and Length.

​The perimeter of a rectangle is 46m. The width is double the length plus five.

Find the Width and Length.


First:
P = 2L + 2W

W = 2L + 5

so 46 = 2L + 2(2L+5), and solve for L...

6 = L so length is 6. Plus back into 2(6) + 5 and get 17 for width.

I. School Dance

 Mrs. Glynn and the student council planned the Homecoming Dance. They took in $3,000 to pay for the DJ, decorations, police detail and other expenses. Tickets cost $15 or $10 with a can good donation. 250 students bought tickets to the dance. How many tickets of each type were sold?

Multiple Choice

What inequality does the number line graph represent?

• x≥ 3
• x > 3
• x < -3
• x ≤ 3

Multiple Choice

Solve:
2x + 5 <  3x - 6

• x < 11
• x > 11
• x > -11
• x < -11

Multiple Choice

3(x - 3) ≤ 2(x + 2)

• x ≤ -5
• x ≥ 5
• x ≥ 13
• x ≤ 13

Multiple Choice

Express the following in Interval Notation
{ x  | -8 ≤ x < 8 }

• [-8, 8]
• [-8,8)
• (-8, 8]
• (-8, 8)

Multiple Choice

Express the following in Interval Notation
{ x | -9 < x ≤ -4 }

• [-9, -4]
• (-9,-4]
• [-9, -4]
• (-9,-4)

Multiple Choice

Write the following in interval notation
x < 3 or x ≥ 5

• (3, -∞) or (∞, 5]
• [-∞, 3) or [5, ∞]
• (-∞, 3) or [5, ∞)
• (3, -∞] or [∞, 5]

Multiple Choice

Write the inequality in interval notation.

• (-2,5)
• (-∞,-2)⋃(5,∞)
• [-2,5]
• (-∞,-2]∪[5,∞)

Multiple Choice

Write the inequality in interval notation.

• [-4, -1)
• (-4, -1)
• (-4, -1]
• [-4, -1]

​Multiplying Complex Numbers

Multiple Choice

Multiply: 
(4 – 3i)(-7 – 2i)

• A.  -23 + 13i
• B.  -23 - 29i
• C.  -34 + 13i
• D.  -34 - 29i

Square Root of a Negative Real Number

Multiple Choice

Simplify $$\sqrt[]{-32}$$

• $$32$$

• $$-32i$$

• $$-4\ \sqrt[]{2}$$

• $$4i\ \sqrt[]{2}$$

Multiple Choice

Simplify.

• -5i
• 5
• 5i
• -5

Multiple Choice

Simplify:

$$\sqrt{-9}\cdot\sqrt[]{64}$$  

• $$24i$$  

• $$-24i$$  

• $$3i\sqrt{64}$$  

• $$8i\sqrt{9}$$  

Multiple Choice

Simplify:

$$\sqrt{-98}$$  

• $$7i\sqrt{2}$$  

• $$2i\sqrt{7}$$  

• $$49i\sqrt{2}$$  

• $$2\sqrt{49i}$$  

Multiple Select

Which of the following absolute value inequalities would be an "OR"?

(CHOOSE ALL THAT APPLY)

• $$\left|4x-1\right|>5$$  

• $$∣5x+\frac{1}{2}∣​\ge1$$  

• $$∣7x+5∣>6$$  

• $$\left|-3x+7\right|<11$$  

• $$∣2x−10∣\le50$$  

Multiple Select

Which of the following absolute value inequalities would be an "AND"?

(CHOOSE ALL THAT APPLY)

• $$\left|4x-1\right|>5$$  

• $$∣5x+\frac{1}{2}∣​\ge1$$  

• $$∣7x+5∣>6$$  

• $$\left|-3x+7\right|<11$$  

• $$∣2x−10∣\le50$$  

Multiple Choice

Solve the absolute value inequality.

$$6\left|x+3\right|-10\ge-4$$  

• $$x\le−4\ or\ x\ge−2$$  

• $$-2<x<4$$  

• $$−4<x<−2$$  

• $$x\le−4\ or\ x\ge2$$  

​Methods for Solving Quadratics

• ​Factoring

• ​Isolation/Using Square Roots

• ​Completing the Square

• ​Quadratic Formula

Poll

Which method are the MOST confident in using?

• Solving Quadratics by Factoring

• Solving Quadratics by Isolation/Using Square Roots

• Solving Quadratics by Completing the Square

• Solving Quadratics by Quadratic Formula

Poll

Which method are the LEAST confident in using?

• Solving Quadratics by Factoring

• Solving Quadratics by Isolation/Using Square Roots

• Solving Quadratics by Completing the Square

• Solving Quadratics by Quadratic Formula

Poll

Which method do you feel is the best way to solve the following?

$$x^2-3x-54=0$$  

• Factor

• Isolation/Solve with Square Roots

• Complete the Square

• Quadratic Formula

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Multiple Choice

Use Zero Product Property to solve

x² + 2x - 15 = 0

• x = 3 or x = 5

• x = 5 or x = -3

• x = -5 or x = 3

• x = -3 or x = -5

Multiple Choice

What is the vertex?
f(x) = -x² - 4x + 12.

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Multiple Choice

What is the vertex and axis of symmetry?

$$f\left(x\right)\ =\ -x^{2\ }+\ 6x\ -\ 2$$  

• Vertex: (3,7)

  AOS: x = 3

• Vertex: (3,7)

  AOS: y = 3

• Vertex: (-2,6)

  AOS: x = -2

• Vertex: (2,6)

  AOS: x = 2

Multiple Choice

Does the following function have a maximum or a minimum? $$f\left(x\right)=x^2+4x+7$$  

• Maximum

• Minimum

Multiple Choice

Identify the y-intercept:

$$y=\ x^2-2x-3$$  

• (0, -2)

• (0, -3)

• (-2, 0)

• (-3, 0)

Multiple Choice

Which equation matches the graph?

• y=(x-2)²+3

• y=(x-2)²-3

• y=(x+2)²+3

• y=(x+2)²-3

Multiple Choice

What is the end behavior of the parent function?

• as x --> ∞, y --> -∞

  as x --> -∞, y --> -∞

• as x --> ∞, y --> ∞

  as x --> -∞, y --> ∞

• as x --> ∞, y --> -∞

  as x --> -∞, y --> ∞

• as x --> ∞, y --> ∞

  as x --> -∞, y --> -∞