Alg2 Fall Semester Final Review/Practice

Alg2 Fall Semester Practice/Review

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Algebra 1 Review

Multiple Choice

Solve.

3 (2x + 5) = -18 + 9

• x = -5
• x = -4

• x = 10
• x = 3

Multiple Choice

(7 + 41) ÷ 2 – 15 =

• 19
• 9
• 25
• 3

Multiple Choice

What would be my first step? 3 + 4 x 6 - 4 =

• addition
• multiplication
• subtraction
• exponents

Multiple Choice

10 + 45 ÷ 9 -(14 ÷ 2)  = 

• 9
• 8
• 53
• 18

Draw

Write an example to fit in each number set category

Fill in the Blanks

When you multiply two negative numbers, what is the sign of the solution?

Transformations of Abs Value Function

Multiple Choice

Which function shows horizontal shift and a vertical stretch?

• f(x) = -2|-x | 
• f(x) = -3|x| - 7
• f(x) = -|-x + 1| + 4
• f(x) = 5|x - 4| - 1

Multiple Choice

Which function is graphed?

• f(x) = -|2x - 3| + 5
• f(x) = -|x + 5| - 3
• f(x) = -|2x + 6| + 5
• f(x) = -2|x + 5| - 3

Multiple Choice

What is the vertex of the absolute value function?

• (4, 0)
• (0, 4)
• (-infinity, infinity)
• [4, infinity)

Multiple Choice

Describe the transformation from the Absolute Value Parent Function.

• Shift up 4 units
• Shift down 4 units
• Shift left 4 units
• Shift right 4 units

Multiple Choice

y = |x - 3| makes the graph slide . . .

• left 3
• right 3
• up 3
• down 3

Multiple Choice

y = |x| - 7 makes the graph slide . . .

• left 7
• right 7
• up 7
• down 7

Quadratics

Multiple Choice

If $$f\left(x\right)=a\left(x-h\right)^2+k$$  has a horiz. shift of -2, a vertical shift of +3 and a vertical stretch of 4, what are the values of a, h, and k?

• $$a=4;\ h=-2;\ k=3$$  

• $$a=2;\ h=4;\ k=-3$$  

• $$a=4;\ h=2;\ k=3$$  

• $$a=3;\ h=2;\ k=-4$$  

Multiple Choice

If $$f\left(x\right)=a\left(x-h\right)^2+k$$  has a horiz. shift of -2, a vert. shift of 3 and a vert. stretch of 4, what is the equation for  $$f\left(x\right)$$  ?

• $$f\left(x\right)=4\left(x+2\right)^2+3$$  

• $$f\left(x\right)=4\left(x-2\right)^2+3$$  

• $$f\left(x\right)=3\left(x+2\right)^2+4$$  

• $$f\left(x\right)=2\left(x-4\right)^2+3$$  

Reorder

Put the steps to Completing the Square in the correct order

• Move constants to one side

• add $$\left(\frac{b}{2}\right)^2$$ to both sides

• Factor the trinomial

• Take the square root of both sides.

• Solve both cases.

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Fill in the Blanks

Complete the square for

x² - 11x +

(find the missing value that goes in the blank; keep answers in fraction form)

Multiple Choice

How do you convert a quadratic equation from standard form to vertex form?

• By graphing the equation.

• By using the quadratic formula.

• By completing the square.

• By factoring the equation.

• None of these make sense to do

Multiple Choice

Factor:

• (x + 3)(x + 10)

• (x - 3)(x - 10)

• (x + 3)(x - 10)

• (x - 3)(x + 10)

Multiple Choice

Factor
3a² + 4a + 1

• (7a-10)(a-8)
• Not factorable
• (3a+1)(a+1)
• (3a-1)(a-1)

Multiple Choice

Factor:
 4x²-16x-9

• (2x-9)(2x+1)
• (2x+9)(2x-1)
• (4x-1)(x+9)
• (x+1)(4x-9)

Imaginary Numbers, et al.

Multiple Choice

Solve: $$x^2+36=0$$  

• $$\pm6$$  

• $$-6$$  

• $$6i$$  

• $$\pm6i$$  

Multiple Choice

$$\left(3-i\right)-\left(2+4i\right)=$$  

• $$10+10i$$  

• $$1-5i$$  

• $$6-4i^2$$  

• $$10$$  

Multiple Choice

$$\left(3-i\right)\left(2+4i\right)=$$  

• $$10+10i$$  

• $$1-5i$$  

• $$6-4i^2$$  

• $$10$$  

Multiple Choice

• 6i√5

• -8√5

• 8i√5

• -8i√5

Multiple Choice

Real and Imaginary parts of 3.5 - 2.7 i are___?

• Re=3.5

  Im=2.7

• Re=3.5

  Im=-2.7

• Re=-3.5

  Im=2.7

• Re=-3.5

  Im=-2.7

Fill in the Blanks

What degree is the following polynomial?

$f\left(x\right)=2x-5x^3+3x^7-9x^2+14$  

Explanation Slide...

The Fundamental Theorem of Algebra states that a polynomial of degree n has a total of n real and complex solutions.

Fill in the Blanks

Based on the Fundamental Theorem of Algebra, how many real and complex solutions exist for this polynomial: $f\left(x\right)=2x-5x^3+3x^7-9x^2+14$  

Multiple Choice

Is $$\left(x-1\right)$$  a factor of $$f\left(x\right)=x^4-9x^3+8x^2+3x-3$$  ?

• Yes, because $$f\left(1\right)=0.$$  

• Yes, because $$f\left(-1\right)=0.$$  

• No, because $$f\left(1\right)=0.$$  

• No, because $$f\left(-1\right)=0.$$  

Multiple Choice

Describe the roots of the following polynomial function

• This graph has two imaginary roots because it is a polynomial of degree two.
• This graph has two imaginary roots because it has one hump.
• This graph has two imaginary roots because it touches the x-axis at two points.
• This graph is imaginary because it the graph has shifted up.

Poll

Are you ready for the Final?

• Absolutely, Captain! Bring it on!

• Yes.

• Um...I suppose. We'll see.

• No.

• Other: my thoughts and feelings are not listed here.