Math 3 Exam Review

Multiple Choice

Give the increasing interval

•   $$\left(-\infty,\infty\right)$$

•   $$\left(-2,0\right)$$

•  (-1,3)

•   $$\left(-2,\infty\right)$$

The increasing section is highlighted. You give your answer in terms of the x values. It starts at an x-value of -2 and continues to increase until an x-value of 0.

​

Answer: (-2,0)

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A glass cube with a side length measuring 5 cm. has a mass of 306.25 g. Calculate the density of the glass cube.

density=mass/volume

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Find the value of x, rounded to the nearest hundredth:

$$8^{\left(3x-1\right)}=177$$  

Multiple Choice

Given Circle C, Find the measure of arc RU

• $$41\degree$$  

• $$82\degree$$  

• $$98\degree$$  

• $$262\degree$$  

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Given parallelogram FROG, find the $$m\angle R$$  

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A $$134\degree$$  sector of a pizza is covered in pepperoni. What is the length of pizza crust for this sector? Round your answer to the nearest hundredth

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What is the value of x?

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Given SW= $$11-3x$$  and WT= $$6x-7$$  . Find the length of diagonal SU.

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Evaluate given the piecewise graph:

4f(1) - 3f(3) - f(5)

​Blue: f(1)=2

Green: f(3)=2

Yellow: f(5)=0

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Find $$f^{-1}\left(8\right)$$

Multiple Choice

Factor the following binomial: 8x³-27

• (2x+3)(4x²-6x+9)

• (2x-3)(4x²+6x+9)

• (2x-3)(4x²+6x-9)

• (2x-3)(2x²+6x+9)

Multiple Choice

(x²+11x+24)/(x²+4x-32)

• A.(x+7)/(x+4)

• B. -3/4

• C.(x+3)/(x+4)

• D.(x+3)/(x-4)

Multiple Choice

Divide and Simplify

• $$\frac{1}{6}$$  

• $$\frac{x+10}{6x+60}$$  

• $$\frac{x+8}{6x+60}$$  

•   $$\frac{\left(x+10\right)\left(x+8\right)}{6x+60}$$  

Multiple Choice

QS is a tangent to circle P, PQ = 5, and RS = 8.

 Find QS.

• 144

• 14

• 12

• 13

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Does the polynomial function have any root with a multiplicity of 2 (a double root)?  $$f\left(x\right)=x^5-3x^4-27x^3+19x^2+114x-72$$  

If so, type in the root.  If not, type "none"

​The only zero that bounces is at -3.

Multiple Choice

A quartic polynomial has roots at  $$\frac{4}{3}$$ ,  $$1$$ , and  $$-1$$ (multiplicity two).   Which of the following gives its factored form equation?

• $$f\left(x\right)=\left(3x-4\right)\left(x+1\right)^2\left(x-1\right)$$  

• $$f\left(x\right)=\left(3x-4\right)\left(x-1\right)^2\left(x+1\right)$$  

• $$f\left(x\right)=\left(4x-3\right)\left(x+1\right)^2\left(x-1\right)$$  

• $$f\left(x\right)=\left(4x-3\right)\left(x-1\right)^2\left(x+1\right)$$  

Multiple Choice

What is 3f(-1)-f(-4) + 2f(13)?

• 2

• 1

• -1

• 4

​3f(-1)-f(-4)+2f(13)

3(-2)-0+2(4)

-6+8

2

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

Multiple Choice

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9

• $$3x^2-3x+8-\frac{9}{x+1}$$

• $$3x^2+3x+8+\frac{7}{x+1}$$

• 3x³ + 3x² + 8x + 7

Multiple Choice

Working alone at a constant rate, Carla can wash a load of dishes in 42 minutes. If Carla works together with Dan and they both work at constant rates, it takes them 28 minutes to wash the same load of dishes. Working at a constant rate, how long would it take Dan to wash the load of dishes by himself?

• 50 minutes

• 1 hour

• 84 minutes

• 2 hours

Multiple Choice

Given $$g\left(x\right)=\frac{\left(4x+13\right)}{x-3}\$$  and  $$h\left(x\right)=\ \frac{x+2}{2x+6}$$  what is the value of A, B,and C if  $$g\left(x\right)\ +h\left(x\right)=\frac{Ax^2+Bx\ +C}{2\left(x+3\right)\left(x-3\right)}$$  

• A = 9, B = 49, C = 72

• A = 9, B = -49, C = -72

• A = -9, B = 49, -72

• A = -9, B =-49 C= 72

Multiple Select

The function $$f\left(x\right)=A\sin\left(Bx\right)\ +H$$  has the following characteristics. 

Period of  $$10\ \min$$  

 Minimum value of 20 Maximum value of 32 Determine the Sine functions that models the data. Multiple Answers

• $$f\left(x\right)\ =\ 6\sin\left(\frac{\pi}{5}x\right)+26$$  

• $$f\left(x\right)=\ -6\sin\left(\frac{\pi}{5}x\right)+26$$  

• $$f\left(x\right)=\ 6\sin\left(10x\right)+26$$  

• $$f\left(x\right)=\ -6\sin\left(10x\right)+26$$  

​Period:

​Max is 32 and min is 20, so that means the amplitude is HALF the distance= 6

If amplitude is 6, the midline would be 20+6= 26

Multiple Select

Given the polynomial $$f\left(x\right)=-2x^3-10x^2+5x\ -43$$  , which statements regarding the polynomials end behavior are true?

• $$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$$  

• $$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty\ \$$  

• $$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$  

• $$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$  

​As x goes to negative infinity, y goes to positive infinity.

As x goes to positive infinity, y goes to negative infinity.

Multiple Choice

Describe how the function y = 2^x is transformed to make y = 2^{x - 5} + 3

• Translated left 5 and down 3

• Translated right 5 and down 3

• Translated left 5 and up 3

• Translated right 5 and up 3

Multiple Choice

Which function does NOT have the set of all real numbers as its domain?

Multiple Choice

A polynomial, f(x), has a lead coefficient of 1 and exactly two distinct zeros. What choice shows f(x) from the zeros above?

Multiple Choice

The volume of a rectangular prism is represented by the expression a³+4a²-3a-18. If the length is (a-2) and the height and width are​ equal, what is the width of the​ prism?

• a+3

• a-3

• a+2

• a-2

Multiple Choice

Let p(n)=n³+2n²-23n+k. If you divide p(n) by (n+6), the remainder is -1. What is the remainder if you divide p(n) by (n-5)?

• 65

• 1

• 12

• 55

Multiple Choice

cos 5π/6

• -1/2

• 1/2

• √3/2

• -√3/2

Multiple Choice

What is the radius of the circle with this equation x² + y² - 10x + 8y - 23 = 0?

• 4

• 2

• 8

• 23

Multiple Choice

What is the center for the circle with this equation x² + y² - 10x + 8y - 23 = 0?

• (5,4)

• (-5, 4)

• (-4,5)

• (5,-4)

Multiple Choice

Is $$\left(x+1\right)$$  a factor of $$3x^3+2x^2+11$$  ?

• Yes

• No

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What is the sum of the remainder when a³ - 4 is divided by (a+2) and (a-1)?