Foundations of Algebra

​FTCE 5-9 Math Test -Foundations of Algebra Day 2

Multiple Choice

What is the solution to –4|–2x + 6| = –24? #1

• x = 0

• x = 0 or x = –6

• x = 0 or x = 6

• no solution

Multiple Choice

What is the solution to 3|–3x + 9| = –18? #2

• x = –5

• x = 5 or x = 1

• x = –5 or x = 1

• no solution

Match

Match the following. #3

• |x| = 5

• |2x| = 4

• |x+2| = 6

• |x-3| = 2

• $$\left|\frac{x}{5}\right|=-6$$  

x = 5, -5

x = 2, -2

x = 4, -8

x = 1, 5

No Solution

• x = 5, -5

• x = 2, -2

• x = 4, -8

• x = 1, 5

• No Solution

Multiple Choice

| 3x - 6 | - 9 = -3 #5

• No Solution

• x = 0 and x = 4

• x = 2 and x = -2

• x = -4 and x = 4

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Multiple Choice

Solve. #11

• n > 1 or n < -7

• n > -1 or n < -7

• -7 < n < -1

• no solution

Multiple Choice

Solve. #12

|4v + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5

• -4.5 ≤ v ≤ -1.4

• -1.5 ≤ v ≤ 4.5

• v ≤ -1.5 or v ≥ 4.5

Multiple Choice

Solve.
6 - 2|m -3| > -4 #14

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8

Multiple Choice

| 2x + 12 | < 8

Which is the correct first step? #15

• 2x + 12 < 8 and 2x+12 > -8

• 2x + 12 < 8 or 2x+12 > -8

• 2x + 12 < 8 and 2x+12 < -8

• 2x + 12 < 8 or 2x+12 < -8

Multiple Choice

Select the inequality shown. #21

• x > 3

• x ≥ 3

• x < 3

• x ≤ 3

Multiple Choice

Select the inequality shown. #22

• x > 1

• x ≥ 1

• x < 1

• x ≤ 1

Match

Match the following inequalities to the number line that best represents the solution set. #23

  

 

 

  

• $$1<x$$   

• $$x>1$$  

• $$x\le1$$  

• $$1\ge x$$   

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Multiple Choice

$$y\le-\frac{5}{3}x-2$$ Match the inequality with the graph shown. #29

Multiple Choice

$$y\le-\frac{3}{5}x+3$$ Match the inequality with the graph shown. #30

Multiple Choice

$$y>1$$ Match the inequality with the graph shown. #31

Multiple Choice

$$y\ge-\frac{4}{5}x+5$$ Match the inequality with the graph shown. #32

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Multiple Choice

What is the slope of the line passing through the points (3,5) and (-1,7)? #41

• -1/2

• -1

• -2

• 1/2

Multiple Choice

Find the slope of:

(7,1) and (-2,1) #42

• 0

• -1/2

• undefined

• -8

Multiple Choice

Find the slope between the two points: #43

(12,-2) and (4, -6)

• -1/2

• 5/7

• -2

• 1/2

Multiple Choice

Which statement below accurately represents the graph? #46

• $100 is earned for each hour worked

• $100 is earned for every 2 hours worked

• $500 is earned for every 8 hours worked

• $200 is earned for every 3 hours worked

Multiple Select

A balloon artist creates balloon hats for children at a store’s grand opening. The graph shows the number of balloons the artist has remaining, y, after creating x hats.

What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Select three options. #47

• positive slope

• negative slope

• constant slope

• increasing function

• decreasing function

Multiple Choice

The table shows the height of water in a pool as it is being filled.

The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? #48

• The height of the water increases 2 inches per minute.

• The height of the water decreases 2 inches per minute.

• The height of the water was 2 inches before any water was added.

• The height of the water will be 2 inches when the pool is filled.

Multiple Choice

What is the standard form of a linear equation?

• Ax+By=C

• y=mx+b

• y-y1 = m(x-x1)

• m = (y2-y1)/(x2-x1)

Multiple Choice

Find the slope. #52

• -2/3

• 2/3

• -3/2

• 3/2

Multiple Choice

Find the slope and y-intercept of the following: #53

y = -8x + 13

• slope = -8/13, y-intercept = 1

• slope = -8, y-intercept = 13

• slope = 8/13, y -intercept = -8

• slope = 13, y-intercept = -8

Multiple Choice

What is the slope of the line y=8x + 1? #54

• m=undefined

• m=0

• m=8

• m = 1

Multiple Choice

Determine the slope and y-intercept from the following equation: 4x + y = -10. #57

• slope: 4   y-intercept:  (0,10)

• slope: -4   y-intercept:  (0,-10)

• slope: -4   y-intercept:  (0,10)

• slope: 4   y-intercept:  (0,-10)

Multiple Choice

Match the equation to the correct graph: #61

$$y=-\frac{1}{2}x+7$$  

Multiple Choice

Write the equation of the line. #62

• y= -1x-3

• y= -3x-1

• y=-1/3x-1

• y= -3x-3

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Multiple Choice

Write the equation of the line containing (-3,4) and (-1,-2). #66

• y = -3x - 5

• y = -3x + 1

• y = -3x + 13

• y = 3x + 1

Multiple Choice

Find the equation of the line that passes through the points:(2, 2) and (3, 4). #67

• y = 2x + 2

• y = -2x - 2

• y = -2x + 2

• y = 2x - 2

Multiple Choice

Write the equation of the line containing (-3,4) and (-1,-2). #69

• y = -3x - 5

• y = -3x + 13

• y = -3x + 1

• y = 3x + 1

Multiple Choice

Identify whether the function is linear, quadratic, or exponential. #71

• Linear Growth

• Linear Decay

• Quadratic (Local Max)

• Quadratic (Local Min)

• Exponential Decay

Multiple Choice

Identify whether the function is linear, quadratic, or exponential. #72

• Linear Growth

• Linear Decay

• Quadratic (Local Max)

• Quadratic (Local Min)

• Exponential Decay

Multiple Choice

Identify whether the function is linear, quadratic, or exponential. #73

• Linear Growth

• Linear Decay

• Quadratic (Local Max)

• Exponential Growth

• Exponential Decay

Multiple Choice

Which equation below is a quadratic that has been translated 5 units up? #76

• $$f\left(x\right)=x^2-5$$  

• $$f\left(x\right)=x^2+5$$  

• $$f\left(x\right)=\left(x-5\right)^2$$  

• $$f\left(x\right)=\left(x+5\right)^2$$  

• $$f\left(x\right)=\sqrt{x}+5$$  

Multiple Select

Describe the transformation: (click on two answers)

$$f\left(x\right)=-\left(x-7\right)^2$$  #77

• Reflection over the x-axis

• Reflection over the y-axis

• Shift 7 units left

• Shift 7 units right

Multiple Choice

If the blue is f(x)=x^2, then the red must be...#79

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

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Multiple Choice

Two lines that are parallel will have ...#81

• negative reciprocal slopes

• No slope

• equal slopes

• none of the above

Multiple Choice

Write the equation of a line PARALLEL to y = 2x + 3 that passes through the point (3, 1). #82

• $$y=2x\ -3$$

• $$y=2x-5$$

• $$y=2x\ +\ 1$$

• $$y=-\frac{1}{2}x+\frac{5}{2}$$

Multiple Choice

Which of the following lines is PARALLEL to the graph of $$y=6x-3$$  ? #83

• $$y=-6x+5$$  

• $$y=-\frac{1}{6}x-3$$  

• $$y=6x+1$$  

• $$y=\frac{1}{6}x-3$$  

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Multiple Choice

Two lines that are perpendicular lines have ...#86

• negative reciprocal slopes

• No Slope

• equal slopes

• none of the above

Multiple Choice

Write the equation of a line PERPENDICULAR to -2x + 5y - 3 = 0 that passes through the point (2, -3). #89

• y = -5/2x - 11/2

• y = -5/2x + 2

• y = -5/2x + 8

• y = 2/5x + 19/5

Multiple Choice

Write an equation of a line that passes through the point (-9,2) and is perpendicular to the line y = 3x - 12. #90

• y = (-1/3)x - 1

• y = (1/3)x - 2

• y = -3x + 12

• y = 3x - 1