Name: ______Date: ______Academic: ___

Chapter 4 Review: Functions

Identifying a Function:

1)Which ordered pairs should be removed to make the graph a function?
/ 2)The graph represents y as a function of x.

Identify an additional point that can be plotted so that the graph continues to represent y as a function of x?
3)Which set of ordered pairs can be plotted on the graph so that the graph continues to represent a function?
/ 4)In the table shown, x is the input and y is the output.

For the table to represent a function, which values cannot be substituted for the missing x value?

Comparing Functions:

1)Function A is a linear function. Some values of Function A are shown in the table.
Function B is a linear function with a y-intercept of 3 and an x-intercept of -5.
Compare the slope and y-intercept of the two functions.
2)Company A sells 500 pencils for $62.50. The equation represents the cost of buying x number of pencils from Company B.
  1. Determine which company has a lower price per pencil.
  1. Complete the sentence: The price per pencil at Company B is ______the price per pencil at Company A.

3)Ryan and Taylor are both saving money to buy new video game equipment. Ryan’s savings plan can be modeled by the function where m represents the number of months since Ryan started his plan, and s represents the amount of money saved in dollars. The table shown represents Taylor’s savings plan. Complete the sentences to compare the two functions.
  1. Ryan’s rate of change is ______Taylor’s rate of change.
  2. Ryan’s starting balance is ______Taylor’s starting balance.

4) Shannon and Anna went shopping for shirts. Shannon’s purchases are shown in the table and Anna’s purchases are modeled by the equation shown. Complete the sentence below.

______found the better buy because the shirts cost $______less.
5)The gasoline mileage for two cars can be compared by finding the distance each car traveled and the amount of gasoline used. The table shows the distance that car M traveled using x gallons of gasoline. The graph shows the distance, y, that car P traveled using x gallons of gasoline.
Based on the information in the table and the graph, compare the approximate miles per gallon of car M to car P. Show your work or explain your answer.
6)Function A and Function B are linear functions. Function A is represented by the table of values. Function B is represented by the equation.

Compare the y-intercept and rate of change of Functions A and B.
7)Two functions are shown.

  1. What is the rate of change of both functions? Which function has a greater rate of change?
  1. What is the initial value of each function? Which function has a greater initial value?
  1. Determine the output of each function if the input is 6.

Linear vs. Nonlinear:

1)Determine if each equation represents a linear or nonlinear function.
/ 2)The graph of a function is shown on the coordinate plane.
Which statements are true? Select all that apply.
  1. The function is linear between and .
  2. The function is linear between and .
  3. The function is decreasing between and .
  4. The function is increasing and linear between and .
  5. The function is decreasing and nonlinear between and .

3)Which functions are nonlinear? Select all that apply.
/ 4)Which equations represent linear functions? Select all that apply.
/ 5)Which equations define y as a nonlinear function of x? Select all that apply.

Qualitative Graphs:

1)The graph belowshows the speed of a roller coasterduring the first 30 seconds. Describe thechange in speed over time.
/ 2)The graph below shows thealtitude of a hiker during a hike. Describethe change in altitude over time.

Chapter 5 Review: Triangles

Parallel Lines:

1)Two parallel lines, a andb, are cut by transversal w. The measures of two angles formed are given in the diagram. What is the measurement of the angle labeled (3x)? / 2)Two parallel lines, a andb, are cut by transversal p. What is the measure of ?
3)The figure shows line parallel to line. The lines are intersected by 2 transversals. All lines are in the same plane.
  1. Explain why triangle is similar to triangle.
  1. Given that, determine.

Triangles:

1)Find the value of x in each triangle.
  1. b. c. d.

Pythagorean Theorem:

1)Tonya used side lengths a, b, and c to make different triangles. When Tonya only changed the length of side c, she noticed patterns with the side lengths used and the types of triangles formed. Which statement is true from Tonya’s investigation?
  1. If the length of side c is equal to the triangle formed is a right triangle.
  2. If the length of side c is equal to the triangle formed is a right triangle.
  3. If the length of side c is equal to the triangle formed is a right triangle.
  4. If the length of side c is equal to the triangle formed is a right triangle.
/ 2)Jonathan is building a box in the shape of a rectangular prism with dimensions of 8 inches by 12 inches by 9 inches. He plans to place a diagonal brace inside the box from Point A to Point D. A diagram of his box is shown. What is the length of the diagonal brace?

3)The top of a tree broke and fell over. The remaining tree trunk is 5 feet tall. The tip of the tree rests on the ground 12 feet from the base of the trunk. A diagram of the tree is shown. What is the length of the broken piece of the tree?
/ 4)A triangle is formed with side lengths of 24 centimeters, 26 centimeters, and 10 centimeters. Is the triangle a right triangle?

Distance:

1)The graph shows the locations of an eagle’s nest, a tree, and a pond. On the coordinate grid, each unit represents a mile.
What is the distance from the pond to the tree? Round to the nearest tenth of a mile. / 2)Two cars leave Jackson, Mississippi. One travels 8 miles north and then 6 miles east. The second car travels 12 miles south and 9 miles west. The location of each car is shown on the graph. What is the distance, in miles, between the cars?

Chapter 6 Review: Transformations

Transformations:

1)Triangle is shown on the coordinate plane.

Triangle is rotated counterclockwise about the origin to form the image triangle (not shown). Then triangle is reflected across the x-axi to form triangle (not shown). What are the signs of the coordinates of Point and ? / 2)Alice drew two triangles on the coordinate plane as shown. Describe the series of transformations that proves that the two triangles are congruent. Triangle is the preimage.

3)Given: is located on the coordinate plane.
measures 136°
If the triangle is rotated 90° counterclockwise about the origin to form, what is the measure of ? / 4)The vertices of quadrilateral are located at (-7, 3), (-7, 5), (-5, 5), and (-5, 3). What are the coordinates of the vertices of image after has been rotated 270° counterclockwise about the origin?
5)Rectangles and are shown on the coordinate plane. Describe the sequence of transformations that can be used to verify that rectangle is similar to rectangle?
/ 6)Triangle is given.Triangle is rotated clockwise around the origin resulting in . What are the coordinates of ?
7)In the coordinate plane shown, triangle is congruent to triangle. Triangle is similar to triangle .
  1. Describe a single transformation that shows that triangle is congruent to triangle. Include all the necessary information to complete the transformation.
  1. Describe a sequence of transformations that shows that triangle is similar to triangle. Include all the necessary information to complete each transformation.
/ 8)Three congruent figures are shown in the coordinate plane.

  1. Describe the sequence of transformations that occurred to transform figure 1 into figure 2.
  1. Describe the sequence of transformations that occurred to transform figure 1 into figure 3.

9)Four members of the Johnsonville Middle School band transport the school flag about the field during the halftime show. The figure whosn represents the four students, labeled A, B, C, D, who roll a rectangular platform with the school flag on the football field. After each movement, the students return to the original location. The band director wants to examine different flag movements for the opening routine.
  1. Complete the sentence. For the student’s first move, the rectangle ABCD is reflected across the y-axis to produce rectangle A’B’C’D’. Line segment A’B’ is parallel to line segment ______and is ______.
  1. The director then suggests that the stuents move on the field so that rectangle rotates clockwise about the origin. Where would student C be located after the rotation?
  1. For the next movement, the director instructed the students to move on the field so that rectangle is translated 50 yards to the right and 5 yards down. What are the coordinates of rectangle ?
  1. The students then moved on the field so that the flagformed a congruent rectangle with coordinates and . Describe the transformations that occurred to transform rectangle to rectangle .
  1. Next, the band director asked the students to move where rectangle was reflected across the x-axis to produce rectangle . What are the coordinates of ?
  1. While the students had rectangle reflected across the x-axis to produce rectangle , the director took two measurements. What is the length of ? ______What is the length of ? ______
  1. After a short break, the students transformed rectangle into a congruent image with vertices and . Describe the transformations that occurred to produce .
  1. Finally, the director decides he wants rectangle translated 5 yards to the right and 20 yards upward for the opening routine. Write the rule that shows the effect of the translation on the coordinates of the rectangle.

Chapter 8: Volume and Surface Area

Volume:

1)Austin uses a mold to make cone-shaped cupcakes. The diameter of the mold is 3 inches, and the height of the mold is 2 inches. If one cubic inch is about 0.55 ounce, how many ounces will 10 cupcakes weigh? Round to the nearest hundredth of an ounce. / 2)A cylinder and a cone are stacked on top of each other. They both have 2-foot diameters and heights of 9 feet. What is the combined volume, in cubic feet?
3)The figure shows a right-circular cylinder and a right-circular cone. The cylinder and the cone have the same base and the same height.
  1. What is the volume, in cubic feet, of the cone?

  1. What is the ratio of the cone’s volume to the cylinder’s volume?

Chapter 9: Scatter Plots and Probability

Scatter Plots:

Year / Digital Music Revenue (billions of $)
2009 / 4.4
2010 / 4.7
2011 / 5.3
2012 / 6.0
2013 / 6.4
2014 / 6.9
1)The table represents a company’s digital music revenue for six years.
  1. Is there an outlier? If so, what is it?
  1. Does the scatter plot have linear or nonlinear association?
  1. Is there positive or negative association?
/ 2)A scatter plot is shown on the coordinate plane. Draw a line of best fit for the data.

3)Ms. Downing created a scatter plot to show the relationship between the grades her students scored on a test and the number of hours each student studied. Draw a line of best fit.
/ 4)Nine people were surveyed to investigate the patterns of association between the time they spent playing video games and their ages. The data are shown in the scatter plot.

  1. Is there an outlier? If so, what is it?
  1. Is there clustering? If so, circle it.
  1. Does the scatter plot have linear or nonlinear association?
  1. Is there positive or negative association?

Two-Way Tables:

1)One weekend, 156 students went to see a movie at the local theater. Their popcorn and drink purchases were recorded in the two-way table shown.

  1. Find the relative frequencies by column. Round to the nearest thousandth.
  1. What is the relative frequency, rounded to the nearest tenth of a percent, of students who purchased popcorn?
/ 2)The table shows the results of a random survey of students in grade 7 and grade 8. Every student surveyed gave a response. Each student was asked if he or she exercised less than 5 hours last week or 5 or more hours last week.

  1. How many students were surveyed?
  1. Find and interpret the relative frequencies by row.

Probability of Compound Events:

1)A coin and a dice are tossed at the same time.
  1. Draw a tree diagram to determine all of the possible outcomes.
  1. Find the probability of getting a head on the coin and a 6 on the dice.
  1. Find the probability of getting a tail and an even number.
/ 2)Martina read that approximately 10% of all people are left-handed. She wants to design a simulation to approximate the probability of selecting exactly 2 right-handed people when 3 people are randomly selected.
  1. In the simulation, Martina has a spinner with sections of equal size. One section is labeled “L” (left) and the rest of the sections are labeled “R” (right). For this simulation to be accurate as possible, what is the total number of sections that the spinner should have?
  1. Martina spins the arrow on the spinner 3 times and records the resulting letters. Martina performs the simulation 30 times. The results of the simulation are shown. Based on the results of this simulation, when 3 people are randomly selected, exactly 2 right-handed people are selected approximately ______percent of the time.