Questions

1) In direct variation, as the x-values increase, the y-values __________.

a.) increase

b.) decrease

2) In inverse variation, as the x-values increase, the y-values __________.

a.) increase

b.) decrease

3) Study the numbers in the table. To stay with the same pattern, what number should replace the question mark?

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4) In the table in the previous problem, how do the y-values change as the x-values increase by one?

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5) Complete the equation for the table: y = ? x

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6) The equation in the previous problem is an example of what type of variation?

a.) direct variation

b.) inverse variation

7) Study the numbers in the table. To stay with the same pattern, what number should replace the question mark? (Hint: The answer is a decimal number.)

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8) In the table in the previous problem, as the x-values increase by one, how can the y-values be calculated?

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9) Complete the equation for the table: xy = ?

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10) The equation in the previous problem is an example of what type of variation?

a.) direct variation

b.) inverse variation

11) Write five ordered pairs for the points that are emphasized (red) in the graph.

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12) For the graph in the previous problem, which equation represents the relationship between x and y?

a.) y = 3x

b.) xy = 2

c.) y = 2x

d.) y = (1/2)x

13) The graph and equation in the previous two problems are an example of what kind of variation?

a.) direct variation

b.) inverse variation

14) Write six ordered pairs for the points that are emphasized (red) in the graph.

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15) For the graph in the previous problem, which equation represents the relationship between x and y?

a.) y = 10x

b.) xy = 20

c.) y = 20x

d.) xy = 10

16) The graph and equation in the previous two problems are an example of what kind of variation?

a.) direct variation

b.) inverse variation

17) The equation, xy = 60, is an example of what kind of variation?

a.) direct variation

b.) inverse variation

18) The equation, y = 7x, is an example of what kind of variation?

a.) direct variation

b.) inverse variation

19) The equation, y = (1/4)x, is an example of what kind of variation?

a.) direct variation

b.) inverse variation

20) The equation, y = 36/x, is an example of what kind of variation?

a.) direct variation

b.) inverse variation

21) For the given proportion, cross multiply to write an equation, and then select the type of variation.

a.) direct variation

b.) inverse variation

22) For the given proportion, cross multiply to write an equation and then select the type of variation.

a.) direct variation

b.) inverse variation

23) The picture displays the results of the captured water life from a certain section of a pond. Suppose this sample represents the correct ratio of the number of fish to the number of turtles in the whole pond. Which of the formulas is correct for finding the number of turtles (T) given the number of fish (F)?

a.) T = 3F + 7

b.) T = (3/7) F

c.) T = 7F + 3

d.) T = (7/3) F

24) The equation determined in the previous problem is an example of what type of variation?

a.) direct variation

b.) indirect variation

25) Translate trapezoid ABCD left 3 and up 5. What are the ordered pairs of the vertices of the image?

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26) Translate trapezoid ABCD right 7 and down 7. What are the ordered pairs of the vertices of the image?

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27) Rotate trapezoid ABCD 180 degrees clockwise around the origin. What are the ordered pairs of the vertices of the image?

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28) True or False.

True

False

29) True or False.

True

False

30) True or False.

True

False

31) In a regular triangular pyramid, the equilateral triangular base has an edge of 12 centimeters and a height of 10.4 centimeters. The height of the pyramid is 9.8 centimeters. What is the volume of the triangular pyramid? (Hint: V = (1/3)Bh)

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32) In the previous problem, the slant height of each of the other triangles is 5.3 centimeters. What is the surface area of the pyramid?

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33) Explain how to find the height of a pyramid if the base area and the volume are known. (Hint: Work backwards.)

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34) What is the volume of a cylinder if the radius of the circular base is 4.7 centimeters and height of the cylinder is 7 centimeters? Express the answer in thousandths.

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35) What is the volume of a rectangular prism that measures 3.5 centimeters by 4.2 centimeters by 5.8 centimeters?

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36) Given the surface area of a cube is 294 square centimeters, what is the length of the edge of the cube?

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37) What is the volume of the cube mentioned in the previous problem?

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38) Evaluate.

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39) Evaluate.

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40) Find the product.

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41) Evaluate.

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42) Find the product.

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43) Find the product.

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44) An assembly worker is making 3-legged and 5-legged stools. She has 67 legs to use in all for the day’s work. What is the largest number of 3-legged stools she can make and still use all the legs to make 5-legged stools with the rest of the legs?

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45) Please provide an explanation for the solution to the previous problem.

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46) A car averages from 15 to 21 miles per gallon of fuel. If the car is giving the best performance on fuel mileage, what is the maximum distance that the car could be driven using 10 gallons of fuel?

a.) 150 miles

b.) 180 miles

c.) 210 miles

d.) 315 miles

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