Algebra I Readiness Assessment-timed 2016

1.

4

24

98

7

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Explanation

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2.

3

18

108

216

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Explanation

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3. Which of the following has a unit rate of 17 miles per hour?

60 miles in 2 hours

85 miles in 5 hours

90 miles in 10 hours

120 miles in 15 hours

The unit rate represents the amount of miles traveled in one hour. To find the unit rate, we divide the total miles by the total hours. In this case, the unit rate for 85 miles in 5 hours is 17 miles per hour, as 85 divided by 5 equals 17. Therefore, the correct answer is 85 miles in 5 hours.

Explanation

The unit rate represents the amount of miles traveled in one hour. To find the unit rate, we divide the total miles by the total hours. In this case, the unit rate for 85 miles in 5 hours is 17 miles per hour, as 85 divided by 5 equals 17. Therefore, the correct answer is 85 miles in 5 hours.

4. The runners completing a 10K run were asked how many days per week they train. If 200 runners were surveyed, how many runners said that they train 4 days per week?

8 runners

12 runners

80 runners

120 runners

Based on the information given, 200 runners were surveyed about their training frequency. The question specifically asks for the number of runners who train 4 days per week. The correct answer is 80 runners, indicating that out of the 200 surveyed runners, 80 of them reported training 4 days per week.

Explanation

Based on the information given, 200 runners were surveyed about their training frequency. The question specifically asks for the number of runners who train 4 days per week. The correct answer is 80 runners, indicating that out of the 200 surveyed runners, 80 of them reported training 4 days per week.

5. For birthday parties, the skating rink charges $100 to reserve the rink and then $5 per person. Write an expression to represent the cost for any number of people.

100 – 5n

100 + 5n

5(n + 100)

5(n – 100)

The expression 100 + 5n represents the cost for any number of people at the skating rink for a birthday party. The $100 is the cost to reserve the rink and the $5 per person is added for each person attending the party. By multiplying the number of people (n) by 5 and adding it to the $100 reservation fee, we can calculate the total cost for any number of people.

Explanation

The expression 100 + 5n represents the cost for any number of people at the skating rink for a birthday party. The $100 is the cost to reserve the rink and the $5 per person is added for each person attending the party. By multiplying the number of people (n) by 5 and adding it to the $100 reservation fee, we can calculate the total cost for any number of people.

6. Subtract $7 over 9 minus 1 third$

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Explanation

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7.

3 gallons

12 gallons

2 gallons

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Explanation

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8. Find the approximation of

square root of 39

.

6.0

6.2

7.0

7.5

The given options are all approximations of a certain value. Among these options, 6.2 is the closest approximation to the given value.

Explanation

The given options are all approximations of a certain value. Among these options, 6.2 is the closest approximation to the given value.

9. Which statement is true?

0.75

6.12>6.16

The statement "6.12 > 6.16" is true because 6.12 is indeed greater than 6.16.

Explanation

The statement "6.12 > 6.16" is true because 6.12 is indeed greater than 6.16.

10.

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Explanation

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11. The table shows the number and type of animals that are on exhibit at the 4-H fair.Find the percentage of animals that are horses.

12%

25%

50%

312%

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Explanation

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12.

What is the ratio of side AB to side BC, in simplest form?

1:1

2:3

3:2

4:3

The ratio of side AB to side BC is 3:2. This means that the length of side AB is 3 times the length of side BC. The ratio is in its simplest form because the numbers 3 and 2 do not have any common factors other than 1.

Explanation

The ratio of side AB to side BC is 3:2. This means that the length of side AB is 3 times the length of side BC. The ratio is in its simplest form because the numbers 3 and 2 do not have any common factors other than 1.

13. What value of x makes this equation true?2x + 18 = 5x

X = -6

X = 4

X = 2.6

X = 6

To find the value of x that makes the equation true, we can start by simplifying the equation. By subtracting 2x from both sides, we get 18 = 3x. Then, dividing both sides by 3, we find that x = 6. Therefore, the value of x that satisfies the equation is 6.

Explanation

To find the value of x that makes the equation true, we can start by simplifying the equation. By subtracting 2x from both sides, we get 18 = 3x. Then, dividing both sides by 3, we find that x = 6. Therefore, the value of x that satisfies the equation is 6.

14. In trail mix, the ratio of cups of peanuts to chocolate candies is 3 to 2. How many cups of chocolate candies would be needed for 9 cups of peanuts?

6 cups

3 cups

4 cups

8 cups

The ratio of cups of peanuts to chocolate candies in trail mix is 3 to 2. This means that for every 3 cups of peanuts, there are 2 cups of chocolate candies. To find out how many cups of chocolate candies would be needed for 9 cups of peanuts, we can set up a proportion. If 3 cups of peanuts require 2 cups of chocolate candies, then 9 cups of peanuts would require x cups of chocolate candies. Solving the proportion, we find that x = (9 * 2) / 3 = 6. Therefore, 6 cups of chocolate candies would be needed for 9 cups of peanuts.

Explanation

The ratio of cups of peanuts to chocolate candies in trail mix is 3 to 2. This means that for every 3 cups of peanuts, there are 2 cups of chocolate candies. To find out how many cups of chocolate candies would be needed for 9 cups of peanuts, we can set up a proportion. If 3 cups of peanuts require 2 cups of chocolate candies, then 9 cups of peanuts would require x cups of chocolate candies. Solving the proportion, we find that x = (9 * 2) / 3 = 6. Therefore, 6 cups of chocolate candies would be needed for 9 cups of peanuts.

15. The seventh grade class is going on a trip to the state fair. The trip costs $52. Included in that price is $11 for a concert ticket and the cost of two passes, one for rides and one for game booths. Each of the passes cost the same price. Write an equation representing the cost of the trip and determine the price of one pass.

2x – 11 = 52; $31.50

3x = 52; $17.33

2x = 52; $26

52 = 11 + 2x; $20.50

The equation 52 = 11 + 2x represents the cost of the trip. The left side of the equation represents the total cost of the trip, which is $52. The right side of the equation represents the sum of $11 for the concert ticket and the cost of two passes, which are both represented by 2x. By subtracting 11 from both sides of the equation, we can isolate the variable 2x. Therefore, the price of one pass is $20.50.

Explanation

The equation 52 = 11 + 2x represents the cost of the trip. The left side of the equation represents the total cost of the trip, which is $52. The right side of the equation represents the sum of $11 for the concert ticket and the cost of two passes, which are both represented by 2x. By subtracting 11 from both sides of the equation, we can isolate the variable 2x. Therefore, the price of one pass is $20.50.

16. Solve for x.

x space minus space 2 over 5 space equals space 3 over 10

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Explanation

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17. Simplify

5 x cubed italic space italic times italic space 6 x to the power of italic 2 italic space italic times italic space x

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Explanation

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18. Find the circumference.

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Explanation

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19. A rectangle has vertices P(1, 0), Q(6, 0), R(6, 6), and S(1, 6).What is the area of rectangle PQRS?

To find the area of a rectangle, we can use the formula: Area = length × width. In this case, the length of the rectangle is the distance between points P(1, 0) and Q(6, 0), which is 6 - 1 = 5 units. The width of the rectangle is the distance between points P(1, 0) and S(1, 6), which is 6 units. Therefore, the area of rectangle PQRS is 5 × 6 = 30 square units.

Explanation

To find the area of a rectangle, we can use the formula: Area = length × width. In this case, the length of the rectangle is the distance between points P(1, 0) and Q(6, 0), which is 6 - 1 = 5 units. The width of the rectangle is the distance between points P(1, 0) and S(1, 6), which is 6 units. Therefore, the area of rectangle PQRS is 5 × 6 = 30 square units.

20. Which equation corresponds to the statements "the length L of the rectangle is four less than twice the width W" ?

W = 4 - 2L

W = 4L - 2

L= 2W - 4

L = 4 - 2W

The given statement "the length L of the rectangle is four less than twice the width W" can be translated into an equation as L = 2W - 4. This equation represents the relationship between the length and width of the rectangle, where the length is equal to twice the width minus four.

Explanation

The given statement "the length L of the rectangle is four less than twice the width W" can be translated into an equation as L = 2W - 4. This equation represents the relationship between the length and width of the rectangle, where the length is equal to twice the width minus four.

21. Solve

y squared minus 16 equals 9

.

Y= 5 and -5

Y= 25 and -25

Y = 13 and 5

Y = 3 and -3

The given answer, y = 5 and -5, suggests that the value of y can be either 5 or -5. This means that the equation has two possible solutions for y, where y can take on either of these values.

Explanation

The given answer, y = 5 and -5, suggests that the value of y can be either 5 or -5. This means that the equation has two possible solutions for y, where y can take on either of these values.

22. If hamburger meat costs $2.25 per pound, how much does 0.8 pound of hamburger cost?

$2.81

$1.13

$1.80

$2.13

To find the cost of 0.8 pounds of hamburger meat, we can multiply the cost per pound ($2.25) by the weight in pounds (0.8). This gives us $1.80, which is the cost of 0.8 pound of hamburger meat.

Explanation

To find the cost of 0.8 pounds of hamburger meat, we can multiply the cost per pound ($2.25) by the weight in pounds (0.8). This gives us $1.80, which is the cost of 0.8 pound of hamburger meat.

23. What is the area of a triangle with a height of 20 meters and a base of 16 meters?

The area of a triangle is calculated by multiplying the base length by the height and dividing the result by 2. In this case, the base length is 16 meters and the height is 20 meters. Multiplying these values gives us 320 square meters. Dividing by 2 gives us the final answer of 160 square meters.

Explanation

The area of a triangle is calculated by multiplying the base length by the height and dividing the result by 2. In this case, the base length is 16 meters and the height is 20 meters. Multiplying these values gives us 320 square meters. Dividing by 2 gives us the final answer of 160 square meters.

24. The chart below lists the life expectancy in years for people in the United States every five years from 1970 to 2005. What would you expect the life expectancy of a person in the U.S. to be in the year 2015?

75 years

80 years

90 years

95 years

Based on the given chart, the life expectancy in the United States has been increasing every five years from 1970 to 2005. Therefore, it can be expected that the life expectancy of a person in the U.S. in the year 2015 would be higher than the previous recorded data of 75 years. The closest option to this expectation is 80 years, which is the correct answer.

Explanation

Based on the given chart, the life expectancy in the United States has been increasing every five years from 1970 to 2005. Therefore, it can be expected that the life expectancy of a person in the U.S. in the year 2015 would be higher than the previous recorded data of 75 years. The closest option to this expectation is 80 years, which is the correct answer.

25. Which statement does not represent the data set?{1, 5, 3, 5, 1, 2, 6, 4, 1}

Mean = 4

Median = 3

Mode = 1

Range = 5

The mean is calculated by summing up all the values in the data set and dividing it by the total number of values. In this case, the sum of the values is 28 and there are 9 values, so the mean is 28/9 = 4.

Explanation

The mean is calculated by summing up all the values in the data set and dividing it by the total number of values. In this case, the sum of the values is 28 and there are 9 values, so the mean is 28/9 = 4.

26.

In the picture of the three triangles, two are similar. Which statement below is true?

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Explanation

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27. Evaluate 5(n + 3) - 7n if n= $1 half$ .

20

7.5

6

14

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Explanation

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28. What is the simple interest on an investment of $1500 at 5% for 5 years? (I = Prt)

$37,500

$1,875

$375

$37.50

The correct answer is $375. This can be calculated using the formula for simple interest, I = Prt. In this case, the principal amount (P) is $1500, the interest rate (r) is 5%, and the time period (t) is 5 years. Plugging these values into the formula, we get I = 1500 * 0.05 * 5 = $375. Therefore, the simple interest on the investment is $375.

Explanation

The correct answer is $375. This can be calculated using the formula for simple interest, I = Prt. In this case, the principal amount (P) is $1500, the interest rate (r) is 5%, and the time period (t) is 5 years. Plugging these values into the formula, we get I = 1500 * 0.05 * 5 = $375. Therefore, the simple interest on the investment is $375.

29. Divide

fraction numerator 9 r cubed over denominator 2 r squared end fraction

.

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Explanation

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30. Evaluate

12

15

44

-36

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Explanation

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31. Which expression is NOT equivalent to the others?

4(m + 2)

3m + 8 + m

4m + 4

2(1 + m) + m + 6 + m

All the given expressions involve multiplying a number by 4 and adding a constant value. However, the expression 4m + 4 is the only one that does not involve adding any additional terms or variables. Therefore, it is not equivalent to the other expressions, which include additional terms and variables.

Explanation

All the given expressions involve multiplying a number by 4 and adding a constant value. However, the expression 4m + 4 is the only one that does not involve adding any additional terms or variables. Therefore, it is not equivalent to the other expressions, which include additional terms and variables.

32. What table of ordered pairs corresponds to the function y = -3x + 1?

The table of ordered pairs that corresponds to the function y = -3x + 1 can be generated by substituting different values of x into the equation and solving for y. For example, when x = 0, y = 1. When x = 1, y = -2. When x = 2, y = -5. Therefore, the table of ordered pairs would be (0, 1), (1, -2), (2, -5), and so on.

Explanation

The table of ordered pairs that corresponds to the function y = -3x + 1 can be generated by substituting different values of x into the equation and solving for y. For example, when x = 0, y = 1. When x = 1, y = -2. When x = 2, y = -5. Therefore, the table of ordered pairs would be (0, 1), (1, -2), (2, -5), and so on.

33. If a rectangle, measuring 2 in. by 7 in., is enlarged by using a scale factor of 2, what will the area be of the new rectangle?

56

28

14

98

When a rectangle is enlarged using a scale factor of 2, all of its dimensions are multiplied by 2. In this case, the length of the rectangle is 2 inches and the width is 7 inches. When we multiply both of these dimensions by 2, we get a new rectangle with a length of 4 inches and a width of 14 inches. To find the area of this new rectangle, we multiply the length by the width: 4 inches * 14 inches = 56 square inches. Therefore, the area of the new rectangle is 56.

Explanation

When a rectangle is enlarged using a scale factor of 2, all of its dimensions are multiplied by 2. In this case, the length of the rectangle is 2 inches and the width is 7 inches. When we multiply both of these dimensions by 2, we get a new rectangle with a length of 4 inches and a width of 14 inches. To find the area of this new rectangle, we multiply the length by the width: 4 inches * 14 inches = 56 square inches. Therefore, the area of the new rectangle is 56.

34. The Irrational Club wants to build a tree house. They have a 13-foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground?

12 feet

144 feet

169 feet

14 feet

The ladder forms a right triangle with the ground and the height of the tree house. Using the Pythagorean theorem (a^2 + b^2 = c^2), where a is the height of the tree house, b is the distance from the base of the ladder to the bottom of the tree, and c is the length of the ladder, we can solve for a. Plugging in the given values, we have a^2 + 5^2 = 13^2. Simplifying, we get a^2 + 25 = 169. Subtracting 25 from both sides, we have a^2 = 144. Taking the square root of both sides, we get a = 12. Therefore, the tree house will be 12 feet off the ground.

Explanation

The ladder forms a right triangle with the ground and the height of the tree house. Using the Pythagorean theorem (a^2 + b^2 = c^2), where a is the height of the tree house, b is the distance from the base of the ladder to the bottom of the tree, and c is the length of the ladder, we can solve for a. Plugging in the given values, we have a^2 + 5^2 = 13^2. Simplifying, we get a^2 + 25 = 169. Subtracting 25 from both sides, we have a^2 = 144. Taking the square root of both sides, we get a = 12. Therefore, the tree house will be 12 feet off the ground.

35. Consider the list of numbers below. Which statement is true?

3.4 comma space square root of 7 comma space square root of 13 comma space 250 %

The list of numbers is not provided in the question, so it is not possible to determine which statement is true.

Explanation

The list of numbers is not provided in the question, so it is not possible to determine which statement is true.

36. The graph shown is the solution to which of the following inequalities?

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Explanation

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37. Graph the function $y equals x squared minus 1$ for the domain of {-2, -1, 0, 1, 2}.

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Explanation

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38. The volume of a cube is $1 over 64$ $i n cubed$ . What is the edge length?

4 in.

In.

8 in.

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Explanation

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39. Solve the following inequality. -0.5x - 5

less or equal than

-1.5

X -7

X 7

X -7

The given inequality is -0.5x - 5 ≤ -1.5. To solve this inequality, we need to isolate the variable x. We can do this by adding 5 to both sides of the inequality, which gives -0.5x ≤ -1.5 + 5. Simplifying further, we get -0.5x ≤ 3.5. To isolate x, we divide both sides of the inequality by -0.5. However, when dividing by a negative number, the direction of the inequality changes. Therefore, we have x ≥ -7. So, the correct answer is x ≥ -7.

Explanation

The given inequality is -0.5x - 5 ≤ -1.5. To solve this inequality, we need to isolate the variable x. We can do this by adding 5 to both sides of the inequality, which gives -0.5x ≤ -1.5 + 5. Simplifying further, we get -0.5x ≤ 3.5. To isolate x, we divide both sides of the inequality by -0.5. However, when dividing by a negative number, the direction of the inequality changes. Therefore, we have x ≥ -7. So, the correct answer is x ≥ -7.

40. Which is the graph of the function y = 4x – 1?

The graph of the function y = 4x - 1 is a straight line with a slope of 4 and a y-intercept of -1. The slope of 4 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 4. The y-intercept of -1 means that the line crosses the y-axis at the point (0, -1). Therefore, the correct answer is the graph that represents a straight line with a slope of 4 and a y-intercept of -1.

Explanation

The graph of the function y = 4x - 1 is a straight line with a slope of 4 and a y-intercept of -1. The slope of 4 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 4. The y-intercept of -1 means that the line crosses the y-axis at the point (0, -1). Therefore, the correct answer is the graph that represents a straight line with a slope of 4 and a y-intercept of -1.

41. Gas prices are projected to increase by 124% in the next two years. A gallon of gas currently costs $3.80. What is the projected total cost of a gallon of gas two years from now?

$8.51

$4.71

$7.60

$5.04

The correct answer is $4.71. This can be calculated by multiplying the current cost of a gallon of gas ($3.80) by the projected increase (124%). 3.80 * 1.24 = 4.71.

Explanation

The correct answer is $4.71. This can be calculated by multiplying the current cost of a gallon of gas ($3.80) by the projected increase (124%). 3.80 * 1.24 = 4.71.

42. Solve the system of linear equations by finding the ordered pair that satisfies both equations.

(-1, 0)

(0, -1)

(1, 0)

(0, 1)

The ordered pair (0, -1) satisfies both equations in the system of linear equations.

Explanation

The ordered pair (0, -1) satisfies both equations in the system of linear equations.

43. Determine the surface area of rectangular prism with height 5 inches, width 7 inches, and length 12 inches.

To determine the surface area of a rectangular prism, we need to find the area of each face and then add them together. The rectangular prism has 6 faces, with each face having a length and width. The top and bottom faces have dimensions of 12 inches by 7 inches, giving an area of 84 square inches each. The front and back faces have dimensions of 12 inches by 5 inches, giving an area of 60 square inches each. The left and right faces have dimensions of 7 inches by 5 inches, giving an area of 35 square inches each. Adding all the areas together, the surface area of the rectangular prism is 84 + 84 + 60 + 60 + 35 + 35 = 358 square inches.

Explanation

To determine the surface area of a rectangular prism, we need to find the area of each face and then add them together. The rectangular prism has 6 faces, with each face having a length and width. The top and bottom faces have dimensions of 12 inches by 7 inches, giving an area of 84 square inches each. The front and back faces have dimensions of 12 inches by 5 inches, giving an area of 60 square inches each. The left and right faces have dimensions of 7 inches by 5 inches, giving an area of 35 square inches each. Adding all the areas together, the surface area of the rectangular prism is 84 + 84 + 60 + 60 + 35 + 35 = 358 square inches.

44. Compare the two functions rates of change.

Function 1 has the greater rate of change.

Function 2 has the greater rate of change.

Both functions have the same rate of change.

The rates of change cannot be determined.

The given answer states that Function 2 has the greater rate of change. This means that the rate at which Function 2 is changing is higher than the rate at which Function 1 is changing. It implies that the values of Function 2 are changing at a faster pace or with a steeper slope compared to Function 1. The answer suggests that Function 2 has a more significant and noticeable change in its values over a given interval of time or input values.

Explanation

The given answer states that Function 2 has the greater rate of change. This means that the rate at which Function 2 is changing is higher than the rate at which Function 1 is changing. It implies that the values of Function 2 are changing at a faster pace or with a steeper slope compared to Function 1. The answer suggests that Function 2 has a more significant and noticeable change in its values over a given interval of time or input values.

45. Simplify

fraction numerator left parenthesis 6.45 space x space 10 to the power of 11 right parenthesis left parenthesis 0.32 space x space 10 to the power of negative 4 right parenthesis end exponent over denominator left parenthesis 6.45 space x space 10 to the power of 3 right parenthesis end exponent end fraction

Answer must be in scientific notation.

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Explanation

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46. Data for ten students' math and science scores are provided in the chart below. Describe the relationship between the math and science scores.

There is a positive relationship between the math and science scores. As math scores increase, science scores increase.

There is a negative relationship between the math and science scores. As math scores increase, science scores decrease.

There is no relationship between the math and science scores.

The correct answer explains that there is a positive relationship between the math and science scores. This means that as the math scores of the students increase, their science scores also increase. This suggests that there is a correlation between the two subjects, indicating that students who perform well in math also tend to perform well in science.

Explanation

The correct answer explains that there is a positive relationship between the math and science scores. This means that as the math scores of the students increase, their science scores also increase. This suggests that there is a correlation between the two subjects, indicating that students who perform well in math also tend to perform well in science.

47. Solve for a. $negative 1 half left parenthesis 36 a minus 6 right parenthesis space equals 3 over 4 left parenthesis 4 minus 24 a right parenthesis space$

All real numbers

A = 0

A = -1

No solution

The equation "Solve for a" indicates that we need to find the values of "a" that satisfy the given conditions. The answer "all real numbers" means that any real number can be a solution for "a". This implies that there are no restrictions or limitations on the possible values of "a" and any real number can be substituted in the equation.

Explanation

The equation "Solve for a" indicates that we need to find the values of "a" that satisfy the given conditions. The answer "all real numbers" means that any real number can be a solution for "a". This implies that there are no restrictions or limitations on the possible values of "a" and any real number can be substituted in the equation.

48. Write the equation of a line, in slope-intercept form, passing through the points (6, 2) and (3, 0).

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Substituting the values of the given points, we get m = (0 - 2) / (3 - 6) = -2 / -3 = 2/3. Now, we can substitute the slope and one of the points into the equation to find the y-intercept. Using the point (6, 2), we get 2 = (2/3)(6) + b. Solving for b, we find b = 2 - 4 = -2. Therefore, the equation of the line is y = (2/3)x - 2.

Explanation

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Substituting the values of the given points, we get m = (0 - 2) / (3 - 6) = -2 / -3 = 2/3. Now, we can substitute the slope and one of the points into the equation to find the y-intercept. Using the point (6, 2), we get 2 = (2/3)(6) + b. Solving for b, we find b = 2 - 4 = -2. Therefore, the equation of the line is y = (2/3)x - 2.

49.

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Explanation

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50. Jamal needs to purchase a counter top for his kitchen. Jamal measured the counter top as 5 feet in length. The actual length is 4.5 feet. What is Jamal's percent error?

90%

11%

5%

10%

The percent error is calculated by taking the absolute difference between the measured and actual values, dividing it by the actual value, and then multiplying by 100. In this case, the absolute difference between the measured and actual length is 0.5 feet. Dividing this by the actual length of 4.5 feet gives a fraction of 1/9. Multiplying this fraction by 100 gives a percent error of approximately 11%.

Explanation

The percent error is calculated by taking the absolute difference between the measured and actual values, dividing it by the actual value, and then multiplying by 100. In this case, the absolute difference between the measured and actual length is 0.5 feet. Dividing this by the actual length of 4.5 feet gives a fraction of 1/9. Multiplying this fraction by 100 gives a percent error of approximately 11%.