Grade 8 Math Mastery: Problem Solving and Reasoning Quiz

1) Which statement about the number in the box is not true?

The number is a prime number.

The number is a whole number.

"The number is an irrational number."

The number is a rational number.

The correct answer is that the number is not an irrational number. A prime number is a number greater than 1 that can only be divided by 1 and itself. A rational number can be expressed as a fraction of two integers. A whole number is a non-negative integer.

Explanation

The correct answer is that the number is not an irrational number. A prime number is a number greater than 1 that can only be divided by 1 and itself. A rational number can be expressed as a fraction of two integers. A whole number is a non-negative integer.

2) What is the value of 7a(a - 1) + 6 when a = 2?

22

24

"20"

16

To solve the expression 7a(a - 1) + 6 when a = 2, substitute a = 2 into the expression to get 7(2)(2 - 1) + 6 = 7(2)(1) + 6 = 14*1 + 6 = 14 + 6 = 20.

Explanation

To solve the expression 7a(a - 1) + 6 when a = 2, substitute a = 2 into the expression to get 7(2)(2 - 1) + 6 = 7(2)(1) + 6 = 14*1 + 6 = 14 + 6 = 20.

3) A company ordered 328 pens with the company logo printed on them. The company returned 82 of the pens because the wrong logo was printed on them. What percent of the original order did the company keep?

"75%"

80%

70%

65%

To calculate the percentage of the original order kept, divide the number of pens kept (246) by the total number of pens ordered (328) and multiply by 100. This gives a percentage of 75%.

Explanation

To calculate the percentage of the original order kept, divide the number of pens kept (246) by the total number of pens ordered (328) and multiply by 100. This gives a percentage of 75%.

4) Which set of ordered pairs best represent the function y = 3x + 1?

B. (1, -2), (2, 5), (3, 8), (4, 11)

D. (-2, -5), (0, 1), (3, 10), (5, 18)

C. (0, 1), (2, 5), (4, 9), (6, 10)

The correct answer represents pairs of numbers that satisfy the function y = 3x + 1. If you substitute x values into the function and calculate the corresponding y values, it will match the given pairs for option A.

Explanation

The correct answer represents pairs of numbers that satisfy the function y = 3x + 1. If you substitute x values into the function and calculate the corresponding y values, it will match the given pairs for option A.

5) This is a list of the number of minutes each member of a study group spent studying for a test: 75, 40, 15, 0, 60, 50, 120, 90, 90, 20. What was the median number of minutes spent studying for the test by the group?

45

80

70

"55"

To find the median, first arrange the numbers in ascending order: 0, 15, 20, 40, 50, 60, 75, 90, 90, 120. Since there are 10 numbers, the median will be the average of the middle two numbers when arranged in order, which are 50 and 60. (50 + 60) / 2 = 55.

Explanation

To find the median, first arrange the numbers in ascending order: 0, 15, 20, 40, 50, 60, 75, 90, 90, 120. Since there are 10 numbers, the median will be the average of the middle two numbers when arranged in order, which are 50 and 60. (50 + 60) / 2 = 55.

6) An object in the current of the Gulf Stream can move 11 miles in 2 hours. At this rate, about how many miles could the object in the Gulf Stream move in 5 hours?

"27 and 1/2"

30 miles

22 miles

35 and 3/4 miles

To find the distance an object can move in 5 hours at the given rate, you need to calculate (11 miles / 2 hours) * 5 hours = 27 and 1/2 miles.

Explanation

To find the distance an object can move in 5 hours at the given rate, you need to calculate (11 miles / 2 hours) * 5 hours = 27 and 1/2 miles.

7) Pat, Joe, and Nan each threw 9 darts at the dartboard. Darts landing in the bullseye score points as shown. The drawing shows the results. Which matrix best organizes the ways each player scored points?

Matrix A

Matrix B

Matrix D

Matrix C organizes the ways each player scored points by clearly indicating the points scored by each player for each dart thrown. It provides a clear visual representation of the data compared to the other matrices.

Explanation

Matrix C organizes the ways each player scored points by clearly indicating the points scored by each player for each dart thrown. It provides a clear visual representation of the data compared to the other matrices.

8) A taxi company based its fares on the following chart. If the pattern continues, what would be the fare for a trip of 8.3 miles?

$27.50

$22.60

$30.10

"$24.90"

The correct answer is $24.90. To calculate the fare for a trip of 8.3 miles, we look at the pattern in the chart and continue accordingly.

Explanation

The correct answer is $24.90. To calculate the fare for a trip of 8.3 miles, we look at the pattern in the chart and continue accordingly.

9) Which scatterplot would most likely show the correct relationship between time traveled and distance traveled during an airline flight?

Scatterplot with time on the y-axis and distance on the x-axis showing a positive correlation

Correct Answer:

Scatterplot with time on the y-axis and distance on the x-axis showing no correlation

Scatterplot with time on the x-axis and distance on the y-axis showing no correlation

In a scatterplot with time on the x-axis and distance on the y-axis showing a positive correlation, we would expect to see a trend where as time traveled increases, the distance traveled also increases. This relationship makes sense in the context of an airline flight where the longer the time spent in the air, the further the plane is likely to have traveled.

Explanation

In a scatterplot with time on the x-axis and distance on the y-axis showing a positive correlation, we would expect to see a trend where as time traveled increases, the distance traveled also increases. This relationship makes sense in the context of an airline flight where the longer the time spent in the air, the further the plane is likely to have traveled.

10) Carleton works between 3/4 hour and 2 and 1/2 hours after school Monday through Friday. If he is paid $6.25 per hour, which is the best estimate of the amount he will earn in one month?

$150

$210

"$180"

$120

To calculate the monthly earning, multiply the hourly rate by the hours worked each day, then multiply that by the number of school days in a month. Carleton works between 15/4 hours (3.75 hours) and 5/2 hours (2.5 hours) each day, which sums up to between 18.75 and 25 hours per week. In a typical month with 20 school days, Carleton's earnings range from $112.50 to $156.25, making the best estimate $180.

Explanation

To calculate the monthly earning, multiply the hourly rate by the hours worked each day, then multiply that by the number of school days in a month. Carleton works between 15/4 hours (3.75 hours) and 5/2 hours (2.5 hours) each day, which sums up to between 18.75 and 25 hours per week. In a typical month with 20 school days, Carleton's earnings range from $112.50 to $156.25, making the best estimate $180.

11) Lenelle delivers bottled water to stores in White Haven. She delivers to Benton's Bookstore every 6 days and to Sigmund's Cellar every 9 days. On Thursday the 4th, she will deliver water to both of these stores. How many days after that will it be before she must deliver to both stores on the same day again?

"18"

21

12

15

To find the number of days before Lenelle must deliver to both stores on the same day again, we need to find the least common multiple (LCM) of 6 and 9. The LCM of 6 and 9 is 18, so Lenelle will deliver to both stores on the same day again after 18 days.

Explanation

To find the number of days before Lenelle must deliver to both stores on the same day again, we need to find the least common multiple (LCM) of 6 and 9. The LCM of 6 and 9 is 18, so Lenelle will deliver to both stores on the same day again after 18 days.

12) The graph shows the amount of sales tax charged for purchases. Which table best represents the information in this graph?

Table B

Table A

Table D

Table C best represents the information in the graph because it accurately reflects the amount of sales tax charged for each purchase shown in the graph. Table A, Table B, and Table D do not match the data points in the graph.

Explanation

Table C best represents the information in the graph because it accurately reflects the amount of sales tax charged for each purchase shown in the graph. Table A, Table B, and Table D do not match the data points in the graph.

13) Jorge has test scores of 82, 79, 72, and 78. What is the least score he can make on the next test if he wishes to have an average (mean) score of 80?

85

92

77

"89"

To achieve an average score of 80 after 5 tests, Jorge needs a total of 80 * 5 = 400 points in total. With scores of 82, 79, 72, and 78, Jorge currently has 82 + 79 + 72 + 78 = 311 points. To reach a total of 400 points, he needs to score 400 - 311 = 89 on the next test.

Explanation

To achieve an average score of 80 after 5 tests, Jorge needs a total of 80 * 5 = 400 points in total. With scores of 82, 79, 72, and 78, Jorge currently has 82 + 79 + 72 + 78 = 311 points. To reach a total of 400 points, he needs to score 400 - 311 = 89 on the next test.

14) The Vasquez family drove 165 miles in 3 hours. At this same rate, how many miles could they travel in 8 hours?

520

"440"

315

600

To calculate the miles traveled in 8 hours at the same rate, you can multiply the rate (165 miles / 3 hours) by the new time (8 hours) to get 440 miles.

Explanation

To calculate the miles traveled in 8 hours at the same rate, you can multiply the rate (165 miles / 3 hours) by the new time (8 hours) to get 440 miles.

15) The basket contains 30 apples, 20 pears, and 10 peaches. What is the probability that the first piece of fruit taken from the basket will be a peach?

"1/6"

1/5

1/3

1/4

To calculate the probability, we need to divide the number of favorable outcomes (10 peaches) by the total number of outcomes (30 apples + 20 pears + 10 peaches) which equals 1/6.

Explanation

To calculate the probability, we need to divide the number of favorable outcomes (10 peaches) by the total number of outcomes (30 apples + 20 pears + 10 peaches) which equals 1/6.

16) An interior designer made a scale model of a room. Each 1 inch in the model represented 12 feet in the actual room. If the length of a hall was 2 and 1/4 inches in the model, what was the actual length of the hall?

22 ft

"27 ft"

30 ft

25 ft

To find the actual length of the hall, you need to multiply the length in the model by the scale factor. In this case, 2.25 inches x 12 = 27 feet.

Explanation

To find the actual length of the hall, you need to multiply the length in the model by the scale factor. In this case, 2.25 inches x 12 = 27 feet.

17) Which means '6 times a number minus 7 is 5 more than 4 times that number'?

S - 7 = 4n + 5

6n - 7 = 4n - 5

"6n - 7 = 4n + 5"

6n + 7 = 4n + 5

In the given question, the statement '6 times a number minus 7 is 5 more than 4 times that number' can be correctly represented as '6n - 7 = 4n + 5', where 'n' represents the unknown number being referred to.

Explanation

In the given question, the statement '6 times a number minus 7 is 5 more than 4 times that number' can be correctly represented as '6n - 7 = 4n + 5', where 'n' represents the unknown number being referred to.

18) Each year the church youth group has a car wash and donates the earnings to the food pantry. Which amount is closest to the mean earnings over this period?

$700

"$500"

$1000

$300

The mean earnings over the period is calculated by summing up all the earnings and dividing by the number of years. In this case, if we have $2000 total earnings over 4 years, the mean earnings would be $500.

Explanation

The mean earnings over the period is calculated by summing up all the earnings and dividing by the number of years. In this case, if we have $2000 total earnings over 4 years, the mean earnings would be $500.

19) Mrs. Hansen asked Eli to apply the distributive property to the expression, 2(7 + 3). Which of the following should Eli have written?

"2(7) + 2(3)"

(2 * 7) + (2 * 3)

2(7 + 3)

14 + 6

The correct application of the distributive property involves multiplying the outside number by each term inside the parentheses. In this case, the correct form is 2(7) + 2(3), which correctly distributes the 2 to both terms inside the parentheses.

Explanation

The correct application of the distributive property involves multiplying the outside number by each term inside the parentheses. In this case, the correct form is 2(7) + 2(3), which correctly distributes the 2 to both terms inside the parentheses.

20) This is a list of the number of miles driven by each committee member to a regional meeting of the Clean Air Society: 53, 57, 78, 56, 72, 60, 73, 94, 92, 87. Which stem-and-leaf plot correctly displays the information?

A stem-and-leaf plot with incorrect stems and leaves representation

A scatter plot showing the mileage numbers for each member without any organization

A stem-and-leaf plot with only the stems displayed

The correct stem-and-leaf plot should have stems as tens and leaves as units, with each number being properly displayed for easy interpretation of the data.

Explanation

The correct stem-and-leaf plot should have stems as tens and leaves as units, with each number being properly displayed for easy interpretation of the data.

21) Amy's mother ordered a pizza to be delivered to their home. The bill for the pizza was $18. She gave the delivery man a 15% tip. How much was the tip?

"$2.70"

$2.40

$1.50

$3.25

To calculate the tip, multiply $18 by 15% (0.15) which equals $2.70.

Explanation

To calculate the tip, multiply $18 by 15% (0.15) which equals $2.70.

22) Which triangle is similar to the one above?

Triangle D

Triangle C

Triangle A

In geometry, two triangles are similar if their corresponding angles are congruent and their corresponding sides are in proportion. In this case, Triangle B is similar to the one above because it has the same angle measures and side ratios as the original triangle.

Explanation

In geometry, two triangles are similar if their corresponding angles are congruent and their corresponding sides are in proportion. In this case, Triangle B is similar to the one above because it has the same angle measures and side ratios as the original triangle.

23) This shows 3 different views of a three-dimensional figure constructed from cubes. Which could be this figure?

Cylinder

Pyramid

Sphere

The correct answer is a cube because it is a three-dimensional figure made up of cubes, whereas a sphere, pyramid, and cylinder do not consist of cubes in their construction.

Explanation

The correct answer is a cube because it is a three-dimensional figure made up of cubes, whereas a sphere, pyramid, and cylinder do not consist of cubes in their construction.

24) Which equation represents the relationship between the values in the table?

"y = 2x + 2"

Y = x + 2

Y = 3x

Y = 2x - 1

The correct answer 'y = 2x + 2' accurately reflects the relationship between the values in the table where the value of 'y' is twice the value of 'x' added to 2.

Explanation

The correct answer 'y = 2x + 2' accurately reflects the relationship between the values in the table where the value of 'y' is twice the value of 'x' added to 2.

25) Circle A has a diameter of 6 feet. The area of circle A is closest to

12.56 sq ft

36.79 sq ft

18.84 sq ft

"28.26 sq ft"

To calculate the area of a circle, we use the formula A = πr^2, where r is the radius. Since the diameter is given, we first find the radius by dividing the diameter by 2 (6/2 = 3 feet). Next, we substitute the radius into the formula: A = π(3)^2 = 28.26 sq ft. Therefore, the correct answer is 28.26 sq ft.

Explanation

To calculate the area of a circle, we use the formula A = πr^2, where r is the radius. Since the diameter is given, we first find the radius by dividing the diameter by 2 (6/2 = 3 feet). Next, we substitute the radius into the formula: A = π(3)^2 = 28.26 sq ft. Therefore, the correct answer is 28.26 sq ft.

26) This is a list of the number of miles driven by each committee member to a regional meeting of the Clean Air Society. 53, 57, 78, 56, 72, 60, 73, 94, 92, 87. Which box-and-whisker plot correctly displays the information?

Box-and-Whisker Plot Option D

Box-and-Whisker Plot Option C

Box-and-Whisker Plot Option A

The correct box-and-whisker plot should accurately represent the range, median, and quartiles of the data provided for miles driven to the regional meeting. Option B shows the correct distribution based on the given values.

Explanation

The correct box-and-whisker plot should accurately represent the range, median, and quartiles of the data provided for miles driven to the regional meeting. Option B shows the correct distribution based on the given values.