State Testing Practice - Part B (Grade 6)

How did Marissa collect the data she used to make the dot plot?

• by researching

• by measuring

• by surveying

• by counting

Answer explanation

Marissa collected the data for the dot plot by counting the occurrences of each item. This method allows for a clear representation of data frequency, which is essential for creating an accurate dot plot.

Which expression represents the situation “add seven to the product of a number and ten”?

• 10(z + 7)

• 7 + z + 10

• 10z + 7

• 7z + 10z

Answer explanation

The expression "add seven to the product of a number and ten" translates to 10z (the product of a number z and 10) plus 7, which is correctly represented by 10z + 7.

An online retailer charges $30 for 12 cans of tennis balls. Which statements are correct? Mark all that apply.

• The cost of 180 cans of tennis balls is $500.

• The cost of 150 cans of tennis balls is $350.

• The cost of 100 cans of tennis balls is $250.

• The cost of 250 cans of tennis balls is $625.

• The cost of 120 cans of tennis balls is $300.

Answer explanation

The cost per can is $2.50. Thus, 180 cans cost $450, not $500; 150 cans cost $375, not $350; 100 cans cost $250; 250 cans cost $625; and 120 cans cost $300. The correct statements are about 180, 250, and 120 cans.

Rachel earns a constant hourly rate for working part time at a clothing store. The graph below shows her earnings. (Refer to the graph titled 'RACHEL'S EARNINGS') Which equation represents the relationship between the number of hours Rachel worked, x, and her earnings, y?

• y = 10x

• y = 30x

• x = 10y

• x = 30y

Answer explanation

The graph indicates a linear relationship between hours worked and earnings. Since the correct answer is y = 10x, it shows Rachel earns $10 for each hour worked, confirming her constant hourly rate.

A contractor digs a rectangular hole that is 10 1/2 feet deep. He removes 6,510 cubic feet of dirt. What is the width of the hole if the length is 40 feet?

• A. 15 1/2 feet

• B. 162 3/4 feet

• C. 420 feet

• D. 620 feet

Answer explanation

To find the width, use the formula for volume: Volume = Length × Width × Depth. Here, 6,510 = 40 × Width × 10.5. Solving for Width gives Width = 15.5 feet, which matches choice A.

A contractor digs a rectangular hole that is 10 1/2 feet deep. He removes 6,510 cubic feet of dirt. The contractor will use the dirt removed from the hole to fill boxed garden beds in the city. Each garden bed is 15 feet long, 4 2/3 feet wide, and 3 feet deep. How many garden beds can be filled with the removed dirt?

• 3

• 31

• 110

• 144

Answer explanation

The volume of one garden bed is 15 * (4 2/3) * 3 = 220 cubic feet. With 6,510 cubic feet of dirt, 6,510 / 220 = 29.5, which rounds down to 31 garden beds that can be filled.

There are 26 students in William’s math class. The mean height of the students is 160 cm, and the median height is 156 cm. The interquartile range of the heights is 18 cm, and the mean absolute deviation of the heights is 4.6 cm. Part A Fill in the blanks to complete the statement. Mean and median are measures of ________________, while interquartile range and mean absolute deviation are measures of _________________.

Answer explanation

Mean and median are measures of center, as they indicate the central tendency of the data. Interquartile range and mean absolute deviation are measures of variability, as they describe the spread or dispersion of the heights.

There are 26 students in William’s math class. The mean height of the students is 160 cm, and the median height is 156 cm. The interquartile range of the heights is 18 cm, and the mean absolute deviation of the heights is 4.6 cm. Part B Fill in the blanks to complete the statement. Of the 26 students in William’s math class, ______ students have a height less than or equal to 156 cm, and ______ students have a height greater than or equal to 156 cm.

Answer explanation

The median height of 156 cm indicates that half the students are below and half are above this height. Since there are 26 students, 0 students have a height less than or equal to 156 cm, and 26 students have a height greater than or equal to 156 cm.

Cecil says that there are as many students with heights greater than or equal to the mean as those with heights less than or equal to the mean. Is Cecil correct? Explain your reasoning.

Evaluate responses using AI:

OFF

Answer explanation

Cecil is incorrect. The mean divides the data into two halves, but the number of students can vary. There can be more students above or below the mean, especially if the distribution is skewed.

What does the mean absolute deviation tell you about the data set? Give an example of one thing you can tell about the height data based on the mean absolute deviation.

Evaluate responses using AI:

OFF

Answer explanation

The mean absolute deviation (MAD) measures the average distance of each data point from the mean, indicating data variability. For height data, a low MAD suggests that most heights are close to the average, while a high MAD indicates more variation.