# FREE NAEP Mathematics Grade 8 Questions and Answers

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#### The points with the coordinates (2, 1) and are the endpoints of a line segment (8, 9). What are the coordinates of this line segment's midpoint?

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According to the midpoint formula, the midpoint coordinates (x, y) are averages of the corresponding endpoint coordinates.
The midpoint's x-coordinate is: x = (x1 + x2) / 2 x = (2 + 8) / 2 x = 10 / 2 x = 5
The midpoint's y-coordinate is: y = (y1 + y2) / 2 y = (1 + 9) / 2 y = 10 / 2 y = 5
The midpoint of this line segment is located at these coordinates (5, 5).

#### Take the temperature in degrees Fahrenheit, subtract 32 from it, and multiply the result by to get the temperature in degrees Celsius. How many degrees Celsius, to the nearest degree, does a furnace have to be at to reach 393 degrees Fahrenheit?

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Use these steps to calculate the temperature in degrees Celsius at 393 degrees Fahrenheit in the furnace:
First: deduct 32 from 393 so that 393 - 32 = 361
Second: Multiply 361 * 5/9 to get 200.5556.
The temperature is approximately 201 degrees Celsius, rounded to the nearest degree.
The furnace's temperature is 393 degrees Fahrenheit, but it is 201 degrees Celsius (to the nearest degree).

#### Cheng is preparing treat bags for her sister's birthday celebration. She distributes 65 candies evenly among 15 bags, ensuring that each bag contains as many candies as possible. How many pieces does she still have?

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By dividing the total number of candy pieces by the number of bags, we can determine how many pieces remain (15). The remainder of 65 divided by 15 is 5. Since she wishes to distribute the candies evenly, she places four candies in each bag, leaving her with five remaining candies that cannot be distributed evenly. Consequently, after filling the 15 bags, she will have five candies remaining.

#### Which of the following comes closest to a 15 percent tip on a \$24.99 restaurant bill?

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We can use the following method to determine the roughly 15% tip on a \$24.99 restaurant bill. By moving the decimal point one place to the left, start by calculating the first ten percent of the check. 10% of \$24.99 would equal \$2.499. Next, divide \$2.499 by 2, which equals \$1.2495, to determine 5 percent, which is equal to half of 10 percent. Last but not least, multiply 10% and 5% to get the 15% gratuity: \$2.499 + \$1.2495 = \$3.7485. The closest approximation of a 15% tip on a \$24.99 check, rounded to the nearest cent, is \$3.75.

#### A specific kind of measuring tool can measure length with an accuracy of 0.05 centimeters. When this instrument reads 3.7 centimeters, it means that the length is at least that much longer?

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This is due to the instrument's limitation of measuring lengths to the nearest 0.05 centimeters. This means that if the device indicates a length of 3.7 centimeters, the actual length may be 3.65 centimeters or 3.75 centimeters. We know that the actual length must be at least 3.65 centimeters because the instrument cannot be any more accurate than this. The instrument would not have read 3.7 centimeters if the actual length was less than 3.65 centimeters. We can infer that the actual length is 3.65 centimeters at least.

#### Which of the following always represents an odd integer?

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Any whole number that cannot be divided evenly by 2, leaving a remainder of 1, is considered an odd integer. Two odd integers can be multiplied together by writing them as (2k+1) and (2m+1), where k and m can be any two integers. When we combine these two odd numbers:
(4km + 2k + 2m + 1) = (2k+1) * (2m+1)
Because it can be written as another integer multiplied by 2, the expression 4km + 2k + 2m is an even number. Though this even number becomes an odd integer when we add 1 to it.

#### The perimeter of a rectangular playground is 390 feet. The playground has a width of 75 feet. How long does it last?

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We apply the equation for a rectangle's perimeter, which is equal to twice the sum of its length and width. The result of entering the given values into the formula is 390 = 2 * (Length + 75). We can calculate the playground's length and discover that it is 120 feet long. The playground has a 120 foot length and a 75 foot width.

#### A company had 90 employees the previous year. The number of employees increased this year by 10%. This year, how many people work for the company?

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Determine the additional number of employees: 10% of the 90 employees.
10% more than 90 equals 0.10 * 90, or 9 employees.
To calculate the total for this year, multiply the increase by the number of employees from last year:
Total employees equals 90 (from last year) plus 9 (an increase) for a total of 99 workers. This year, the company has 99 employees.

#### The rate of ascent for an airplane is 66.8 feet per minute. It descends twice as quickly as it ascends. How many feet will the airplane descend in 30 minutes, presuming a constant rate of descent?

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The aircraft is climbing at a rate of 66.8 feet per minute.
The rate of descent is double that of ascent.
Rate of descent = 2 x Rate of climb
a rate of descent equal to 2 * 66.8 = 133.6 feet per minute
We can determine the total distance of descent in 30 minutes by:
Total descent distance = Rate of descent * Time
Total descent distance = 133.6 feet per minute multiplied by 30 minutes = 4,008 feet; the aircraft will descend 4,008 feet in 30 minutes

#### How does increasing the value of x by 2 in the equation y = 4 x affect the value of y?

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Evaluate the initial value of x as ""x"", and the enhanced value of x as ""x + 2"".
Original equation: y = 4x
compare the two equations after doubling x: y = 4(x + 2) and y = 4(x - 2)
Original equation: y = 4x
After doubling the value of x: y = 4(x + 2)
To determine the impact on y, we can simplify the second equation:
y = 4(x + 2)
y = 4x + 8
Comparing the two equations, we can see that the value of y in the second equation (after increasing x by 2) is 8 more than the original value of y.
This is the impact on y's value: 8 more than the initial amount.

#### A restaurant served dinner to Ms. Helen and her three friends. \$67 was the total. Moreover, they left a \$13 tip. They left a tip that was roughly what % of the total bill.

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We can divide the tip amount by the bill amount, then multiply the result by 100% to get the tip percentage. As a result, we have:
\$13 tip / \$67 bill * 100% = 19.40%
Even though the actual tip percentage is a little bit higher than 19%, it is close enough to 20% to be considered a 20% tip.

#### How many 200-milliliter portions of juice can be poured from a 2-liter pitcher?

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"Simply divide the serving size by the juice's total volume (2 liters) (200 milliliters). Juice that is 2 liters in volume is equivalent to 2 * 1000, or 2000 milliliters, since 1 liter is equal to 1000 milliliters.
2000 milliliters is split by 200 milliliters as follows:
200 milliliters of 2000 milliliters each equals ten.
A pitcher with 2 liters of juice in it can be used to pour 10 servings of 200 milliliters each."

#### The characteristics of a particular 4-sided figure are as follows. There is only one set of opposite sides that are parallel and one set of opposite sides that are the same length. The lengths of the parallel sides are not equal. Which of the following statements about the sides with equal lengths must be accurate?

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Parallelism is not possible between sides that are of equal length. This is due to the fact that the figure only has one pair of opposite sides that are parallel; however, if the sides of equal length were also parallel, there would be more than one pair of parallel sides, which would be in opposition to the stated properties. In light of this, it is true to say that They are not parallel.

#### Mario's math book weighs 5 pounds, her science book weighs 6, her history book weighs 4, and her English book weighs 3. How many various arrangements of one or more books can Li cram into her bag without the books' combined weight exceeding 12 pounds?

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Mario can arrange her books into 4 + 6 + 4 + 1 = 11 different configurations.

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#### 1 + 3=41 + 3 + 5 = 91+3 + 5 + 7 = 161 + 3 + 5+7 + 9 = 25 . How many consecutive odd integers must add up to 144 in order for the sum to be 144, as suggested by the pattern in the four examples above?

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Perfect squares (2, 2, 3, 4, and 5) make up each line's sum. We must determine how many consecutive odd integers are needed to produce the number 144, which is 122. The solution consists of 12 successive odd integers.