Question 1

Mary has 2 quarts of ice cream. She shares a half of a quart with her friend, Bill. How many pints does she have left?
A)1
B)2
C)3
D)4

Accepted Answer

Mary has 3 pints left. There are 2 pints in a quart. If Mary has 2 quarts of ice cream, she has 4 pints. If she gives half of a quart away, she is giving away 1 pint. The result is 3 pints.

Question 2

Is 40Ã·5>, =, or < 49Ã·7? A)> B)= C)< D)None of the above

Accepted Answer

40Ã·5 > 49Ã·7. In other words, 8 > 7.

Question 3

A point is reflected first over the line y = x, then over the x-axis, then over the y-axis. The resulting point has the coordinates (73, 14). The coordinates of the original point were which of the following?
A)(-14, -73)
B)(-73, 14)
C)(73, -14)
D)(73, 14)

Accepted Answer

The coordinates of the original point were (-14, -73).
Solution
Assume the original point is (a, b).
1. When the point is reflected over line y = x, the point coordinates become (b, a).
2. When reflected over the x-axis, the coordinates then become (b, -a).
3. When reflected over the y-axis, the coordinates then become (-b, -a)
If the final point is (73, 14), the original point was (-14, -73)

Question 4

A: {3, 6, 7}
B: {2, 8}
What is the union of Set A and Set B?
A){2, 3, 6, 7, 8}
B){3, 6, 7}
C){2, 8}
D)None of the above

Accepted Answer

The union of Set A and Set B is {2, 3, 6, 7, 8}. This is a combination of both sets.

Question 5

What kind of triangle has 1 angle that is 90Â°?
A)A right triangle
B)An acute triangle
C)An obtuse triangle
D)A scalene triangle

Accepted Answer

A triangle that has 1 angle that is 90Â° is a right triangle. A right triangle has 1 right angle.

Question 6

A radius of a circle is 3 cm. What is its area? A)3)14 cm² B)28.26 cm² C)282.6 cm² D)2)826 cm²

Accepted Answer

A circle with a radius of 3 cm has an area of 28.26 cm². The formula for the area of a circle is 3.14 (?) multiplied by the radius squared. 3Â² = 9, so 3.14 x 9 is 28.26 cm².

Question 7

Which of the following uses the doubling method of informal counting to solve the following:
3 + 4 =
A)(1 + 1 + 1) + (1 + 1 + 1 + 1) = 7
B)(3 + 4) + (3 + 4) - (3 + 4) = 7
C)3 + 4 = (3 + 3) +1 = 6 + 1 = 7
D)2 + 2 + 2 + 1 = 7

Accepted Answer

The doubling method would be 3 + 4 = (3 + 3) +1 = 6 + 1 = 7. Using the doubling method of informal counting involves taking apart a number so that it is the same number as the one being added to it and then adding the difference. It is a way to do mental math easily in one's head.

Question 8

Which of the following is a prime number?
A)50
B)25
C)23
D)6

Accepted Answer

23 is a prime number. A prime number is a number that can only be divided by itself and by the number 1, without a remainder. 50, 25, and 6 can all be divided by numbers other than itself and 1. Even numbers greater than 2 are never prime.

Question 9

Round 567.342 to the nearest hundredth. What is the answer?
A)600
B)560
C)567.34
D)567.3

Accepted Answer

567.342 rounded to the nearest hundredth is 567.34. The 4 is in the hundredths place. Since it is followed by the number 2, which is less than 5, you would round down and keep the 4.

Question 10

If y = 2x + 1, what is the arithmetic mean of 2x, 2x, y, and 3y, in terms of x?
A)2x
B)2x + 1
C)3 x + 1
D)None of the above

Accepted Answer

the arithmetic mean of 2x, 2x, y, and 3y, where y = 2x +1 is 3x + 1.
Solution
The arithmetic mean (average) is equal to the sum of the items divided by the number of items.
Average = (2x + 2x + y + 3y)/4 = (4x + 4y)/4 = x + y
Substituting 2x +1 for y: x + (2x + 1) = 3x + 1
Check (assume x = 3): (6 + 6 + 7 + 3(7))/4= 10 = 3(3)+1

Question 11

If x, y, and z are integers with x?y and y>z, which of the following could x, y, and z represent (respectively)?
A)-3, -2, -3
B)3, 2, 3
C)1, 2, 3
D)3, 2, 1

Accepted Answer

Â­x=Â­3, y=Â­Â­Â­Â­Â­2, z=Â-3.-3 is less than or equal to Â­2, andÂ­Â­2 is greater than Â-3.

Question 12

Olivia is writing a recipe for orange-colored fruit salad. She uses 4 apricots for every cantaloupe, 2 peaches for every apricot, and one orange for every cantaloupe. If she uses 8 oranges, how many whole pieces of fruit total will be used for the fruit salad?
A)212
B)232
C)112
D)132

Accepted Answer

There will be 112 whole pieces of fruit total used for the fruit salad. There will be 8 oranges, 8 cantaloupes, 32 apricots, and 64 peaches.

Question 13

According to the US Standard system, which of the following would be used to measure the volume of water in a bath tub?
A)Gallons
B)Liters
C)Cups
D)Meters

Accepted Answer

According to the US Standard system, gallons would be used to measure the volume of water in a bath tub. Other countries do not use gallons as a way of measurement. A US Standard liquid gallon is approximately 4.5 liters.

Question 14

Identify the pattern in the following set of numbers:
2, 5, 8, 11, 14, 17
A)There is no pattern.
B)The set starts with 2 and ends in 17.
C)The set starts with 2 and jumps 3 each time.
D)The set starts with 2 and jumps 2 each time.

Accepted Answer

The pattern is that the set starts with 2 and jumps 3 each time.

Question 15

Solve: 5Â²
A)625
B)10
C)25
D)125

Accepted Answer

5 squared is 25. 5 multiplied by itself is 25.

Question 16

Which property is the following equation an example of?
9 x 1/9 = 9
A)The distributive property
B)The multiplicative inverse property
C)Associative property
D)Additive inverse property

Accepted Answer

9 x 1/9 = 9 is an example of the multiplicative inverse property. The multiplicative inverse property involves multiplying a number by its reciprocal, or putting it into a fraction with 1 as the numerator. When you multiply it by its reciprocal, you get the original number.

Question 17

What is 1 Â½ as a simple fraction in lowest terms?
A)1/2
B)2/3
C)3/2
D)1)5

Accepted Answer

1 Â½ as a simple fraction in lowest terms is 3/2. 1 Â½ is a mixed fraction. To simplify it, you multiply the denominator (2) by the whole number (1) and then add the product (2) to the numerator (1): 2 x 1 = 2, then 2 + 1 = 3. Put your answer over the denominator (2). The answer is 3/2.

Question 18

Tim ate 8/10 of a pizza. State the fraction for the amount of pizza that was left over in its simplest form.
A)2/10
B)4/5
C)1/8
D)1/5

Accepted Answer

Tim had 1/5 of the pizza left, as stated in simplest form. Since Tim ate 8/10 of the pizza, he had 2/10 remaining. 2/10 in its simplest form is 1/5.

Question 19

Fill in the blank: The right-hand column shown in the table below lists _______ for the indefinite integral F(x).
F'(x) = f (x) F(x) = f(x)dx
1/x Log | x |
Sin x -cos x
Cos x Sin x
A)Derivatives
B)Elementary functions
C)Elementary integrals
D)None of the above

Accepted Answer

The right-hand column shown in the give table lists the elementary functions for the indefinite integral F(x). The corresponding derivatives are shown in the left-hand column of the table. Tables of standard integrals can be developed for easy reference when evaluating other integrals.

Question 20

What percentage is Â¼?
A)20%
B)25%
C)50%
D)4%

Accepted Answer

Â¼ = 25%. You can divide the numerator by the denominator to get the percentage. 1 Ã· 4 = .25 which is equal to 25%.

Quiz 8: Comprehensive Examination: Mathematics

Mary has 2 quarts of ice cream. She shares a half of a quart with her friend, Bill. How many pints does she have left?

Is 40Ã·5>, =, or < 49Ã·7?

A point is reflected first over the line y = x, then over the x-axis, then over the y-axis. The resulting point has the coordinates (73, 14) . The coordinates of the original point were which of the following?

A: {3, 6, 7} B: {2, 8} What is the union of Set A and Set B?

What kind of triangle has 1 angle that is 90Â°?

A radius of a circle is 3 cm. What is its area?

Which of the following uses the doubling method of informal counting to solve the following: 3 + 4 =

Which of the following is a prime number?

Round 567.342 to the nearest hundredth. What is the answer?

If y = 2x + 1, what is the arithmetic mean of 2x, 2x, y, and 3y, in terms of x?

If x, y, and z are integers with x?y and y>z, which of the following could x, y, and z represent (respectively) ?

Olivia is writing a recipe for orange-colored fruit salad. She uses 4 apricots for every cantaloupe, 2 peaches for every apricot, and one orange for every cantaloupe. If she uses 8 oranges, how many whole pieces of fruit total will be used for the fruit salad?

According to the US Standard system, which of the following would be used to measure the volume of water in a bath tub?

Identify the pattern in the following set of numbers: 2, 5, 8, 11, 14, 17

Solve: 5Â²

Which property is the following equation an example of? 9 x 1/9 = 9

What is 1 Â½ as a simple fraction in lowest terms?

Tim ate 8/10 of a pizza. State the fraction for the amount of pizza that was left over in its simplest form.

Fill in the blank: The right-hand column shown in the table below lists _______ for the indefinite integral F(x) . F'(x) = f (x) F(x) = f(x) dx 1/x Log | x | Sin x -cos x Cos x Sin x

What percentage is Â¼?