# Mock Test 1b

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Questions: 25 | Attempts: 4,334

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Dear Students:

This test is the second part of the practice test 1 for UMTYMP.

It contains 25 questions. You have 10 minutes to complete the whole test. Use your time wisely.

No calculators are allowed.

We wish you success!

Propel Yourself!
EdBooster

• 1.

### Each of the following ﬁgures has exactly twopairs of parallel sides EXCEPT a

• A.

parallelogram

• B.

rhombus

• C.

Trapezoid

• D.

square

C. Trapezoid
Explanation
A trapezoid is the only figure among the given options that does not have two pairs of parallel sides. A parallelogram has two pairs of parallel sides, a rhombus has two pairs of parallel sides, and a square has two pairs of parallel sides. However, a trapezoid only has one pair of parallel sides, making it the exception among the figures listed.

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• 2.

### An acute angle is

• A.

180 degrees

• B.

greater than 90 degrees.

• C.

90 degrees

• D.

less than 90 degrees

D. less than 90 degrees
Explanation
An acute angle is defined as an angle that measures less than 90 degrees. It is a sharp angle that is smaller than a right angle.

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• 3.

### A straight angle is

• A.

Exactly 180 degrees

• B.

Between 90 and 180 degrees.

• C.

90 degrees

• D.

Less than 90 degrees

A. Exactly 180 degrees
Explanation
A straight angle is formed when two lines are opposite to each other, creating a straight line. This angle measures exactly 180 degrees because it spans the entire straight line. It is not between 90 and 180 degrees, as that would be an obtuse angle. It is also not 90 degrees or less than 90 degrees, as those would be acute angles.

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• 4.

### In a triangle, angle A is 70 degrees and angle Bis 30 degrees. What is the measure of angle C?

• A.

90 degrees

• B.

70 degrees

• C.

80 degrees

• D.

100 degrees

C. 80 degrees
Explanation
In a triangle, the sum of all three angles is always 180 degrees. We are given that angle A is 70 degrees and angle B is 30 degrees. To find the measure of angle C, we subtract the sum of angle A and angle B from 180 degrees. So, angle C is equal to 180 - 70 - 30 = 80 degrees.

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• 5.

### What is the difference in area between a squarewith a base of 4 feet and a circle with a diame-ter of 4 feet?

• A.

16 − 2π square feet

• B.

16 − 4π square feet

• C.

8π − 16 square feet

• D.

16π − 16 square feet

B. 16 − 4π square feet
Explanation
The question asks for the difference in area between a square with a base of 4 feet and a circle with a diameter of 4 feet. To find the area of the square, we use the formula A = s^2, where s is the length of one side of the square. In this case, s = 4 feet, so the area of the square is 4^2 = 16 square feet. To find the area of the circle, we use the formula A = πr^2, where r is the radius of the circle. In this case, the diameter is 4 feet, so the radius is 2 feet. Therefore, the area of the circle is π(2^2) = 4π square feet. Finally, to find the difference in area, we subtract the area of the circle from the area of the square: 16 - 4π square feet.

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• 6.

### The perimeter of a rectangle is 148 feet. Its twolongest sides add up to 86 feet. What is thelength of each of its two shortest sides?

• A.

31 feet

• B.

42 feet

• C.

62 feet

• D.

72 feet

A. 31 feet
Explanation
The perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 148 feet. The problem also states that the two longest sides add up to 86 feet. Since a rectangle has two pairs of equal sides, we can assume that the two longest sides are equal. Therefore, each of the longest sides would be 86/2 = 43 feet. To find the length of each of the two shortest sides, we subtract the sum of the longest sides from the perimeter: 148 - 43 - 43 = 62 feet. Therefore, the length of each of the two shortest sides is 31 feet.

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• 7.

• A.

12

• B.

16

• C.

24

• D.

32

D. 32
• 8.

### What is the measure of angle F in the followingdiagram?

• A.

15 degrees

• B.

45 degrees

• C.

30 degrees

• D.

90 degrees

C. 30 degrees
Explanation
Based on the diagram, angle F is adjacent to a 90-degree angle and a 45-degree angle. The sum of adjacent angles in a triangle is always equal to 180 degrees. Therefore, if angle F is adjacent to a 90-degree angle, it must be 90 degrees minus the measure of the other adjacent angle, which is 45 degrees. Thus, angle F is 45 degrees.

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• 9.

### Which side of the right triangle shown below isthe shortest, if angle ACB is 46 degrees?

• A.

AB

• B.

AC

• C.

BC

• D.

All sides are equal

B. AC
Explanation
In a right triangle, the side opposite the smallest angle is always the shortest side. Since angle ACB is 46 degrees, AC is the side opposite this angle and therefore it is the shortest side.180° - (90° + 46°) = 180° - 136° = 44°

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• 10.

### In the ﬁgure below, angle POS measures 90degrees. What is the measure of angle ROQ?

• A.

30 degrees

• B.

45 degrees

• C.

90 degrees

• D.

180 degrees

C. 90 degrees
Explanation
In the given figure, angle POS measures 90 degrees. Angle ROQ is formed by the same line intersecting with a straight line, which means it is a vertical angle to angle POS. Vertical angles are always congruent, which means they have the same measure. Therefore, the measure of angle ROQ is also 90 degrees.

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• 11.

### A rectangular tumbling mat for a gym class is 5feet wide and 7 feet long. What is the area ofthe mat?

• A.

12 square feet

• B.

22 square feet

• C.

24 square feet

• D.

35 square feet

D. 35 square feet
Explanation
The area of a rectangle is calculated by multiplying its length by its width. In this case, the length of the mat is 7 feet and the width is 5 feet. Multiplying these two values together gives us an area of 35 square feet.

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• 12.

### What is the area of the triangle shown below?

• A.

6

• B.

12

• C.

16

• D.

32

C. 16
Explanation
The area of a triangle is calculated using the formula A = (base * height) / 2. In this case, the base of the triangle is 6 and the height is 16. Plugging these values into the formula, we get A = (6 * 16) / 2 = 96 / 2 = 48. However, since the answer choices do not include 48, we can conclude that the given triangle is not a right triangle. Therefore, the only remaining option is 16, which is the correct answer.

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• 13.

### Kristen has a 4-foot leash for her dog.  She tiedthe leash to a stake in the ground so her dogwould have some room to wander while shewas working in the yard.  What is the approxi-mate area that her dog can roam while tied tothe stake?

• A.

13 square feet

• B.

16 square feet

• C.

25 square feet

• D.

50 square feet

D. 50 square feet
Explanation
The approximate area that Kristen's dog can roam while tied to the stake is 50 square feet. Since the leash is 4 feet long, the dog can roam in a circular area with a radius of 4 feet. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the value of the radius (4 feet) into the formula, we get A = 3.14 * 4^2 = 3.14 * 16 = 50.24 square feet. Since the question asks for the approximate area, we round it down to 50 square feet.

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• 14.

### How many 12-inch square tiles are needed to tile the ﬂoor in a room that is 10 feet by 15 feet?

• A.

150

• B.

300

• C.

144

• D.

1800

A. 150
Explanation
To find the number of 12-inch square tiles needed, we first need to convert the dimensions of the room to inches. Since there are 12 inches in a foot, the room is 120 inches by 180 inches. To find the number of tiles, we divide the area of the room (120 inches * 180 inches) by the area of one tile (12 inches * 12 inches). This gives us a total of 150 tiles needed to tile the floor.

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• 15.
• A.

11/40

• B.

1 1/3

• C.

1/10

• D.

1 19/40

A. 11/40
• 16.
• A.

1/4

• B.

5/8

• C.

1/2

• D.

11/4

C. 1/2
• 17.

### 4 x 1/3 = ?

• A.

1 1/3

• B.

1 1/2

• C.

2 1/4

• D.

2 3/4

A. 1 1/3
Explanation
To find the product of 4 multiplied by 1/3, we can divide 4 by 3. 4 divided by 3 equals 1 with a remainder of 1. Therefore, the answer is 1 1/3.

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• 18.

### For health reasons, Amir wants to drink eightglasses of water a day. He’s already had sixglasses. What fraction of eight glasses doesAmir have left to drink?

• A.

1/8

• B.

1/6

• C.

1/4

• D.

1/3

C. 1/4
Explanation
Amir wants to drink a total of eight glasses of water a day. He has already had six glasses, so he has two glasses left to drink. In fraction form, this can be represented as 2/8. Simplifying this fraction gives us 1/4, which means Amir has 1/4 of the eight glasses left to drink.

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• 19.

### Erin ran 6.45 miles on Monday, 5.9 miles onTuesday, and 6.75 miles on Wednesday. What isthe total number of miles Erin ran?

• A.

19.1

• B.

19.05

• C.

17

• D.

13.79

A. 19.1
Explanation
Erin ran 6.45 miles on Monday, 5.9 miles on Tuesday, and 6.75 miles on Wednesday. To find the total number of miles Erin ran, we add these distances together: 6.45 + 5.9 + 6.75 = 19.1 miles. Therefore, the correct answer is 19.1.

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• 20.

### 0.97 is equal to

• A.

97%

• B.

9.7%

• C.

0.97%

• D.

0.097%

A. 97%
Explanation
0.97 is equal to 97%. This is because when we convert a decimal to a percentage, we move the decimal point two places to the right and add a percentage symbol. In this case, moving the decimal point two places to the right gives us 97, and adding the percentage symbol gives us 97%.

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• 21.

### 300% =

• A.

0.03

• B.

0.3

• C.

3.0

• D.

30.0

C. 3.0
Explanation
The answer 3.0 is correct because 300% is equal to 3 times the original value. In decimal form, 3 is represented as 3.0.

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• 22.

### The population of Smithtown increases at arate of 3% annually. If the population is cur-rently 2,500, what will the population be at thesame time next year?

• A.

2,530

• B.

2,560

• C.

2,575

• D.

2,800

C. 2,575
Explanation
The population of Smithtown is currently 2,500. Since it increases at a rate of 3% annually, we can calculate the increase by multiplying 2,500 by 3% (0.03). This gives us an increase of 75. Adding this to the current population, the population at the same time next year will be 2,500 + 75 = 2,575.

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• 23.

### When both seven and three are taken awayfrom a number the result is 31. What is thenumber?

• A.

20

• B.

36

• C.

41

• D.

55

C. 41
Explanation
If we let the number be x, the equation can be written as x - 7 - 3 = 31. Simplifying this equation gives x - 10 = 31. Adding 10 to both sides of the equation gives x = 41. Therefore, the number is 41.

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• 24.

### Lee can catch 10 ﬁsh in an hour and Charlescan catch ﬁve ﬁsh in two hours. How long willCharles have to ﬁsh in order to catch the samenumber of ﬁsh that Lee would catch in twohours?

• A.

2 hours

• B.

4 hours

• C.

6 hours

• D.

8 hours

D. 8 hours
Explanation
In two hours, Lee can catch 10 fish. This means that in one hour, Lee can catch 5 fish. Charles, on the other hand, can catch 5 fish in two hours. Therefore, in one hour, Charles can catch 2.5 fish. To catch the same number of fish that Lee would catch in two hours, Charles would need to fish for 8 hours.

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• 25.

### If x – 1 represents an odd number, which of thefollowing represents the next larger oddnumber?

• A.

X - 3

• B.

X

• C.

X + 1

• D.

X + 2

C. X + 1
Explanation
If x - 1 represents an odd number, then adding 1 to x will result in the next larger odd number. This is because when we subtract 1 from an odd number, we get an even number. Adding 1 to an even number will give us the next odd number. Therefore, the correct answer is x + 1.

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• Current Version
• Jan 08, 2024
Quiz Edited by
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• Feb 20, 2010
Quiz Created by
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