Question 1

Suppose 4 r = 3 s = 10 t, where r, s, and t are positive integers. What is the sum of the least values of r, s, and t for which this equality is true?

Accepted Answer

A) 7 
B) 17 
C) 41 
D) 82 
E) 120 
A) 7 
B) 17 
C) 41 
D) 82 
E) 120

Question 2

In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?

Accepted Answer

A) (1, 2) and (2, 1) 
B) (2, 1) and (2, -1) 
C) (3, 4) and (3, -4) 
D) (3, 4) and (-3, 4) 
E) (5, 0) and (-5, 0) 
A) (1, 2) and (2, 1) 
B) (2, 1) and (2, -1) 
C) (3, 4) and (3, -4) 
D) (3, 4) and (-3, 4) 
E) (5, 0) and (-5, 0)

Question 3

Which of the following is NOT a property of every rectangle?

Accepted Answer

A) The opposite sides are equal in length. 
B) The opposite sides are parallel. 
C) All angles are equal in measure. 
D) All sides are equal in length. 
E) The diagonals are equal in length. 
A) The opposite sides are equal in length. 
B) The opposite sides are parallel. 
C) All angles are equal in measure. 
D) All sides are equal in length. 
E) The diagonals are equal in length.

Question 4

The population of the United States is approximately 250 million, and the national debt is approximately 4 trillion dollars. If this debt were divided equally among the population, what would be the debt, in dollars, per person?

Accepted Answer

A) 16 
B) 1,600 
C) 16,000 
D) 1,600,000 
E) 16,000,000 
A) 16 
B) 1,600 
C) 16,000 
D) 1,600,000 
E) 16,000,000

Question 5

If k can be replaced by any number, how many different values can the expression k + 6 have?

Accepted Answer

A) None 
B) One 
C) Six 
D) Seven 
E) Infinitely many 
A) None 
B) One 
C) Six 
D) Seven 
E) Infinitely many

Question 6

Carlos' basketball team won 75% of its games last season. If they played 80 games, how many games did they win?

Accepted Answer

A) 20 
B) 60 
C) 68 
D) 75 
A) 20 
B) 60 
C) 68 
D) 75

Question 7

What is the least whole number x for which 2 x > 11 ?

Accepted Answer

A) 5 
B) 6 
C) 9 
D) 22 
E) 23 
A) 5 
B) 6 
C) 9 
D) 22 
E) 23

Question 8

A cat lies crouched on level ground 50 feet away from the base of a tree. The cat can see a bird's nest directly above the base of the tree. The angle of elevation from the cat to the bird's nest is 40°. To the nearest foot, how far above the base of the tree is the bird's nest?

Accepted Answer

A) 32 
B) 38 
C) 42 
D) 60 
E) 65 
A) 32 
B) 38 
C) 42 
D) 60 
E) 65

Question 9

Which of the following pairs of geometric figures must be similar to each other?

Accepted Answer

A) Two equilateral triangles 
B) Two isosceles triangles 
C) Two right triangles 
D) Two rectangles 
E) Two parallelograms 
A) Two equilateral triangles 
B) Two isosceles triangles 
C) Two right triangles 
D) Two rectangles 
E) Two parallelograms

Question 10

The first term in a sequence of numbers is 1/2. Each term after the first term is 1 more than twice its previous term. What is the 4th term?

Accepted Answer

A) 2 
B) 4 
C) 5 
D) 11 
E) 23 
A) 2 
B) 4 
C) 5 
D) 11 
E) 23

Question 11

If a 2 by 18 rectangle has the same area as a square, what is the length of a side of the square?

Accepted Answer

A) 4 
B) 6 
C) 8 
D) 10 
E) 12 
A) 4 
B) 6 
C) 8 
D) 10 
E) 12

Question 12

If a triangle is equilateral, which of the following must be true?

Accepted Answer

A) Only two sides are equal. 
B) All sides are equal. 
C) All angles are right angles. 
D) All angles have different degree measures. 
A) Only two sides are equal. 
B) All sides are equal. 
C) All angles are right angles. 
D) All angles have different degree measures.

Question 13

A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.40 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot?

Accepted Answer

A) 4 
B) 8 
C) 12 
D) 16 
E) 32 
A) 4 
B) 8 
C) 12 
D) 16 
E) 32

Question 14

The average weight of 50 prize-winning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?

Accepted Answer

A) 0)0472 
B) 11.8 
C) 52.36 
D) 59 
E) 118 
A) 0)0472 
B) 11.8 
C) 52.36 
D) 59 
E) 118

Question 15

The number of bacteria present in a laboratory sample after t days can be represented by 500(2 t). What is the initial number of bacteria present in this sample?

Accepted Answer

A) 250 
B) 500 
C) 750 
D) 1,000 
E) 2,000 
A) 250 
B) 500 
C) 750 
D) 1,000 
E) 2,000

Question 16

Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is closest to the total amount Ken paid?

Accepted Answer

A) $806 
B) $5,510 
C) $5,760 
D) $5,940 
E) $6,180 
A) $806 
B) $5,510 
C) $5,760 
D) $5,940 
E) $6,180

Question 17

Which of the following inequalities is equivalent to 5 n + 4 < 19 ?

Accepted Answer

A) n  5 
D) n < 10 
A) n  5 
D) n < 10

Question 18

A certain machine produces 300 nails per minute. At this rate, how long will it take the machine to produce enough nails to fill 5 boxes of nails if each box will contain 250 nails?

Accepted Answer

A) 4 min 
B) 4 min 6 sec 
C) 4 min 10 sec 
D) 4 min 50 sec 
E) 5 min 
A) 4 min 
B) 4 min 6 sec 
C) 4 min 10 sec 
D) 4 min 50 sec 
E) 5 min

Question 19

Cos 2(3 x) + sin 2(3 x) =

Accepted Answer

A) 0 
B) 1 
C) 3 
D) 6 
E) 9 
A) 0 
B) 1 
C) 3 
D) 6 
E) 9

Question 20

It takes 28 minutes for a certain bacteria population to double. If there are 5,241,763 bacteria in this population at 1:00 p.m., which of the following is closest to the number of bacteria in millions at 2:30 p.m. on the same day?

Accepted Answer

A) 80 
B) 40 
C) 20 
D) 15 
E) 10 
A) 80 
B) 40 
C) 20 
D) 15 
E) 10

Suppose 4 r = 3 s = 10 t, where r, s, and t are positive integers. What is the sum of the least values of r, s, and t for which this equality is true?

In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?

Which of the following is NOT a property of every rectangle?

The population of the United States is approximately 250 million, and the national debt is approximately 4 trillion dollars. If this debt were divided equally among the population, what would be the debt, in dollars, per person?

If k can be replaced by any number, how many different values can the expression k + 6 have?

Carlos' basketball team won 75% of its games last season. If they played 80 games, how many games did they win?

What is the least whole number x for which 2 x > 11 ?

A cat lies crouched on level ground 50 feet away from the base of a tree. The cat can see a bird's nest directly above the base of the tree. The angle of elevation from the cat to the bird's nest is 40°. To the nearest foot, how far above the base of the tree is the bird's nest?

Which of the following pairs of geometric figures must be similar to each other?

The first term in a sequence of numbers is 1/2. Each term after the first term is 1 more than twice its previous term. What is the 4th term?

If a 2 by 18 rectangle has the same area as a square, what is the length of a side of the square?

If a triangle is equilateral, which of the following must be true?

A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.40 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot?

The average weight of 50 prize-winning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?

The number of bacteria present in a laboratory sample after t days can be represented by 500(2 t). What is the initial number of bacteria present in this sample?

Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is closest to the total amount Ken paid?

Which of the following inequalities is equivalent to 5 n + 4 < 19 ?

A certain machine produces 300 nails per minute. At this rate, how long will it take the machine to produce enough nails to fill 5 boxes of nails if each box will contain 250 nails?

Cos 2(3 x) + sin 2(3 x) =

It takes 28 minutes for a certain bacteria population to double. If there are 5,241,763 bacteria in this population at 1:00 p.m., which of the following is closest to the number of bacteria in millions at 2:30 p.m. on the same day?

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Exam 4: Math: Mathematics Intermediate

Suppose 4 r = 3 s = 10 t, where r, s, and t are positive integers. What is the sum of the least values of r, s, and t for which this equality is true?

In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?

Which of the following is NOT a property of every rectangle?

The population of the United States is approximately 250 million, and the national debt is approximately 4 trillion dollars. If this debt were divided equally among the population, what would be the debt, in dollars, per person?

If k can be replaced by any number, how many different values can the expression k + 6 have?

Carlos' basketball team won 75% of its games last season. If they played 80 games, how many games did they win?

What is the least whole number x for which 2 x > 11 ?

A cat lies crouched on level ground 50 feet away from the base of a tree. The cat can see a bird's nest directly above the base of the tree. The angle of elevation from the cat to the bird's nest is 40°. To the nearest foot, how far above the base of the tree is the bird's nest?

Which of the following pairs of geometric figures must be similar to each other?

The first term in a sequence of numbers is 1/2. Each term after the first term is 1 more than twice its previous term. What is the 4th term?

If a 2 by 18 rectangle has the same area as a square, what is the length of a side of the square?

If a triangle is equilateral, which of the following must be true?

A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.40 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot?

The average weight of 50 prize-winning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?

The number of bacteria present in a laboratory sample after t days can be represented by 500(2 t). What is the initial number of bacteria present in this sample?

Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is closest to the total amount Ken paid?

Which of the following inequalities is equivalent to 5 n + 4 < 19 ?

A certain machine produces 300 nails per minute. At this rate, how long will it take the machine to produce enough nails to fill 5 boxes of nails if each box will contain 250 nails?

Cos 2(3 x) + sin 2(3 x) =

It takes 28 minutes for a certain bacteria population to double. If there are 5,241,763 bacteria in this population at 1:00 p.m., which of the following is closest to the number of bacteria in millions at 2:30 p.m. on the same day?

Math: Basic Math

Math: Math Tricks

Math: Mathematics Easy

Math: Mathematics Advanced

Technology: Technology-Engineering

Technology: Palladium: Properties, Uses, and Mining Methods

Science

Filters