Question 1

As a particle moves along a straight path, its speed v (in cm/sec) at time t (in seconds) is given by the equation below. For what subintervals of the time interval [0, 8] will its speed be at least 15 cm/sec?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

As a particle moves along a straight path, its speed v (in cm/sec) at time t (in seconds) is given by the equation below. For what subintervals of the time interval [0, 8] will its speed be at least 4 cm/sec?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 27 ft  2  of glass is to be used, find the height h.

Accepted Answer

A)   feet 
B)   feet 
C)   feet 
D)   feet 
E)   feet

Question 4

Solve the equation

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Two surveyors with two-way radios leave the same point at 9:00 A.M., one walking due south at 4 mi/hr and the other due west at 2 mi/hr. How long can they communicate with one another if each radio has a maximum range of 2.24 miles? Round the answer to the nearest minute.

Accepted Answer

A) 45 minutes 
B) 30 minutes 
C) 63 minutes 
D) 87 minutes 
E) 55 minutes

Question 6

Solve the equation.

Accepted Answer

A)   
B)   
C)   
D)   
E) no solution

Question 7

Express the inequality  as an interval.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $500 per year. Car B costs $11,600 and has an mpg rating of 50, and insurance is $550 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.

Accepted Answer

A) 27 years 
B) 9 years 
C) 8 years 
D) 17 years 
E) 37 years

Question 9

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 226 grams of a copper-silver alloy that is 13% copper by weight?

Accepted Answer

A) 192.4 g of British sterling silver and 33.6 g of copper. 
B) 196.6 g of British sterling silver and 29.4 g of copper. 
C) 206.5 g of British sterling silver and 19.5 g of copper. 
D) 213.9 g of British sterling silver and 12.1 g of copper. 
E) 212.6 g of British sterling silver and 13.4 g of copper.

Question 10

Solve the equation by factoring.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find the real solutions of the equation

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Write the expression  in the form  , where a and b are real numbers.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Solve the inequality.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Solve the equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Write the expression  in the form  , where a and b are real numbers.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Solve the equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Two surveyors with two-way radios leave the same point at 9:00 A.M., one walking due south at 4 mi/hr and the other due west at 2 mi/hr. How long can they communicate with one another if each radio has a maximum range of 2.98 miles? Round the answer to the nearest minute.

Accepted Answer

A) 52 minutes 
B) 116 minutes 
C) 40 minutes 
D) 73 minutes 
E) 84 minutes

Question 18

Solve the equation.

Accepted Answer

A)   
B)   
C) All real numbers except -4 
D) All real numbers except 4 
E) No solution

Question 19

Solve the formula for  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Solve the inequality.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 2: Equations and Inequalities

As a particle moves along a straight path, its speed v (in cm/sec) at time t (in seconds) is given by the equation below. For what subintervals of the time interval [0, 8] will its speed be at least 15 cm/sec?

As a particle moves along a straight path, its speed v (in cm/sec) at time t (in seconds) is given by the equation below. For what subintervals of the time interval [0, 8] will its speed be at least 4 cm/sec?

A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 27 ft ² of glass is to be used, find the height h.

Solve the equation

Two surveyors with two-way radios leave the same point at 9:00 A.M., one walking due south at 4 mi/hr and the other due west at 2 mi/hr. How long can they communicate with one another if each radio has a maximum range of 2.24 miles? Round the answer to the nearest minute.

Solve the equation.

Express the inequality as an interval.

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 226 grams of a copper-silver alloy that is 13% copper by weight?

Solve the equation by factoring.

Find the real solutions of the equation

Write the expression in the form , where a and b are real numbers.

Solve the inequality.

Solve the equation.

Write the expression in the form , where a and b are real numbers.

Solve the equation.

Two surveyors with two-way radios leave the same point at 9:00 A.M., one walking due south at 4 mi/hr and the other due west at 2 mi/hr. How long can they communicate with one another if each radio has a maximum range of 2.98 miles? Round the answer to the nearest minute.

Solve the equation.

Solve the formula for .

Solve the inequality.