Algebra Questions

1.

Evaluate the expression 

for the value of  

                   

		-9
		8
		6
		-8

2.

Factor: x2+4x-32

		(x-4)(x+8)
		(x-4)(x-8)
		(x+4)(x-8)
		(x-16)

3.

Factor: 

		(x-5)
		(x+5)2
		(x+5)(x-5)
		(x-5)(x-5)

4.

Evaluate -u2v3 when u=4 and v=-2 

		128
		64
		32
		-128

5.

Using an online calculator, determine whether the value of x=7 is a solution of the equation. 

 Yes   No

6.

Explain why x=7 IS or IS NOT a solution of the equation. 

7.

Solve the equation and check your solution: 

		9
		-11
		-8
		-10

8.

Solve the equation and check your solution: 

		67
		-3
		-67
		All real numbers

9.

Solve the equation and check your solution. 

		10
		6
		7
		9

10.

Solve the quadratic equation by factoring: 

		-1, 5
		-1,-5
		1,-5
		1,5

11.

The imaginary number i represents:

12.

Find real numbers a and b such that the equation is true: 

		a=16, b=4
		a=18, b=6
		a=14, b=2
		a=15, b=14

13.

Find all solutions to the following equation. 

		x = -17/4
		x=9
		No solution
		x=-17

14.

In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for James’ miles.

15.

Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz.

		10h - .25=450
		10h + .25(10h)=450
		h -.25 (10h)=450
		10h - .25(10h)=450

16.

Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work.

17.

The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width.

Hint:  Perimeter  = width +  length  + width + length  

18.

Twice a number is added to the number and the answer is 80. Write an equation to solve this problem.

		2n + n=80
		2n = 80
		2n + 80=n
		80 + n=2n

19.

If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20.

Multiply the following binomials: 

21.

What does this mathematical symbol ∞ represent?   

		Zero
		Infinity
		Pi
		Undefined

22.

A rational expression can be written as a ratio of two polynomial expressions.

 True

 False

23.

Asymptotes are invisible lines which a graphed function will approach very closely but not touch.

 True

 False

24.

Find the domain of the function 

		Domain: all real numbers x except x=6
		Domain: all real numbers x except x=8
		Domain: all real numbers x
		Domain: all real numbers x except x = -6

25.

Find the domain of the function 

		Domain: all real numbers x except x = 7
		Domain:  all real numbers x except x = ±49
		Domain: all real numbers x except x = -7
		Domain: all real numbers x except x = ±7

26.

Find the domain of 

		all real numbers except x = -9
		all real numbers except x = 81
		all real numbers except x = 9
		all real numbers except x = 9 and x = -9

27.

Find the domain of the function and identify any vertical and horizontal asymptotes.

		Domain: all real numbers x except x = 2 Vertical asymptote: x = 2 Horizontal asymptote: y = -1
		Domain: all real numbers x except x = 0 Vertical asymptote: x = 0 Horizontal asymptote: y = -1
		Domain: all real numbers x except x = 2 Vertical asymptote: x = 0 Horizontal asympotote: y = -2
		Domain: all real numbers x except x = -2 Vertical asympotote: x = 0 Horizontal asympotote: y = 2

28.

Select the correct graph of the function. Choose from among the graphs listed below: 1st, 2nd, 3rd, or 4th. 

29.

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by

According to this model, it is possible to remove 100% of the pollutants. 

 True

 False

30.

Based on your answer to the previous problem, explain why you chose your answer (whether it is possible or not to remove 100% of the pollutants).

31.

In the following formula, S(x) is the minimum number of hours of studying required to attain a class score of x. How many hours of study are needed to score 56? Round your answer to the nearest whole number.

32.

The concentration C (in mg/dl), of a certain antibiotic in a patient's bloodstream is given by C(t)=50 t /(t^2 + 25) where t is the time (in hours) after taking the antibiotic. What is the concentration 5 hours after taking the antibiotic?

33.

In order to join a gym, you pay a $200 annual fee, then $10 for each exercise class you attend. Indicate which equation below would allow you to determine the average cost per class if you go to x amount of classes: 1st, 2nd, 3rd, or 4th. 

34.

Which of the following can a graph NEVER cross?

		Vertical asymptote
		Horizontal asymptote
		Slant asymptote
		All of the above

35.

Select the graph of the rational function. Choose from among the graphs below: 1st, 2nd, 3rd, or 4th.

36.

One pipe can fill a pool in 1.5 hours. A second pipe can fill up the pool in 2 hours. Which of the equations below would determine how long it would take to fill the pool when both pipes are used? Select the correct equation:1st, 2nd, 3rd, or 4th.

37.

Using the equation you wrote in the last problem, how long would it take to fill the pool if both pipes are open at the same time? Write your answer in fraction form.

38.

Think of a personal or professional situation where you would need to (or want to) use algebra. In your post, state the situation and create an equation to help you solve it. Also, include the solution.

39.

In order for a film camera with a fixed focal length F to focus on anobject located a distance x from the lens, the lens must be a distance yfrom the film. F, y, and x are related as follows:

Now suppose a camera has a lens with focal length F = 65.

Explain what happens to the distance between the lens and the film as the object moves far away from the lens. When an object far away (x is near infinity), what is the internal distance from the lens and film?

Consider the opposite. Explain what happens to the distance between the lens and the film as the object moves closer and closer to the lens. Is there a distance from the lens at which you can no longer focus?

In general, why is it not possible to cross a vertical asymptote?