MATH 121, Extra Problems for Quiz 2 (1.1 through 2.1)

These are example problems, mostly from tests and quizzes that I have given in the past. Make sure you understand and can do all assigned textbook problems, handouts problems, and problems from homework and online activities.

1.) Determine which quadrant each of the following points lie in. If none, say so.

(a.) (-2, 3) _____ (b.) (3, -2) _____ (c.) (-3, -3) ____

(d.) (0, 3) _____ (e.) (1, 10) _____ (f.) (-2, 1000) _____

2.) If a racewalker takes 1760 steps per mile and walks 5 miles per hour for 3 consecutive hours, how many steps did he take? Express your answer in scientific form.

3.) Find the equation of the line that goes through the point (7, -3) and is perpendicular to the line  2x - 5y = 8.

4.) Find the equation of the line that goes through the point (0, 8) and is parallel to the line 3x -2y = 4.

5.) Find the equation of the line that has x-intercept -6 and y-intercept 7.

6.) Find the equation of the line in the picture.

7. Solve the following equations for x:

a.)	b.)
c.)	d.)
e.)

8.) Calculate the following:

1. 4 is 5 percent of what?
2. What is 5 percent of 4?
3. 5 is what percent of 4?

9.) y is a function of x for which of the following: _________________

(a.) 3x + 4y = 6		(b.)
(c.)		(d.)
(e.)		(f.) x Î {Jan, Feb, March, April, May, June, July, Aug, Sep, Oct, Nov, Dec} y = A student in this class whose birthday is in month x.
(g)	(h) x = 2(y -2)2		(i) x Î {the students in this class} y = the color of student x’s hair
(j) x3y= 3	(k)		(l)

10.) Find the equation of a line that has undefined slope and goes through the point (7, 2).

11.)

State the intervals for x where f(x) is: increasing _____________________ decreasing ____________________ constant ______________________

12.) For each function on the left put the letter of its corresponding domain in the blank.

(a) (-1, ∞ ) (b) [-1, ∞) (c) (1, ∞) (d) [1, ∞) (e) (-∞ , ∞)

(f) (-1, 1) U (1, ∞) (g) [-1, 1) U (1, ∞) (h) (-∞, -1) U (-1, ∞) (j) (-∞, 1) U (1, ∞) (k) (-∞, -1) U (-1, 1)U(1, ∞)

13.) Find the largest subset of the real numbers that can be the domain of if we are only allowed to have real answers.

14.) Graph

15.) Use the same f as in #14 above to evaluate:

1. f(2)
2. f(-1)
3. f(0)

16.) Let g(x) = x² + 2x .  Evaluate: a.) g(1)    b.) g(-2)   c.) -g(-x),    d.) g(a+3)

17.) A cheese manufacturer produces 18,000 pounds of cheese from January 1 through March 24. Suppose that this rate of production continues for the remainder of the year.

1. Express the number y of pounds of cheese produced in terms of the number x of the day in a365 day year.
2. Predict, to the nearest pound, the number of pounds produced for the year.

18.) The owners of Langdon jams has fixed costs of $300 per month plus 40¢ per jar of jam. How many jars do they need to sell per month at $3.00 per jar to break even?

19.) Find the distance between the points (1, 2) and (-5, 7).

20.) Find a formula that expresses the fact that P(x, y) is a distance of 4 units from (1, 1). Describe the set of all such points in a plane.

21.) Find the equation of the perpendicular bisector of the points (-5, 7) and (5, -13) .

22.) Find the equation of the circle that is tangent to: the y axis, the line y = 8, and the x axis in the second quadrant.

23.) Find all points on the line y = x that are a distance of 7 from the point (2, 5) .

24. Solve the following application problems.

1. A laboratory keeps two acid solutions on hand. One is 20 percent acid and the other is 35 percent acid. An order is received for 25 liters of a 26 percent acid solution. How much 20 percent acid solution and how much 35 percent acid solution should be used to fill this order?
2. Two semicircles are placed at opposite ends of a square as shown. Find the side length of the square if the total area enclosed is 100 square units. Recall that the area of a circle is p r² where r is the radius.



3. Suppose your four highest test scores are: 65, 72, 68, 79 out of 100 each. If the final counts as two tests what percent do you need to get on the final to get a 2.5 or above in the course? (A 77% average is needed.)
4. A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a straight river bank instead of fencing as one side of the rectangle. Find the area of the region if the length of the side parallel to the river bank is one and a half times the length of an adjacent side.
5. A runner leaves her house to run on her favorite 6 mile out and back course (3 miles out and 3 miles back) at a rate of 8 minutes per mile. Her husband heads out on the same course 12 minutes later at a rate of 10 minutes per mile. How far from their home will they pass each other?

25.) Find all points on the line y = 3x that are a distance of 6 from the point (1, 2).

26.) Find the equation of the circle that has a diameter with end points (6, 8) and (-3, 2).

27.) Evaluate the equation of the following circle and multiply out the results to put the equation in general form.

28.) Solve the following inequalities. Write your answer in simplified interval notation.

1. 3x + 1 > 12   or   -2x + 2 > 5
2. 3x + 1 < 12   and   -2x + 2 ≤ 5
3. 7 ≤ 3x + 1 ≤ 13
4. 1 ≤ x ≤ 4 and (x < 2 or x ≥ 4)

29.) Four different sets of data yielded the following 4 different linear regression correlation coefficients: r = .04, r = -.5, r = -.95, r = .87. Rank these in order from best fit to worst fit.

1.) (a.) II   (b.) IV   (c.) III   (d.) none   (e.) I   (f.) II

2.) 2.64 × 10⁴

3.)            

4.)            5.)   

6.)

7.) a.) b.) c.) d.) e.)

8.) a.) 80,     b.) 0.2,     c.) 125

9.) (i) a, d, e, i, j, l

10.) x = 7         

11.) increasing: (-∞ , -5) U (2, 5),   decreasing: (-5, 2)   constant: (5, ∞)

12.) e, j, b, a, g respectively

13.) [2, 4) U (4,∞)

14.)

15.) a.) 2, b.) -2, c.) 0

16.) a.) 3,   b.) 0,   c.) -x²+2x,   d.) a² + 8a + 15

17.) a.)     b.) 79,157
18.) approximately 115

19.) 7.81                   20.) (x - 1)² + (y - 1)² = 16 Circle centered at (1, 1) with radius 4.

21.) x - 2y = 6

22.) (x + 4)² + (y - 4)² = 16

23.) (8.22, 8.22), (-1.22, -1.22)

24.) a.) 10 liters at 35% and 15 liters at 20%   b.) x = 7.48 units   c.) 89% or above   d.) 3967.35 ft²   e.) 2 miles

25.) (2.59, 7.78) & (-1.19, -3.58)

26.)      

27.) x² + y² - 2x + 4y - 9 = 0

28.) a.) (-∞, -3/2) U (11/3, ∞),    b.) [-3/2, 11/3),    c.) [2, 4]    d.) [1, 2) U {4}

29.) -0.95, 0.87, -0.5, 0.04