Download Practice Problems for Test 1

MAT 111
Practice Test for Test 1 ( Chapter 1 and 2.1 – 2.2 )
1. (1.1 and 2.2) Calculate the following. Answers must be exact. Simplify any radicals completely.
a. The distance between the points (1,11) and (17, 5)
b. The midpoint between the points (4.5, 9) and (3.2,  50)
c. The slope of the line that contains the points (2,1) and (5,11)
2. (1.2 and 2.1) Find the intercepts of the graph of the functions:
a.
y  x 2  9x  14 (algebraically)
b.
y  7 x 2  4 x  5 (use graphing calculator as needed, rounding correctly to 3 decimal places)
3. (1.2) Solve: 4 x 2  3x  5  2 x  6
4. (1.2) Solve:
a.
x
2x
4
3
 2

x 4 x 4 x2
b.
2
x 1
2

x3
x x
2

3
x x
2
5. (1.3 and 1.4) Solve the following equations. Find all real and complex solutions.
a. 3 x 2  8 x  3
b. 3x 2  7 x  6
c. 3x 3  2 x 2  5 x  0
d. 5 x 2  2 x  1  0
6. (1.4) Perform the indicated operations by hand, showing your work. Write answers in standard a + bi
form.
7i
a. (6  4i)  (1  2i)
b. (5  4i)( 2  3i)
c.
d. 5i (4 - i 22 ) - 7 + 3i 3
e. i 278
1  4i
7.
(1.5) Solve. If solved algebraically, answer must be exact. If solved by graphing, you must sketch your
graph answer must be rounded correctly to 2 decimal places.
a.
3x  1  6  2 x  0
b. x 4  7 x 2  10  0
c. 5  2 4  3x  11
8. (1.6) Jacob purchased some bonds yielding 10% annually and some certificates of deposit yielding 14%
annually. If Jacob’s investment amounts to $24,000 and the annual income is $3000, how much money
is invested in bonds and how much is invested in certificates of deposit?
9. (1.6) A chemistry experiment calls for 2.4 liters of a 2% acid solution. On hand, the lab has containers
of 1% acid solution and 5% acid solution. How much of each must be mixed in order to have what is
needed for the experiment? (You must solve this algebraically to receive credit; no credit for guess and
check.)
10. (1.6) A plane flies from city A to city B in 5 hours with a tailwind of 2 mph. It takes the same plane 9
hours to travel back to city A against the wind. What is the plane’s speed in still air?
11. (1.6) How many cc of pure acid should be added to 30cc of a 40% acid solution to get a 50% acid
solution?
12. (1.6) A health food retailer sells a mixture of dried cherries, blueberries, and pecans for $15.00 per
pound and dried banana chips for $2.25 per pound. The retailer decides to create a new mix by adding
banana chips to the original mix. How many pounds of banana chips must be mixed with 40 pounds of
the original mix to obtain a new mixture that sells for $10.25 per pound with no loss in revenue? (round
to two decimal places.)
13. (1.7) Solve the following inequalities. Write your answers in interval notation.
a.  4x  9  11
b. 3x  5  2( x  1)  4  5(3  x)
c. 2 x  7  1  6
d.
 3  2 4 x  1  11
14. (2.1) Determine what kind of symmetry, if any, the graph of each of the following has:
a.
x 2  y 2  16
b. y  x 2  3
c.
y  x2  2x  3
d. y  x3
15. (2.1) Sketch the graph of the following functions by plotting points, finding any intercepts, and checking
for symmetry.
a.
y  x2
b. y  x3
c.
y x
d. y  x
16. (2.2) Find the equation in y  mx  b form of the following lines.
a. Passing through the points (4,7) and (3, -5)
b. Contains the point (-2, 3) and parallel to the line whose equation is 3x – 4y = -1
c. Passing through the point (5, -2) and perpendicular to 2x – 6y = 1
e.
y
1
x