Download test one

Intermediate Algebra test one
Friday, October 12, 2007
please show your work to get full credit for each problem
1. Is the following a true equation or a
false equation?
8 − 6/2 =
2. Write the solutions to the inequality 3 ≤ x < 5
using interval notation.
8−6
2
3. Draw a number line picture of the solutions of the compound inequality x < −2 or x > 2.
4. Evaluate x − y 2
when x = −3 and y = −4.
5. Evaluate x/y
when x = 2/3 and y = −5/7.
6. For the function f (x) = 3 + 2x + x2 ,
(a) evaluate f (0)
(b) evaluate f (−4)
7. For which values of x is |x| = −x?
8. Simplify the compound inequality x < 4 and x < 6.
10. Solve the linear equation
9. Solve the linear equation
x
+ 7 = 2x
3
x + .25x = 75
11. Solve the following equation for the variable m:
ma = C − mg
12. Solve the linear inequality 45 − 3x ≤ 6
13. Solve the compound inequality 6 < 43 x+2 < 18
14. Solve each absolute value equation:
(a) |x| = −2
(b) |2x + 3| = 15
15. Solve each absolute value inequality:
(a) |x| ≥ 3
(b) |x − 2007| <
1
2
page two
16. In which of the following graphs is the variable y a function of the variable x?
y
y
(a)
y
(b)
@
@
(c)
@
@
x
x
x
17. In which of the following formulas or tables is the variable y a function of x?
(a) y−3x = 6
√
(b) y = ± x
(c)
x
3
4
5
y
8
9
8
18. A line contains the points (x, y) = (2, 6) and (4, 3).
(a) find the line’s slope
(b) find an equation for the line
19. A line has slope − 54 and contains the point (x, y) = (−2, 3). Find an equation for the
line in point-slope format.
20. Calculate the slope of the line which has equation
3
2
3
x− y = −
7
5
2
21. Given the line y = 4x + 3
(a) state the line’s slope
(b) state the slope of a line which is perpendicular to y = 4x + 3
(c) find an equation for the line which is perpendicular to y = 4x + 3 and which passes
through the point (−8, 5).
22. Suppose there is a linear relation between the distance travelled in a taxi and
the cost of the trip.
distance (miles)
12
20
cost
$ 30
$ 40
Use the data given above to calculate the
cost of a 15 mile trip.
23. A certain house in Yakima has increased in value by 10% from last year’s
value. If the house now has a value of
$242,000 , calculate its value last year.
24–27. Graph each linear equation & inequality:
24.
4x − 3y = 12
26.
y ≥ 5 − 34 x
25.
27.
y − 1 = 41 (x + 2)
x ≤ 0 and y < −1