EXAM I
(10 pts) 1. Find an equation of the line which is perpendicular to the line 3x - 2y = 6 and which contains the point (3,1).
(10 pts) 2. a. Solve x4/3 = 16 algebraically (NO
CALCULATOR) .
b. Factor 12x2 + 17x - 40.
(10 pts) 3. a. Find f o g,
where f(x) = x1/2 and g(x) = 9 - x2.
b. Find its domain.
(10 pts) 4. Solve the equation (2x + 7)1/2 = x + 2.
(10 pts) 5. Simplify the expressions: a. 3(72)1/2
x - 2(50)1/2 x
b. (7 - 3/2)(7x 5/2) / (7x) 1/2
(10 pts) 6. (problem not relevant)
(10 pts) 7. Solve x(x - 4) < 5.
(10 pts) 8. Sketch the graph of the function f(x) = | x - 2 | - 1.
(10 pts) 9. A farmer drives a tractor from one town to another, a distance of 120 kilometers. He drives 10 kilometers per hour faster on the return trip, cutting 1 hour off the time. Find how fast he drives each way.
(10 pts) 10. A rectangular garden of width 10 meters and length 15 meters is surrounded by a walkway of width x meters. Describe the perimeter of the walkway in terms of x.