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Course: MATH 75 - 76, Spring 2006School: Lehigh
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75 Math Fall 2006, Lehigh University, Exam I review These are a sampling of problems for review for the first 4o clock test. This sample may not be complete, and is not representative of the test questions. Be sure to prepare from all material from class and homeworks. Remember that use of calculators will not be allowed during the exam. Solve the inequality |2x - 3| < 5 Solve the inequality 2x2 - 6x - 8...
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75 Math Fall 2006, Lehigh University, Exam I review These are a sampling of problems for review for the first 4o clock test. This sample may not be complete, and is not representative of the test questions. Be sure to prepare from all material from class and homeworks. Remember that use of calculators will not be allowed during the exam. Solve the inequality |2x - 3| < 5 Solve the inequality 2x2 - 6x - 8 > 0 Solve the inequality x2 - x + 1 0. Solve for x: |x + 3| = |2x + 1|. Sketch the region {(x, y)| - 2 - 2x y 4 - x} Solve for x assuming a, b, c are positive constants: a(b - cx) b/a (a) Find the equation of the line through (-4, 6) and parallel to the x-axis. (b) Find the equation of the line through (-4, 6) and parallel to the y-axis. 8. Find the equation of the line through (-3, 4) with slope 2. 9. Find the equation of the line through (4, 5) parallel to 2y = 4x + 5. 10. Identify and sketch the graph of the equation: x2 + y 2 - 6x + 2y = 6 11. Identify and sketch the graph of the equation: y = x2 + 1 12. (a) Convert 2/3 radians to degrees. (b) Find sin(2/3) and cos(2/3)? (you may use sin(/6) = 1/2 = cos(/3) and cos(/6) = 3/2 = sin(/3)) 13. If sin() = 4/5 for < 0 < /2 what are cos() and tan()? 14. Find the remaining trigonometric ratios. sec() = -1.5 and < < . 2 15. Find all values of x in the interval [0, 2] that satisfy sin(x) = tan(x). 16. Find all values of x in the interval [0, 2] that satisfy 2 sin2 (x) > 1.
x-1 17. Find the domain of the following function: f (x) = x2 -1 18. Express the surface area of a cube as a function of its volume. 19. A rectangle has area 30 square meters. Express the perimeter of the rectangle as a function of the length of one of its sides. 20. The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs one day and $ 4800 to produce 300 chairs in another day. Assuming a linear relationship between the cost and the number of chairs produced, find the cost if the factory produced 200 chairs. 21. If f (x) = x2 - x + 2 find f (-2), f (a2 ), [f (a)]2 and f (x+h)-f (x) . Simplify the last h answer.
1. 2. 3. 4. 5. 6. 7.
22. Match each equation with its graph(graph1 or graph2 or graph3). Explain your choices. (a) y = x2 (b) y = x5 (c) y = x8
graph2 30 20 10 150 -2 0 -1 0 -10 x -20 -30 -2 -1 2 1 2 1 0 0 100 50 1 2 -2 -1 0 0 1 2 graph3 4 3 graph1 250 200
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