MTH 111 - FALL 2000 - REVIEW SHEET 1 - PRINT YOUR NAME______________________________

 

CIRCLE YOUR SECTION: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

 

Instructions: There will be 2 parts to your tests. Part 1 will consist of multiple choice. Part 2 is open ended . You will receive very little or no credit for an answer without appropriate work.. What you write must be in proper mathematical form. Use standard notation. Use complete sentences.

1. Let P: (-2,), Q: (2, -). Find the (a) slope of the line PQ. (b) distance PQ (c) midpoint M

of the segment PQ (d) equation of the line PQ (d) equation of the line through M perpendicular to PQ.

2. Show that the four points, (3,1), (2,2), (0,1), (1,0) form the vertices of a parallelogram.

3. Which of these set of three points A, B, C, form a right triangle and which set lies on a line?

1. {A: (-2,2), B: (1,3), C: (2,0)} 2. {A: (-2, -1), B: (-1, 1), C: (2,7)}

4. Let P: (1,2) and L: 2x + 3y = 5. Find lines through P (a) parallel to L (b) perpendicular to L

5. Find the domain and the range of : (a) f (x) = (b) f (x) = (c) f (x) =.

6. Write the equation of the circle x2 + y2 = 4x - 6y in the standard form. Find the radius

and the coordinates of the center. Sketch the circle.

7. Which of these functions are odd, even and neither? Give reasons. Sketch the graph of each.

(a) f (x) = x2 - x (b) g (x) = x 4 - x 2 (c) h (x) = x3 - x (d) F (x) = x + (1/x)

8. Let f(x) = and g(x) = . Find (a) g f (1) (b) f f (2t) (c) f g (x) (d) g f (x)

9. Let f(x) = 2x+3 and g(x) = . Then the domain of (a) f / g (b) g / f

10. For the function f (x) = 2x2 - 3x + 6, find (a) the difference quotient:

(b) simplify the difference quotient.

 

11. Find the standard equation of the circle that has (-3, -2) and (5, 6) as endpoints of a

diameter. Find the coordinates of the center and radius. Sketch the circle.

 

 

x + 2 x < -1

12. Sketch the graph of the function f(x) = x x 1

-x - 2 x > 1

 

13. Write (a) equation and (b) function that has the shape of y = | x | but shifted left by 7 units and up by 2 units. Sketch the graph of the shifted graph.

14. (a) Simplify: (x +1 + 2i) (x -1 - 2i) (b) Express in the form a + ib: (2 + 3i) / (3 - 4i)

 

NOTE: This sheet is meant to show only the format of the tests and the final exam. The problems in test 1 will differ from these. To prepare well for the tests, do the homework problems. The test will cover from sections 1.1 through 2.1 in the syllabus. The first test will be held on Oct 2, Monday, between 6:00 - 7:30 PM.

Your instructor will give the location of the test.