Midterm ReviewName:
Unit 1 Exam
1) Sketch a graph of each of the following functions. Using appropriate vocabulary, describe all of the transformations. Show the dotted original.
a)
b)
c)
d)
e)
f)
g)
h)
2)Give the domain and range of each graph below in interval notation
3)Use the graphs to find the following:
a)f(-1)
b)(f – g)(2)
c)f(g(3))
d)Graph y= f(2x)
e)Graph y = f(x+1) – 2
f)Graph y = f(-x)
4)Let f(x) = x2 +3 and g(x) = 3x – 1 Find:
a)(f+g)(3)
b)(f – g)(x)
c)f(g(-1))
d)g(f(x))
e)(fg)(2)
5)Write a trigonometric function that oscillates between 5 and 25
6)Write a trigonometric function that oscillates between -20 and 40
7)Write a trigonometric function that has a period of 4
8)Write a trigonometric equation that has a period of 30
9)In a certain city, the number of daylight hours varies throughout the year beginning in January where there are only 11 hours of daylight to June where there are 15 hours of daylight and back. Write a trigonometric function that will model the number of hours of daylight throughout the year in this city.
Unit 2 Vectors
1)Use the diagram to make a careful sketch of each problem. Draw you answer as a solid vector and make and dotted.
a)3
b)2
c)
d)1/2
2)Use the diagram to express each of the following in terms of and . E is the midpoint of AC.
a)
b)
c)
d)
3)Use the following vectors and to answer the following questions:
a)
b)
c)The angle between and using the formula
d)The magnitude and direction of
e)The magnitude and direction of
4)Given = [3, 48o ] find each of the following:
a)2 in terms of [r, ]
b)-1/2 in terms of [r, ]
c)The component form of
5. A boat wants to sail at 50knots in a direction of 155o. If the wind is blowing at 35knots in a direction of 26o, at what angle and direction should the boat attempt to sail in order to sail the course that it desires?
6. Johnny and Daisy are pulling on an object. Johnny pulls with a force of 13Newtons at 43o and Daisy pulls with a force of 8 Newtons at 115o. Find the magnitude and direction of the resultant force.
Unit 3 Polynomial Modeling
1)
a)Use the x – intercepts to write a polynomial function that is a product of linear factors.
b)Rewrite your rule from part a in standard polynomial form.
c)Explain what type of graph would best model this function and why.
d)Use the labeled control points to produce a regression equation. Write the regression equation below.
2)Use the following points and the method of undetermined coefficients to find a quadratic equation (y = ax2 + bx + c) whose graph would pass through these three points. You must do this using substitution or elimination and show all work clearly.
(0,1)
(2,9)
(-1,6)
3)Use the following points and the method of undetermined coefficients to find a quartic equation (y = ax4 + bx3 + cx2 + dx+e) whose graph would pass through these five points. You must do this using matrices.
(-3,-5)
(-1,2)
(1,-1)
(2, 1)
(5, -3)
4)Perform the polynomial division (2x3 +5x2– x +1) ÷ (x +2).
5)Perform the polynomial division (3x3+17x2 +8x – 48) ÷ (3x – 4).
6)Solve each equation using factoring or the quadratic formula when appropriate. When necessary, write solutions in standard complex form of .
a)3x2 – 4x– 4 = 0
b)2x2– 5x – 3= 0
c)6x2 + 7x– 3 = 0
d)x2 + 2x+ 10 = 0
e)2x2 – 6x= -5
7)Evaluate the following:
a)
b)
c)
8)Let p = 4 – 2i and let q = 2 + 5i. Findeach of the following in a + bi form.
a)p + q
b)p – q
c)pq
d)p ÷ q
9)Let p = 4 – 2i and let q = 2 + 5iand let r = 4. Plot p, q, and r on the complex plane.
10)Find and .
11)Find the x and y intercepts of each function below.
a)
b)
12)Find all asymptotes of each function below.
a)
b)
c)
d)
13)Give the domain of each of the following in interval notation.
a)
b)
14)Create a rational function that has a vertical asymptote at x = 5 and a horizontal asymptote at y = 0.
15)Create a rational function that has an x intercept at (2, 0) a horizontal asymptote at y = 5, and a vertical asymptote at x = -3.