Practice Test Midterm 2 (1050-005)
Name:
ID: U
Question:
1
2
3
4
5
6
7
Total
Points:
12
20
15
15
13
15
10
100
Score:
1. Completely factor the following polynomials
(a) 7 points 15x3 + 35x2 + 30x + 10
(b) 5 points x4 − 5x2 + 4
2. (a) 10 points Graph the polynomial 6(x + 4)(x + 4)(x − 2)(x − 3)(x2 + 1)(x2 + 3)
(b) 10 points Graph the rational function
3(x2 +7)
5(x−2)2 (x−6)
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3. (a) 2 points Simplify
3297
3300
(b) 5 points Solve: 4e2x−3 =
4
e9
(c) 8 points Solve: log2 (x) − log2 (x + 4) = 3
4. (a) 5 points Solve for x: | − 2x + 3| < 5
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

2
(b) 10 points Let f be a function defined by: f (x) = ex


3x − 2
Find the values of f (−2), f (0), f (2) and f (15). Also, graph f .
5. (a) 5 points Solve for x and y:
2x + 8y = −8
−3x + 6y = 12
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if x ∈ [−3, 0)
if x ∈ [0, 2]
if x ∈ (2, ∞)
(b) Consider following system of equations:
3x − 4y + 2z = −9
−4x + 4y + 10z = 32
−x + 2y − 7z = −7
i. 2 points Is x = 1, y = 4, and z = 2 a solution to the system?
ii. 2 points Is x = −1, y = 1, and z = −1 a solution to the system?
iii. 2 points Is x = 25, y = 23, and z = 4 a solution to the system?
iv. 2 points Does the system have infinitely many solutions?
6. (a) 5 points Find the product
2 1 3
3 2 5
−4
6
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(b) 10 points Find the inverse of the matrix
3 2
−1 4

−1 
4
3
3
1
0
1
2  =  1 −1
7. 10 points Use the fact that  3
−1 −1 −1
−2 1
4x + 3y + 3z = 2
3x + y + 2z = 4
−x − y − z = 2
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
3
1  to solve the system of equation
−5