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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) Page 2 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 Page 3 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 Page 4 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 Page 5 (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 Page 6 3 1 to solve the system of equation −5