Mathematics 105
Self-Assessment Test


1.Find a factor of: 4x³ + 2x² - 6x - 3 

a. 2x² - 3         b. 2x² + 3         c. 2x - 1         d. none of these



2.Find a factor of: 8x³ + 27 

a. 2x - 3                         b. 4x² - 6x + 9 

c. 4x² + 12x + 9             d. none



3.Factor completely: x⁴ - 16

a. (x² + 4)(x² - 4)                  b. (x² + 2)²(x² - 2)² 

c. (x² + 4)(x + 2)(x - 2)         d. prime



4.Solve for x:     2x - 5(3 - x) = 7x 

a. -1.5         b. 1.5         c. all real numbers         d. no solution





5.Solve for x:     2x² - 3x + 1 = 0 

a. 1, 1/2        b.  -1, -1/2        c. 1, -1/2        d. -1, 1/2



6.Solve for x:     squareroot (3x - 5) = -2

a. -3         b. 3         c. all real numbers         d. no solution



7. Solve for x: |3x - 4| > -2

a. 2/3 < x < 2                 b. 2/3 > x or x > 2 

c. all real numbers         d. no solution

8.Solve for x: 5(x - 7)² + 3 = 18

a. 7 ± sqrt 3             b. -7 ± sqrt 3 

c. 7 ± sqrt 3/5         d. -7 ± sqrt 3/5





9. Given f(x) = 3x² - 2, find f(-1)

a. 5         b. -1         c. -5         d. 1



10.Rewrite as a logarithm: 3² = 9 

a. log₂9 = 3             b. log₉2 = 3 

c. log₃9 = 2             d. log₉3 = 2





11.Rewrite as an exponential: log_xy = z 

a. x^y = z         b. x^z = y         c. y^z = x         d. z^x = y





12.Rewrite as a single logarithm: 3log x – log y + log z

a. 3 log (x-y+z)             b. log (x³z/y) 

c. log (xz/y)³               d. log (3xz-y)





13. Complete the square: 3x² + 12x + 1

a. 3(x+6)² - 35               b. 3(x+2)² - 3 

c. 3(x+6)² - 107             d. 3(x+2)² - 11





14.Find the center of this circle: (x - 9)² + (y + 4)² = 25 

a. (-9, 4)         b. (-4, 9)         c. (9, -4)         d. (-4, 9)



15.Find the equation of a line through (2, -3) 

    perpendicular to y = 2x - 1 

a.  y = 2x - 7             b.  y = 2x - 8 

c.  y = ½ x - 4           d.  y = -½ x - 2 



16.Solve this system of equations for x:     x + y + z = 0
                                                                x - y + z = 6
                                                                x + 2y - z = -5
a. 2         b. -3         c. 1         d. -2




For problems 17 and 18 use:  y = x² - 4

17.What is the domain? 

a. all real numbers            b. x > 4

c. x < 4                             d. (-4, 4)



18.What is the range?

a. all real numbers            b. x > 4

c. x < 4                             d. y > -4

Answers:

1. a        2. b        3. c        4. d        5. a        6. d  

7. c        8. a        9. d        10. c        11. b        12. b

13. d       14. c        15. c        16. a        17. a        18. d