MAT 101 FINAL EXAM | COLLEGE ALGEBRA - STRAIGHTERLINE | 100% CORRECT ACTUAL QUESTIONS AND ANSWERS

MAT 101 FINAL EXAM | COLLEGE
ALGEBRA - STRAIGHTERLINE | 100%
CORRECT ACTUAL QUESTIONS AND
ANSWERS
MAT 101 FINAL EXAM: COLLEGE ALGEBRA
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Instructions: Please select the best answer for each of the following questions.
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1. What is the solution set for the equation ∣2x−5∣=11∣2x−5∣=11?
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a) {3}
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b) {-3}
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c) {-3, 8}
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d) {8}
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e) {-8, 3}
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2. Simplify the expression: (3x2y−3)−2(3x2y−3)−2.
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a) 9y6x4x49y6
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b) x49y69y6x4
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c) 9x4y6y69x4
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d) y69x49x4y6
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e) x49y59y5x4
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3. Solve the inequality −3≤2x+5<9−3≤2x+5<9.
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a) [-4, 2)
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b) (-4, 2]
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c) [-4, 2]
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d) (-4, 2)
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e) [1, 7]
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4. What is the equation of the line passing through the points (-2, 4) and (3, -6)?
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a) y=−2xy=−2x
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b) y=2x+8y=2x+8
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c) y=−2x+8y=−2x+8
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d) y=−12x+3y=−21x+3
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e) y=2x−12y=2x−12
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,5. Find the slope of a line perpendicular to the line 4x−2y=74x−2y=7.
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a) 2
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b) -2
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c) 1221
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d) −12−21
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e) -4
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6. Which of the following equations represents a function?
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a) x2+y2=25x2+y2=25
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b) x=y2+1x=y2+1
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c) y=x2+1y=x2+1
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d) ∣x∣=∣y∣∣x∣=∣y∣
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e) x=5x=5
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7. What is the domain of the function f(x)=x−4x2−9f(x)=x2−9x−4?
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a) All real numbers
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b) All real numbers except 4
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c) All real numbers except 3 and -3
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d) All real numbers except 9
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e) All real numbers except 4, 3, and -3
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8. Given f(x)=2x2−3x+1f(x)=2x2−3x+1, find f(−2)f(−2).
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a) 15
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b) 3
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c) 11
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d) -13
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e) -1
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9. If f(x)=3x−2f(x)=3x−2 and g(x)=x2+1g(x)=x2+1, find (f∘g)(x)(f∘g)(x).
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a) 9x2−12x+59x2−12x+5
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b) 3x2+13x2+1
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c) 3x2−13x2−1
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d) 3x2+53x2+5
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e) 9x2−12x+49x2−12x+4
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10. What is the inverse function of f(x)=x+1x−2f(x)=x−2x+1?
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a) f−1(x)=2x+1x−1f−1(x)=x−12x+1
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b) f−1(x)=2x−1x+1f−1(x)=x+12x−1
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c) f−1(x)=x−2x+1f−1(x)=x+1x−2
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d) f−1(x)=x+1x−2f−1(x)=x−2x+1
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e) f−1(x)=2x−1x−1f−1(x)=x−12x−1
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11. Find the vertex of the parabola f(x)=x2−6x+10f(x)=x2−6x+10.
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a) (3, 1)
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,b) (-3, 37)
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c) (3, -1)
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d) (-3, -5)
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e) (6, 10)
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12. Find the discriminant of the quadratic equation 2x2+3x−4=02x2+3x−4=0 and determ
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ine the nature of its roots.
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a) 41; Two distinct real roots
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b) -23; Two complex roots
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c) 9; Two rational real roots
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d) 41; One real root
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e) -23; No real roots (two complex roots)
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13. Solve the quadratic equation x2−4x−3=0x2−4x−3=0 by completing the square.
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a) x=2±7x=2±7
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b) x=−2±7x=−2±7
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c) x=2±11x=2±11
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d) x=4±13x=4±13
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e) x=2±3x=2±3
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14. A ball is thrown upward with an initial velocity of 48 ft/sec. Its height in feet after tt s
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econds is given by h(t)=−16t2+48t+5h(t)=−16t2+48t+5. What is the maximum height rea
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ched by the ball? sd sd sd




a) 41 feet
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b) 5 feet
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c) 77 feet
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d) 29 feet
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e) 53 feet
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15. Which of the following is a factor of 2x3−3x2−8x+122x3−3x2−8x+12?
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a) x+2x+2
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b) x−3x−3
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c) x−2x−2
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d) x+4x+4
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e) 2x−32x−3
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16. What is the sum of the roots of the polynomial 3x3−6x2+5x−9=03x3−6x2+5x−9=0?
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a) 2
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b) -2
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c) 5335
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d) -5335
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e) 3
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, 17. Solve for xx: 2x+5−x−2=32x+5−x−2=3.
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a) x=2x=2
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b) x=11x=11
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c) x=6x=6
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d) x=2x=2 and x=11x=11
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e) No real solution
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18. Simplify the complex fraction: xy−yx1y+1xy1+x1yx−xy.
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a) x−yx−y
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b) x−yx+yx+yx−y
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c) x+yx+y
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d) x2−y2x+yx+yx2−y2
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e) y−xy−x
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19. Solve the rational equation: xx−2+2x+2=8x2−4x−2x+x+22=x2−48.
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a) x=−2x=−2
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b) x=4x=4
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c) x=2x=2
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d) x=6x=6
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e) No solution
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20. Solve the inequality x2−4x>0x2−4x>0.
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a) (0, 4)
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b) (-∞, 0) ∪ (4, ∞)
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c) (-∞, 0] ∪ [4, ∞)
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d) [0, 4]
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e) (4, ∞)
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21. If ln⁡(x)=2.5ln(x)=2.5, what is the value of xx?
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a) e2.5e2.5
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b) 2.5e2.5e
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c) 102.5102.5
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d) 2.5×102.5×10
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e) log⁡(2.5)log(2.5)
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22. Simplify the expression: log⁡2(32)−log⁡2(4)log2(32)−log2(4).
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a) 8
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b) 3
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c) 28
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d) 2
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e) 4
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23. Solve for xx: e3x=15e3x=15.
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a) x=ln⁡153x=3ln15
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