Math final

MA-119 Final Examination (A) Spring 2020

Name:_______________________________________________________Section:___________ SHOW ALL WORK! Questions 1 to 18 are 5 points each. Question 19 is 10 points.

1. Solve for x:

log27 x = 2

3

2. Write the domain of the following function using interval notation.

𝑓(𝑥) = √2𝑥 + 6

3. Simplify completely: 5

𝑥2 −

1

𝑥 25

𝑥2 − 1

4. Solve for x:

√6𝑥 + 22 − 1 = 𝑥

SHOW ALL WORK! Page 2

5. Factor completely:

2𝑎𝑥 − 2𝑏𝑥 − 7𝑎𝑦 + 7𝑏𝑦

6. Find the solution set for the equation: |2𝑥 + 9 | − 5 = 22

7. Rationalize the denominator. Simplify, if possible. 2

2 − √2

8. Graph the solution set of the inequality and write the

solution using interval notation:

−3 ≤ 2𝑥 − 4

5 < 2

Name:_______________________________________________________Section:___________

Page 3

9. Solve the quadratic equation by completing the

square. 𝑥2 − 4𝑥 − 7 = 0

10. Simplify completely and express in terms of positive

exponents: 3

34

33 −

−

−

 

  



yx

yx

11. Solve for x to the nearest hundredth:

3𝑥 = 38

12. Simplify and express in bia + form:

(2 − 5𝑖)2

SHOW ALL WORK! Page 4 13. Factor completely: 𝑥3𝑦 − 27𝑦4

14. Solve the following system of equations

𝑥 + 8𝑦 = −15 5𝑥 − 6𝑦 = 17

15. Solve the rational equation for x : 20

𝑥2 − 16 =

3

𝑥 − 4 −

1

𝑥 + 4

Name:_______________________________________________________Section:___________

Page 5

16. Find an equation for the line that is perpendicular to the line 6𝑥 + 2𝑦 = 3.

17. Mike invests $5,000 at 6.1% annual interest compounded monthly. Using the formula:

nt

n

r PA 



  

 += 1 , finf the

value of the investment in 8 years.

18. A rectangular garden whose length is 7 feet longer than its width has an area of 57 square feet. Find the width of

the garden to the nearest tenth of a foot.

SHOW ALL WORK! Page 6 19. For the function 𝑦 = 𝑥2 + 4𝑥 − 5, a) Determine the coordinates of the x-intercepts.

b) Determine the coordinates of the y-intercept.

c) Determine the equation of the axis of symmetry.

d) Determine the coordinates of the vertex.

e) Graph the function, and label and indicate an appropriate scale on the axes.