MATH 107 EXAM

MATH 107 Final Exam UMGC

Spring 2021

1. $1000 is invested in account which offers 1.25%, compounded continuously.

Determine how much is in the account after a) 5 years, b) 10 years, c) 30 years,

and d) 35 years. Round to the nearest cent.

2. Solve the equation: 𝑙𝑜𝑔5(18 − 𝑥 2) = 𝑙𝑜𝑔5(6 − 𝑥).

3. For 𝑓(𝑥) = 4 − 𝑥; 𝑔(𝑥) = 1 − 𝑥2 𝑓𝑖𝑛𝑑: 𝑎) (𝑔 ∘ 𝑓)(−3); 𝑏) (𝑓 ∘ 𝑔) ( 1

2 ) .

4. If possible, find the inverse of 𝑓(𝑥) = 𝑥−2

3 + 4.

5. Find all real solutions for: −𝑦3+4𝑦

𝑦2−9 = 4𝑦.

6. Solve the rational inequality. Express your answer using interval notation; 4𝑥

𝑥2+4 ≥ 0.

7. Find all real solutions for: 3(𝑦2 − 3)2 − 2 = 10.

8. Use the give complex numbers for: 𝑎) 𝑧𝑧 ; 𝑏) 𝑤

𝑧 ∶∷ 𝑧 = 4𝑖, 𝑤 = 2 − 2𝑖.

9. a) Find x- and y- intercepts, if they exist; b) Determine the domain and range; c)

List the intervals on which the function is increasing, decreasing or constant for:

𝑓(𝑥) = |𝑥+4|

𝑥+4 .

10. a) Find the point-slope form and b) the slope-intercept form of the line with

the given slope and passing through the given point: 𝑚 = 2

3 , 𝑃(−2, 1).

Instructions: Please ensure you submit a version that I can read, (pdf, jpeg, doc,

png are readable for me.) Ensure you show your work if you wish to receive

partial credit.

Good luck to each of you.

Dr. Barnes