### Mechanical Engineering Board Exam Reviewer: Algebra, Mathematics, Computation Part 1

Here’s a set of question on the topic Mathematics, specifically on Algebra. These questions are similar to those coming out of the board exam.

1. Which of the following is the solution set of the equation x^2-2x-15 = 0
a. (3, -5)
b. (5, -3)
c. (15, -1)
d. (-15, 1)

2. The next term in the progression 2, 8, 32, 128 is …
a. 128
b. 256
c. 512
d. 1024

3. Solve for x in the equation 3 lnx = 8
a. e^ (8/3)
b. e^ (3/8)
c. e^ (4/3)
d. e^ (3/4)

4. If x + y = 1 and x^2+y^2=2. Find x^4+y^4
a. ½
b. 3/4
c. 15/4
d. 7/2

5. If lnx=5 and lny=2, lnx3/lnx4
a. 10/3
b. 15/8
c. 125/16
d. 5/2

6. Joan can type the whole document in 3 hrs. On the other hand, James, being new to the job can type the same document in 5 hours. If they work together, how long can they finish 2 documents?
a. 3 hrs
b. 3.5 hrs
c. 2.75 hrs
d. 3.75 hrs

7. Three numbers are in the ratio 1: 2: 4. Find the numbers if their sum is 42.
a. 6, 12, 24
b. 4, 12, 36
c. 4, 16, 22
d. 3, 15, 24

8. Find the sum of the coefficients in the expansion of (5x-4)^5
a. 32768
b. 25
c. 243
d. 32

9. Evaluate the expression log 3+ log 2+ 4log7
a. 9.58
b. 4.79
c. 3.43
d. 4.16

10. The sum of an infinite geometric progression is 3 and the common ratio is 1/3. What is the first term?
a. 3
b. 2
c. 1
d. 6

Note: If you noticed a question with no correct answer in the option or the question itself seems to be erroneous, I would appreciate if you can send me an email or comment below. Computation-type review questions are very hard to do and requires extensive validation. I would appreciate any help for the improvement of this blog. Thanks!

1. Thanks was just searching for that kind of evaluations

2. Thanks for the provided test. Assuming algebra isn't the most challenging course in college? Isn't too hard for students?

3. Thanks for the shared set of questions on the topic. This kind of information is useful and helpful for academic students.

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### BOARD EXAM TIP: Which Review Center?

First of all, I would like to apologize for a long time I haven't posted anything but introduction. The reason for that is I'm busy optimizing the design of this site. I'm hoping that the make over is good. Anyway, I would like to dedicate this article to those who are going to take/retake the board exam this coming October. My sincere wish that you bring out the best among yourselves and may the deserving ones pass the exam. Going back to the One-Million-Peso worth question: "Which review center should I enroll?" , I would like to answer that in the most unbiased way I can. Of course, I'm only human and I had also my preferences but I will try my best to hide it. To start with I will enumerate some of the prominent review centers that offer board exam reviews for mechanical engineering in the Philippines. 1. Alcorcon (Cebu & Manila) 2. Excel (Cebu & Manila) 3. Linx Engineering (Manila) 4. MERIT (Manila) 5. PRIME (Cebu) 6. RLB's

### SOLUTION TO MECHANICAL BOARD EXAM PROBLEMS: Power Set-1

Here are the solutions to board problems given at Power Subject Set-1. If you do not understand anything, feel free to write a comment voicing out your concern. I'm still looking for better ways to present my solution. I still don't know how to present equations and mathematical symbols with blogger. Please bear with me. 1. An automobile tire is inflated to 32psig pressure at 50 degree F. After being driven, the temperature rises to 75 degree F. Determine the final gage pressure assuming the volume remains constant. (Electrical Engineering Board Exam Problem) Solution: Since volume is constant, use Charles’ Law on constant volume processes. P1/T1=P2/T2 Note: P and T should be absolute. (32+14.7)/ (50+460) =P2/ (75+460) P2=48.99 psia Converting back to gage pressure, P2g=48.99-14.7 P2g=34.29 psig 2. Four hundred cubic centimeters of gas at a pressure of 740 mmHg absolute and temperature of 18 degree C undergoes a process until the pressure and temperature be

### PAST MECHANICAL BOARD EXAM QUESTION: Machine Design Set-1 (solutions and answers)

The following are the solutions and answers to MODIFIED PAST MECHANICAL BOARD EXAM QUESTION: Machine Design Set-1 posted on this blog last Saturday, November 14, 2009. Again, I want to stress out that most of the questions here are modified from its original form for the purpose of improving the question. Past Mechanical Engineering Board Exam Question Number 1 A 4 inches diameter short shaft carrying 2 pulleys close to the bearings transmits how much horsepower if the shaft makes 120 rpm. A.200HP               B. 199 HP C.198 HP               D. 202 HP P = (D3N )/38 -- for mula for short shafts from PSME code P = (4)3(120)/38 P= 202 HP Past Mechanical Engineering Board Exam Question Number 2 An instrument that measures the hardness of the work piece in terms of elasticity. a. Durometer b. Scleroscope c. Mohs's Scale d. Brinell Tester Source: Machinery’s Handbook