## Sunday, October 3, 2010

### 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?

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