Saturday, October 9, 2010

ME Board Reviewer: Math, Algebra, Computation (ANSWER and SOLUTION)






1. Which of the following is the solution set of the equation x2-2x-15 = 0
Solution:
Think of factors of the last digit that when subtracted gives the coefficient of the middle term
In this case, -15 can only be (3, -5), (-3, 5), (15, -1) or (-15, 1). Among these factors, (3, -5) is the only one whose sum will be equal to -3. So the solution set of the equation will be
X-5=0; x1 = 5
X+3=0; x2 = -3
Alternative Solution:
By trial and error (best when using your calculator), try each choices and see which among them when substituted to x will make the equation true, that is, x2-2x-15 equals zero.


B. (5, -3)


2. The next term in the progression 2, 8, 32, 128 is …
Solution:
The progression above is a Geometric progression since there is a common ratio (r). In this case, the common ratio is 4 and the next terms are obtained by multiplying the previous term by 4. So, next to 128 will be 128X 4 = 512


C. 512


3. Solve for x in the equation 3 lnx = 8
Solution:
Using properties of logarithm: nlna = lna^n
In this case, lnx^3=8
By making both sides an exponent of e (Euler’s number), we can cancel the ln.
e^(lnx^3)=e^8
x^ 3 = e^8
x= e^ (8/3)


A. e^ (8/3)


4. If x + y = 1 and x2+y2=2. Find x4+y4
Solution:
Squaring both sides of x+y =1 we get (x+y) ^2=1^2; x2+2xy+y2=1;
But x2+y2=2 so 2+ 2xy=1 or xy=-1/2;
Square both sides, 4x2y2=1; x2y2=1/4
Let’s square both sides of x2+y2=2; (X2+y2) ^2=2^2 then x4+2x2y2+y4 = 4;
But x2y2=1/4 so, x4+y4+2(1/4) =4
Solving the equation will give us X4 +y4 =7/2


D. 7/2


5. If lnx=5 and lny=2, lnx3/lnx4
Solution:
Using properties of logarithm; lnx3=3lnx and lny4=4lny
So lnx3/lny4 will be 3lnx/4lny = 3(5)/4(2) =15/8


B. 15/8


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?
Solution: 
rate of Joan 1/3; rate of James 1/5
Rate=no job/time time = no of job/rate
If they work together, their rate will be added
t= 2 jobs/ (1job/3hrs+1job/5hrs)
t=3.75 hours


D. 3.75 hrs


7. Three numbers are in the ratio 1: 2: 4. Find the numbers if their sum is 42.
Solution:
add the ratios 1+2+4 = 7
Divide the sum of the numbers by the sum of the ratio; 42/7=6
Multiply 6 by each ratio. The numbers will be 6, 12, and 24


A. 6, 12, 24


8. Find the sum of the coefficients in the expansion of (5x-4)^5
Solution:
To find the sum of the coefficients of an expansion, just replace the variable by 1 in the expression.
In this case, (5x-4) ^5; [(5(1)-3] ^5=32


D. 32


9. Evaluate the expression log 3+ log 2+ 4log7
Solution:
use your calculator
Note: When there’s no base mentioned, it is automatically considered to be 10.


D. 4.16


10. The sum of the infinite geometric progression is 3 and the common ratio is 1/3. What is the first term?
Solution:
For an infinite Geometric progression, the sum is given by the formula S=a1/r where S is the sum and r is the ratio.
In this case, the Sum and the ratio were given so using the formula we can get the first term.
a1=Sr; a1=9(1/3) =3


A. 3


Shortcut to questions.
Note: Writing solution to a math problem in a webpage like these is extremely difficult so I expect that some of you may be confused by the way I wrote the solution. If you have questions and clarifications, don't hesitate to send me a message at admin@tupmechanical.com or post a comment below.

6 comments:

  1. Your answer to #2 is incorrect since 32 times 4 is not 64 so the geometric ratio cannot be 4

    ReplyDelete
  2. @andrew: Thanks. Questions and answers are corrected accordingly.

    ReplyDelete
  3. @admin
    answers to #8 and #10 is incorrect..
    to #8:
    since the coefficient has constant so the formula should be : (coef.X + K)^n - (K)^n
    so the answer should be 1025
    to #10:
    the formula should be S=a1/1-r
    so the answer should be 2..

    ReplyDelete
    Replies
    1. tama ka dude..mali mali talaga toh,,,tsk2x

      Delete
  4. pakireview po ng #5,, mali kasi ang given,,Iny4 dapat...

    ReplyDelete