Monday, April 23, 2012

Question 6


6. Three numbers are in the ratio 2:5:8. If their sum is 60, find the smallest of the numbers.

A. 8
B. 4
C. 6
D. 12

Solution:

Question 5


5. If the polynomial X3 + 4X2-3X+8 is divided by X-5, the remainder is:

A. 175
B. 218
C. 140
D. 200

Solution: Synthetic Division


Question 4

4. If I just sold my two books at P990 each, and on one I gained 10% and on the other I lost 10%, then:

A. I lost P20
B. I gained P198
C. I gained P19.8
D. None of these

Book 1:






Book 2:



Question 3


3. Two students were solving a problem that would reduce it to a quadratic equation. The first student committed an error in the constant term and found the roots to be 5 and 7 while the second student made an error in the first degree term and gave the roots as 2 and 16. If you were to check their solutions, the right equation is:

A. X2 + 12X + 35 = 0
B. X2 + 7X -14 = 0
C. X2 + 18X +32 = 0
D. X2 - 12X +32 = 0

Solution:

1st student’s equation: 

2nd student’s equation:

Therefore, the right equation is :  

Question 2

2. If (5X-3), (X+2) and (3X-11) form an arithmetic progression, find the fifteenth term.


A. -86
B. -79
C. -81
D. -84

Solution:

The formula to find the nth term of an arithmetic progression is:



Where:
an = nth term
a1 = 1st term
n = number of terms
d = difference

In an arithmetic progression, the difference between any two consecutive terms is always the same. Therefore:





Solving for d gives:

 Substituting this into the formula gives:


Question 1


1. A rubber ball is dropped from a height of 15 meters. On each rebound, it rises 2/3 of the height from which it last fell. Find the distance traversed by the ball before it comes to rest. The geometric progression occurs after the first rebound.

A. 96 m
B. 85 m
C. 100 m
D. 75 m

Solution:

It is an infinite geometric series problem that starts after the first rebound. The Formula used is:



Where:
S = sum of the geometric progression
a = starting number
r = common ratio



The result is multiplied by 2 since the ball must travel upwards and downwards.


And finally, the initial drop of the ball, which is 15 meters is added to the result which gives: