1. 4TH QUARTER PERIODIC TEST
REVIEW IN MATHEMATICS III

2. QUESTION 1
 Find the equation of the circle in general form with
center (7, -4) and radius length 7.
x2 + y2 - 14x + 8y + 16 = 0

3. QUESTION 2
 Determine the center and the radius of the circle
x2 + y2 - 6y - 12x = -20.
C(6, 3), r = 5

4. QUESTION 3
 Find the equation of a circle in standard form
tangent to the circle x2 + y2 = 4 and with center at
(0, 5).
x2 + (y - 5)2 = 9

5. QUESTION 4
 What polynomial will have a quotient of 3x3 -2x2 - 3x + 2
when divided by 2x + 3.
6x4 + 5x3 - 12x2 – 5x + 6

6. QUESTION 5
 Find the remainder when 2x300 - 7x201 + 3x105 + 4 is
divided by x + 1.
10

7. QUESTION 6
 If x3 + Px2 + Qx -105 is divisible by both x + 5 and
x - 3, find the values of P and Q.
P = 9 and Q = -1

8. QUESTION 8
 If x2 – 3x + 1 is divided by x + 2m, the remainder is
-1, what is m?
m = -5/2 and 1

9. QUESTION 9
 When 9x3 + Ax2 – 9x + 5 is divided by 3x + 2, the
quotient is 3x2 + Bx – 1 and the remainder is 7. Find
the values of A and B.
A = -3 and B = -3

10. QUESTION 10
 Find all the real zeros of P(x) = 2x3 + 3x2 - 8x + 3.
Zeros: {-3, 1, and 1/2}

11. QUESTION 11
 Express in logarithmic form:

12. QUESTION 12
 Evaluate:

13. QUESTION 13
 Express in expanded form:

14. QUESTION 14
 Solve for x:

15. QUESTION 15
 Eric invests P2,500 at 10.5% annual interest
compounded monthly. How many years will it take
his money to double in value?

16. QUESTION 16
 Under ideal conditions a certain bacteria
population doubles every three hours. Initially
there are 2,000 bacteria in a colony.
a. Find a model for the bacteria population after t hours.
b. How many bacteria are in the colony after 30 hours?
c. When will the bacteria count reach 160,000?