QUARTER I COMPETENCIES Generates Patterns Nth Terms, Means, and Series of Arithmetic Sequence Nth Terms, Means, and Series of Geometric Sequence Problems Involving Sequences Division of Polynomials, Remainder Theorem, and Factor Theorem Polynomial Equations Problems Involving Polynomials and Polynomial Equations
What is the fifth term of the sequence defined by ? B. C. D. Solution: = = =
2. What is the sum of the first consecutive positive integers? B. C. D. Solution: = =
3. What is the result when is divided by ? A. C. B. D. Solution:
4. Which of the following is a positive geometric mean of 16 and 81? B. C. D. Solution:
5. What is the remainder when is divided by ? A. 1 B. 2 C. 3 D. 4 Solution: By remainder theorem, where a is from the dividend x-a. = 2
6. What is the arithmetic mean of and ? B. C. D. Solution:
7. The first term of a geometric sequence is 5, and the second term is 10, what is the sixth term? A. 160 B. 80 C. 320 D. 640 Solution:
8. A mine worker discovers an ore sample containing of radioactive material. It was discovered that the radioactive material has a half life of day. About how much of the radioactive material will be present after days? B. C. D. Solution: = ; = = = ( =
9. A pile of blocks has blocks in the bottom row, blocks in the second row, blocks in the third row and so on until there are only blocks on the top. How many blocks are in the row? B. C. D. Solution:
10. What are the rational zeros of ? B. C. D. Solution: Factors
ADDITIONAL PROBLEMS
11. What is the sum of the first terms of a geometric sequence ? B. C. D.
12. What is the sum, if it exists, of the geometric series ? A. B. C. D.
13. An appropriate formula for the intensity of the light , in lumens that the fireflies produce is given by the formula , where represents the temperature in degree Celsius. What is the intensity of the light emitted by a firefly when the temperature is ? B. C. D.
14. What is the value of if ( ) is divided by having a remainder of ? B. C. D.