STA. IRENE NATIONAL HIGH SCHOOL
Sta. Irene, Prosperidad, Agusan del Sur
Prelim Exam in Math 10
Second Quarter
Name: __________________________________________Section: _________________Score:__________________
“Be honest, even if others are not, even if others will not, even if others cannot. He who walks honestly, walks
securely.” Abhishek Tiwari
Part I. True or False.
Directions: Read each statement carefully and identify whether true or false. Write “HONOR” if the
statement is true. If the statement is false, write “HORROR”.
1. The degree of the polynomial is the largest power on any x term in the polynomial.
2. Every polynomial equation of degree 𝑛 has 𝑛 − 1 real roots.
3. The function ƒ(𝑥) = 𝑥 3 + 2𝑥 2 − 4𝑥 + 3 has four real zeros.
4. The roots of a polynomial equation in x are the values of x that satisfy the equation.
5. The function ƒ(𝑥) = 𝑥 3 + 3𝑥 2 + 3𝑥 + 1 must have at least one real zero.
6. A root can have a multiplicity of 0.
7. The equation 2𝑥 3 − 6𝑥 2 + 𝑥 − 1 = 0 has no rational roots.
8. Using Rational Root Theorem, the possible roots of 3𝑥 5 − 𝑥 4 + 6𝑥 3 − 2𝑥 2 + 8𝑥 − 5 = 0
3
are ± 5 , ±3, and ± 5.
10
9. The only rational root of the equation 𝑥 3 + 6𝑥 2 + 10𝑥 + 3 = 0 is 3.
10. The end behavior of a polynomial equation can be determined by the sign of the constant
term and degree of the polynomial function.
Part II. Multiple Choice
Directions: Read each question carefully and write the letter of the correct answer.
11. Which of the following is NOT true about the polynomial equation below?
𝑦 = 2𝑥 5 + 3𝑥 4 − 14𝑥 3 − 21𝑥 2
A. The polynomial is written in standard form.
B. It is a quintic – a 5th degree polynomial.
C. The leading coefficient is 2.
D. The constant term is −21.
12. Which of the following is NOT a polynomial function?
2
A. 𝑓(𝑥) = 𝜋
C. 𝑓(𝑥) = − 3 𝑥 3 + 1
1
B. 𝑓(𝑥) = −𝑥 + √5𝑥 3
D. 𝑓(𝑥) = 𝑥 5 − 2𝑥 2
13. What should 𝑛 be if 𝑓(𝑥) = 𝑥 𝑛 defines a polynomial function?
A. an integerB. a nonnegative integer C. any number except 0
D. Any number
14. Which of the following could be the value of 𝑛 in the equation 𝑓(𝑥) = 𝑥 𝑛 if 𝑓(𝑥) is a
polynomial function?
A. -2
B. 0
C. 1/4
D. √3
9
8
5
3
15. What is the leading coefficient of the polynomial 5𝑥 + 4𝑥 + 3𝑥 + 2𝑥 + 𝑥?
A. 3
B. 5
C. 8
D. 9
2 (2𝑥
2 (𝑥 2
16. Given 𝑓(𝑥) = 10𝑥
− 3)
+ 3), what is the multiplicity of 𝑥 = 0?
A. 10
B. 3
C. 2
D. 0
4
3
2
17. What is a factored form of 𝑃(𝑥) = 𝑥 + 𝑥 + 𝑥 + 𝑥?
A. 𝑃(𝑥) = 𝑥(𝑥 + 1)(𝑥 2 + 1)
C. 𝑃(𝑥) = 𝑥(𝑥 − 1)(𝑥 2 + 1)
B. 𝑃(𝑥) = 𝑥(1)(𝑥 2 + 1)
D. 𝑃(𝑥) = 𝑥(−1)(𝑥 2 + 1)
18. Which of the following is/are NOT a root of 𝑥(𝑥 + 3)(𝑥 + 3)(𝑥 − 1)(2𝑥 + 1) = 0?
A. 0
B. -3
C. -1
D. ½
19. Which of the following cubic polynomial equations has roots −2, 2, and 4?
A. 𝑥 3 + 4𝑥 2 − 4𝑥 + 16 = 0
C. 10𝑥 3 − 𝑥 2 − 𝑥 + 16 = 0
B. 𝑥 3 − 4𝑥 2 − 𝑥 + 16 = 0
D. 𝑥 3 − 4𝑥 2 − 4𝑥 + 16 = 0
20. How many positive real roots does 𝑥 4 − 𝑥 3 − 11𝑥 2 + 9𝑥 + 18 = 0 have?
A. 0
B. 1
C. 2
D. 3
3
2
21. One of the roots of the polynomial equation 2𝑥 + 9𝑥 − 33𝑥 + 14 = 0 is 2. Find the other
roots.
A. 1/2 and 7
B. -1/2 and 7
C. 1/2 and -7
D. -1/2 and -7
3
5
22. How should the polynomial function 𝑓(𝑥) = 2𝑥 + 𝑥 + 3𝑥 + 4 be written in standard form?
A. 𝑓(𝑥) = 𝑥 3 + 2𝑥 + 3𝑥 5 + 4
C. 𝑓(𝑥) = 4 + 2𝑥 + 𝑥 3 + 3𝑥 5
B. 𝑓(𝑥) = 4 + 3𝑥 5 + 2𝑥 + 𝑥 3
D. 𝑓(𝑥) = 3𝑥 5 + 𝑥 3 + 2𝑥 + 4
23. Which of the following function in factored form represents the
given graph at the right?
A. 𝑦 = (2𝑥 + 3)(𝑥 − 1)2
B. 𝑦 = −(2𝑥 + 3)(𝑥 − 1)2
C. 𝑦 = (2𝑥 + 3)2 (𝑥 − 1)
D. 𝑦 = −(2𝑥 + 3)2 (𝑥 − 1)
24. From the choices, which polynomial function in factored form represents the given graph?
A.
B.
C.
D.
𝑦 = (𝑥 + 2)(𝑥 + 1)(𝑥 − 1)
𝑦 = (𝑥 + 1)(𝑥 − 1)(𝑥 − 2)
𝑦 = 𝑥(𝑥 + 2)(𝑥 + 1)(𝑥 − 1)
𝑦 = 𝑥(𝑥 + 1)(𝑥 − 1)(𝑥 − 2)
25. Which of the following could be
the graph of 𝑦 = 𝑥 4 − 5𝑥 2 + 4?
26. If you will draw the graph of 𝑦 = 𝑥(𝑥 + 2)2 , how will you sketch it with respect to the x-axis?
A. Sketch it crossing both (−2,0) and (0,0).
B. Sketch it crossing (−2, 0) and tangent at (0,0).
C. Sketch it tangent at (−2,0) and crossing (0,0).
D. Sketch it tangent at both (−2,0) and (0,0).
27. Your classmate Peter encounters difficulties in showing a sketch of the graph
of 𝑦 = 2𝑥 3 + 3𝑥 2 − 4𝑥 − 6. You know that the quickest technique is the Leading Coefficient
Test. You want to help Peter in his problem. What hint/clue should you give?
A. The graph falls to the left and rises to the right.
B. The graph rises to both left and right.
C. The graph rises to the left and falls to the right.
D. The graph falls to both left and right.
28. What are the end behaviors of the graph of 𝑓(𝑥) = −2𝑥 + 𝑥 3 + 3𝑥 5 − 4?
A. Rises to the left and falls to the right
B. Falls to the left and rises to the right
C. Rises to both directions
D. Falls to both directions
29. Your friend Cocoy asks your help in drawing a rough sketch of the graph
of 𝑓(𝑥) = −(𝑥 2 + 1)(2𝑥 4 − 3) by means of the Leading Coefficient Test. How will you
explain the behavior of the graph?
A. The graph is falling to the left and rising to the right.
B. The graph is rising to both left and right.
C. The graph is rising to the left and falling to the right.
D. The graph is falling to both left and right.
30. If you will draw the graph of 𝑦 = 𝑥 2 (𝑥 − 1) how will the graph behave at the x-axis?
A. The graph crosses both (0, 0) and (1, 0).
B. The graph crosses (0, 0) and is tangent to the x-axis at (1, 0).
C. The graph crosses (1, 0) and is tangent to the x-axis at (0, 0).
D. The graph is tangent to the x-axis at both (0, 0) and (1, 0).
Part III. Matching Type
Directions: Match column A with the corresponding item in column B. Write the letter of your
answer for each number.
Column A
31. Radius
A.
32. Diameter
B.
33. Chord
C.
34. Semicircle
35. Minor arc
D.
E.
36. Major arc
F.
37. Central angle
G.
Column B
an arc of a circle that measures greater
than the semicircle
an angle whose vertex is the center of the
circle and with two radii as its sides
a segment joining any two points on the
circle
half the measure of the diameter
an arc measuring one-half the
circumference of a circle
an angle whose vertex is on a circle and
whose sides contain chords of the circle
a straight line which touches the circle at
only one point, this point is called the
point of tangency
38. Inscribed angle
39. Tangent
40. Secant
H. twice the measure of the radius and it is
the longest chord
I. a line that intersects a circle at exactly
two points
J. an arc of a circle that measures less than
the semicircle
***Test Ends Here***
GOD BLESS EVERYONE!
“The best way to predict your future is to create it.”
–Abraham Lincoln