This document appears to be a summative test for a 10th grade mathematics class covering topics in polynomials and geometry. It contains 45 multiple choice questions testing students' understanding of polynomial functions, properties of circles, coordinate geometry, and solving geometric problems using coordinates. The test includes questions on identifying the degree and leading term of polynomials, graphing polynomial functions, properties of secants, tangents, and circles, finding distances and areas using coordinates, and identifying geometric shapes from their vertices.

1. SECOND QUARTER SUMMATIVE TEST
GRADE 10 – MATHEMATICS
Name:___________________________________________ Section: ______________________Score:_____________
Directions: Readthe questions carefully. Choose the letter
of the correct answer. Answer the following problems.
Show your solutions on a separate sheet of paper.
1. Which of the following could be the value of n in the
question 𝑓(𝑥) = 𝑥𝑛𝑖𝑓 𝑓 𝑖𝑠 𝑎 𝑝𝑜𝑙𝑦𝑛𝑖𝑚𝑖𝑎𝑙 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛?
a. -3
b. 0
c. 1
2
⁄
d. √5
2. Which of the following is NOT a polynomial function?
a. 𝑓(𝑥) = π
b. 𝑓(𝑥) = −
2
3
𝑥3 + 1
c. 𝑓(𝑥) = −x + √5𝑥3
d. 𝑓(𝑥) = 𝑥
1
5 − 2𝑥2
3. In the polynomial function 𝑓(𝑥) = 6𝑥3 + 7𝑥4 + 10 +
4𝑥2 − 3𝑥, what is the leading coefficient?
a. 7
b. 6
c. 4
d. 3
4. The graph of 𝑝(𝑥) = (𝑥 + 1)(2𝑥 − 3)(𝑥 + 2) crosses
the x-axis _________.
a. once
b. twice
c. trice
d. four times
5. What is the degree of the polynomial function defined
by 𝑓(𝑥) = 3𝑥𝑛−2 + 2𝑥3𝑛−5 − 4𝑥2𝑛+1 𝑖𝑓 𝑛 = 3?
a. 10
b. 7
c. 3
d. 1
6. How should the polynomial function
𝑓(𝑥) =
1
2
𝑥 − 𝑥2 + 11𝑥4 + 2𝑥3 be written in standard
form?
a. 𝑓(𝑥) = 11𝑥4 + 2𝑥3 +
1
2
𝑥 − 𝑥2
c. 𝑓(𝑥) = 11𝑥4 + 2𝑥3 − 𝑥2 +
1
2
𝑥
b. 𝑓(𝑥) = −𝑥2 +
1
2
𝑥 + 2𝑥3 + 11𝑥4
d. 𝑓(𝑥) =
1
2
𝑥 − 𝑥2 + +2𝑥3 + 11𝑥4
7. Which polynomial function in factored form represents
the given graph?
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)
8. Which of the following should be the graph of a
𝑦 = 𝑥4 − 5𝑥2 + 4?
9. Given that 𝑓(𝑥) = 7𝑥−3𝑛 + 𝑥2, what value should be
assigned to n to make f a function of degree 7?
a. −
7
3
b. −
3
7
c.
3
7
d.
7
3
10. Your friend Myrna asks your help in drawing a rough
sketch of the graph of 𝑦 = −(𝑥2 + 1)(2𝑥4 − 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.
11. Consider this revenue-advertising expense situation.
A drugstore that sells a certain brand of vitamin capsule
estimates that the profit in (in pesos) is given by 𝑃 =
−50𝑥3 + 2400𝑥2 − 2000, 0 ≤ 𝑥 ≤ 32 where x is the
amount spent on advertising (in thousands of pesos). An
advertising agency provides four (4) different advertising
packages with costs listed below. Which of these
packages will yield the highest revenue for the company?
a. package A : Php 8,000.00
b. package B : 16,000.00
c. Package C : 32,000.00
d. Package D : 48,000.00
12. A car manufacturer determines that its profit, P, in
thousands of pesos can be modeled by the function
𝑃(𝑥) = 0.00125𝑥4 + 𝑥 − 3 where x represents the
number of cars sold. What is the profit at x = 150?
a. Php 75.28
b. Php 632,959.50
c. Php 3,000,000.00
d. Php 10, 125,297.00
13. A demographer predicts that the population, P, of a
town t year from now can be modeled by the function
𝑃(𝑡) = 6𝑡4 − 5𝑡3 + 200𝑡 + 12,000. What will the
population of the town be two (2) years from now?
a. 12, 456 c. 1, 245, 600
b. 124, 560 d. 12, 456, 000

2. 14. A gymnast dismounts the uneven parallel bars. Her
height, h, depends on the time, t, that she is in the air as
follows: ℎ = −16𝑡2 + 8𝑡 + 8. When will the gymnast be
8 feet above the round?
a.
1
2
b. 1
c. 2
d. 4
15. The dimensions of a pool: height = x – 2, length = 2x
+ 5 meters,and width = 2x – 1 meter. If the volume of the
pool is 182 cubic meters, what is the value of x?
a. 1
b. 2
c. 3
d. 4
16. If an inscribed angle of a circle intercepts a semicircle,
then the angle is _____________.
a. acute
b. right
c. obtuse
d. straight
17. It is a region bounded by an arc and the segment
joining its endpoints.
a. arc length
b. sector of a circle
c. segment of a circle
d. semicircle
18. It is an arc of a circle greater than a semicircle.
a. arc length
b. minor arc
c. major arc
d. obtuse arc
19. If two inscribed angles of a circle intercept congruent
arcs or the same arc,then the angles are ____________.
a. complementary
b. congruent
c. overlapping
d. supplementary
20. What do you call a line segment whose endpoints are
on the circle and its twice the length of the radius?
a. angle
b. chord
c. diameter
d. radii
21. The sum of the opposite angles of an inscribed
quadrilateral is ___________?
a. 900
b. 1200
c. 1500
d. 1800
22. If line segment AD is a diameter of circle R and
m∠𝐴𝐷𝑆 = 350, find m∠SAD.
a. 480
b. 490
c. 500
d. 550
23. In the figure on the right, which of the following
angles is an inscribed angle?
a. ∠UXV
b. ∠UXW
c. ∠XWY
d. ∠VWY
24. In circle Ron the right, whatis ∠QSTif ∠QRT= 1200
.
a. 500
b. 600
c. 700
d. 800
25. In the figure on the right, ∠XYZ = 800
and
∠XZY = 550
, what is the measure of line segment YZ?
a.900
b. 1000
c. 1100
d. 1200
26. The line and circle intersect; the point of intersection
is called?
a. point of secant
b. point of tangency
c. point of view
d. point of line
27. Which of the following statement is TRUE?
a. The secant of a circle is its center point.
b. A secant of a circle intersects the circle’s edge
at two points.
c. A tangent of a circle intersects the circle’s edge
at two points.
d. A secant of a circle intersects the circle’s edge
at one point only.
28. In the figure, MS is a segment of the circle
called______.
a. diameter
b. tangent
c. segment
d. secant
29. Which of the following illustrates a tangent line?
a. Line that intersects the circle at three points.
b. Line that intersects a circle at only one point.
c. Interesting line segment joining the center of the circle.
d. Line that passes through the center to any point of the
circle.

3. 30. Which of the following phrase is TRUE about secant
line?
a. never intersects the circle.
c. the center to nay point of the circle.
b. intersects the circle at two points.
d. intersects the circle at exactly one point.
31. Which are the steps to follow in finding he area of the
segment of the circle?
I. Find the area on the circle.
II. Determine the ratio of the circle.
III. Subtract the area of the triangle to the area of the
sector.
IV. Identify the given measure of an arc and the radius of
the circle.
a. IV, I, II, III
b. I, II, III, IV
c. IV, II, I III
d. II, IV, I, III
32. The segment of a circle is the region bounded by an
arc and the segment joining endpoints. In the figure
below, which of the following is considered the segment
of a circle?
a. segment AC
b. segment ES
c. segment SC
d. segment AB
33. It is a line segment that goes from one point to another
on the circle’s circumference.
a. chord c. secant
b. diameter d. tangent
33. Which of the following statement is TRUE about
sector of a circle?
a. Region bounded by intersecting lines the circles.
b. Region bounded by an arc 180 degrees in measures.
c. Region of the circle bounded by an arc and the segment
joining endpoints.
d. Region bounded by an arc of the circle and the two radii
to the endpoints.
34. It is a region of the circle bounded by an arc and the
segment joining endpoints.
a. segment of a circle c. radius
b. sector of a circle d. tangent
35. Which of the following phrase is TRUE about secant
line?
a. never intersects the circle.
c. the center to nay point of the circle.
b. intersects the circle at two points
d. intersects the circle at exactly one point.
36. If the measure of angle CXI is 1400
, what is the
measure of angle CXO?
a. 400
b. 450
c. 500
d. 900
For items numbers 37 – 29 refer to Figure 2
37. Inscribed angle BDC measures 300
, What is the
measure of angle EDC?
a. 450
b. 500
c. 750
d. 900
38. What is the measure of the intercepted arc of an
inscribed angle C?
a. 3x c. 3x + 1
b. 6x d. 3x + 2
39. Angle EFB measure 1500
. What is the measure of
inscribed angel C?
a. 150
c. 250
b. 200
d. 300
40. Refer to figure 3. What is the area of a segment of a
circle?
a. 4.36 cm2
b. 4.56 cm2
c. 4.66 cm2
d. 4.76 cm2
.
41. What is the distance between points D (-10 , 2) and
E (6 , 10)
a. 16
b. 20
c. 10√2
d. 8√5
42. A map is drawn on a grid where 1 unit is equivalent
to 2 km. On the same map, the coordinates of the point
corresponding to San Rafael is (1 , 4). Suppose San
Quintin is 20 km away from San Rafael. Which of the
following of the following could be the coordinates of the
point corresponding to san Rafael?
a. (17 , 6) c. (9 , 10)
b. (17 , 10) d. (-15 , 16)
43. What figure is formed when the points K (-2 , 10) ,
L(8 , 8) , M (6 , 2) and (-4 , 4) are connected
consecutively?
a. trapezoid
b. parallelogram
c. square
d. rectangle
44. The coordinates of the vertices of a rectangle are W (-
2 , 6) , I (10 , 6) , N (10 , -3) , and D (-2 , -3). What is the
length of a diagonal of the rectangle?
a. 15 b. 12
c. 9 d. 7.5
45. What proof uses figures on a coordinate plane to prove
geometric properties?
a. indirect proof
b. direct proof
c. coordinate proof
d. two-column proof