Grade 10 2nd Quarter Exam

Republic of the Philippines
Department of Education
REGION VII, CENTRAL VISAYAS
SCHOOLS DIVISION OFFICE OF DANAO CITY
D.T. DURANO MEMORIAL INTEGRATED SCHOOL
Upland National Road, Población, Danao City
2nd QUARTER TEST IN GRADE 10

SY. 2023-2024
I. Write the letter that you think best answers each of the following questions on your answer sheet.
1. What should n be if f(x) = x n defines a polynomial function?

A. an integer C. any number
B. a nonnegative integer D. any number except 0
2. Which of these polynomial functions has a leading coefficient of 6 and a constant term of -6?
A. P ( x )=2 x 6 +6 x 2−6 C. P ( x )=6 x 3−16 x 2−6 x
B. P ( x )=6 x 3−18 x 2+2 x−6 D. P ( x )=−6 x 6−12 x 2+6
3. Which of these is/are TRUE about the graph of P ( x )=( x 2−7)( 2 x−2)( x +2)?
A. it has y-intercept of 28. C. it has 5 x- intercepts
B. the end behaviour of the graph is upward both sides D. both a and b
4. A drugstore that sells a certain brand of vitamin capsule estimates that the profit P (in pesos) is given by
3 2
P ( x )=500 x +2400 x −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 C. Package C: Php 32,000.00
B. Package B: Php 16,000.00 D. Package D: Php 48,000.00
5. Your friend Rebekah asks your help in drawing a rough sketch of the graph of
y=− ( x 2+1 ) (2 x 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.
6. 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).
7. Which of the following could be the graph of y=x 4−5 x 2+ 4 ?

A. B. C. D.
8. Which polynomial function in factored form represents the given graph?
A. y=(2 x+3)¿
B. y=(2 x+3)¿
C. y=¿
D. y=−¿
9. How should the polynomial function P ( x )=15−2 x 4 +11 x 12−35 x 7 be written in standard form?
A. P ( x )=15−2 x 4 +11 x 12 −35 x 7 C. P ( x )=−2 x 4 +11 x 12−35 x 7 +15

B. P ( x )=15−2 x 4 ±35 x 7 +11 x 12 D. P ( x )=11 x 12−35 x 7−2 x 4 +15
10. You are asked to illustrate the sketch of f ( x )=x 3−3 x 5 + 4 using its properties. Which will be your
sketch?
A. B. C. D.
11. Your classmate Dave encounters difficulties in showing a sketch of the graph of
3 2
y=2 x +3 x −4 x−6.You know that the quickest technique is the Leading Coefficient Test. You want to
help Dave 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.
12. What is the measure of the central angle that subtends an arc of 50 ° ?
45 ° B. 100 ° C. 25 ° D. 50 °
A.
13. An 11 cm-diameter pizza is divided equally to 6 persons. All of these are true about the measures of the
pizza EXCEPT ____________.
A. The area and the sector is 15.83 cm2 C. each arc measures 60 °
B. The length of the arc is 5.76 cm D. the area of each triangle formed is 15.98 cm2
14. Which of the following illustrates this theorem? “The measure of an angle formed by two secants of a
circle intersecting a point in the interior of the circle is half the sum of the measures of the intercepted
arcs.”
A. B. C. c. D..
15. Referring to the circle at the right, what is the m∠ x ?

36 ° x
A. B. 54 ° C. 90 ° D. 108 °
0
108
16. An arc of a circle measures 72 ° . If the radius of the circle is 6 cm, about how long is the arc?
A. 1.884 cm B. 2.4 cm C. 3.768 cm D. 7.54 cm
17. What is the total measure of the central angles of a circle with no common interior points?
A. 480 B. 360 C. 180 D. 120
18. What is the distance between the points M (−2,−3) and N (1,5) ?
A. 17 B. √ 17 C. √ 7 D. -17
19. What is the radius of a circle whose center is at the origin and (−3, 4 ) is a point on the circle?
A. 5 B. √ −25 C. – 5 D. √ 5
20. What are the coordinates of the midpoint of a segment whose endpoints are (−4 ,−2) and (3 , 7) ?
A. (−3,−5 ) B. (3 , 5) C. (3 ,−5 ) D. (−3 ,5 )
21. What type of a triangle formed of the given points, A(−2,−4) , B(2 ,−1 ) and C (8 ,−9) ?
A. equiangular B. equilateral C. scalene D. isosceles
22. What figure is formed when the points A(11,1) , B(0 , 0) ,C (−1,−3) and D(10 ,−2) are connected
consecutively?
A. parallelogram B. rectangle C. square D. trapezoid
23. Which of the following illustrates a center-radius form of the equation of a circle?
2 2
A. x 2 + y 2 −4 x+6 y+2=0 C. ( x +2 ) + ( y −3 ) =9
x −x 1 )2 + ( y 2 − y 1 ) 2
B. ( 2 D. x 2 + y 2 =0
24. In center-radius form, what is the equation of the circle centered at (h,k)?
A. x 2 + y 2 =0 2 2
C. h +k =r
2
( x−h )2 + ( y−k )2 =r 2 2 2
D. ( x +2 ) + ( y −3 ) =9
B.
25. A radius of a circle has endpoints (5 , 2) and (−2 ,6 ) . What is the equation that defines the circle if its
center is at the second quadrant?
2 2 2 2
A. ( x−5 ) +( y −2) =65 C. ( x+ 5) +( y−2 ) =65
2 2 2 2
B. ( x+ 2) +( y−6 ) =65 D. ( x−2 ) +( y −6 ) =65
26. A circular garden of radius 10m has its center in the third quadrant and is tangent to the y-axis at (0, -1).
What is the equation of the circle?
2 2 2 2
A. ( x+10) +( y +1) =100 C. ( x+10) +( y +1) =10
2 2 2 2
B. ( x−10 ) +( y −1) =100 D. ( x−10 ) +( y −1) =10
II. Identification. Identify each statement and write the answer on your answer sheet.
1. It is an angle whose vertex is on a circle and whose sides contain chords of the circle.
2. It is an arc measuring one-half the circumference of a circle.
3. An arc of a circle whose measure is greater than that of a semicircle.
4. An arc of a circle whose measure is less than that of a semicircle.
5. The region bounded by an arc and a segment joining its endpoints.
6. The region bounded by an arc of the circle and the two radii to the endpoints of the arc.
7. An arc that lies in the interior of an inscribed angle and has endpoints on the angle.
8. An angle formed by two rays whose vertex is the center of the circle.
9. A line that intersects a circle at exactly two points.
10. A line coplanar with the circle and intersects it at one and only one point.
III. Performance Task:
Graph the circle on a coordinate plane whose center and radius are (2, -3) and 4 respectively. Then
give the general equation of a circle in proper procedure.
RUBRIC FOR THE GRAPH AND EQUATION FORMULATED

SCORE DESCRIPTORS
4 Both graph and equation are correctly made.
3 Either from the graph or equation is wrong.
1 Both graph and equation are wrong.

Grade 10 2nd Quarter Exam

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Republic of the Philippines

2nd QUARTER TEST IN GRADE 10

1. What should n be if f(x) = x n defines a polynomial function?

7. Which of the following could be the graph of y=x 4−5 x 2+ 4 ?

A. P ( x )=15−2 x 4 +11 x 12 −35 x 7 C. P ( x )=−2 x 4 +11 x 12−35 x 7 +15

15. Referring to the circle at the right, what is the m∠ x ?

RUBRIC FOR THE GRAPH AND EQUATION FORMULATED

4 Both graph and equation are correctly made.

3 Either from the graph or equation is wrong.

1 Both graph and equation are wrong.

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