Division of Lanao del Norte
Division Unified Quarterly Examination
MATHEMATICS 10 - SECOND QUARTER
S.Y. 2018 – 2019
NAME: _________________________________SECTION:__________DATE:______SCORE:__________
I. MULTIPLE CHOICE: Read each item carefully and write the letter of the correct answer on the blank
provided.
______1. What should n be if f(x) = xn defines a polynomial function?
A. an integer C. all real number
B. a non-negative integer D. positive integer except 0
______2. How should the polynomial function f(x) = 2x+x3 +3x5 +4 be written in standard form?
A. f(x)= x3+2x+3x5+4 C. f(x)= 4+2x+x3+3x5
B. f(x)= 4+3x5+2x+x3 D. f(x)= 3x5+x3+2x+4
______3. Which of the following illustrates a polynomial function?
A. C.
B. D.
______4. The graph of y = x(x+2)2 is shown below, how will you describe it with respect
to the x – axis?
A. The graph crosses both (-2, 0) and (0, 0)?
B. The graph crosses (-2, 0) and is tangent at (0, 0)
C. The graph is tangent to (-2, 0) and crosses at (0, 0)
D. The graph is tangent to both (-2, 0) and (0, 0)
______5. In how many points does the graph of y = x3-4x2+x+6 intersect the x-axis?
A. one C. three
B. two D. four
For number 6-7, refer to the given figure below.
______6. Which of the following illustrates a secant to circle O?
A. C.
B. D.
______7. The shaded region in the figure is a/an
A. area of a sector of a circle C. sector of a circle
B. arc length of a circle D. segment of a circle
______8. What is the relationship of the wheels of a car to the road?
A. Wheels are secants to the road.
B. Wheels are perpendicular to the road.
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C. Wheels are tangents to the road.
D. Wheels are parallel to the road.
______9. Determine the length of side EC on the given parallelogram COME
C(1, 5) O
A.
B.
E M(6, 0)
C.
D.
______10. Which of the following represents the distance d between the two points (x1, y1) and (x2, y2) ?
A. d=
B. d=
C. d=
D. d=
______11. Which of the following equations describes a circle on the Cartesian plane with radius of 4 units?
A. (x-4)2 + (y-4)2 = 22 C. (x+2)2 - (y+2)2 = 42
B. (x-2)2 + (y-2)2 = 42 D. (x-4)2 + (y-4)2 = 162
______12. The center of the circle is (-1, 2) and its radius is 4 units. Write the equation of the circle in center-
radius form.
A. (x -1)2 + (y-2)2 = 16 C. (x + 1)2 + (y+2)2 = 16
B. (x -1)2 + (y+2)2 = 16 D. (x + 1)2 + (y-2)2 = 16
______13. What is the center of the circle defined by the equation (x -2)2 + (y+5)2 = 4?
A. (2, 5) C. (2, -5)
B. (-2, 5) D. (-2, -5)
______14. Which of the following is the equation of a circle whose radius is 5cm and whose center is at (-2, 1)?
A. x2+y2+4x+2y+20=0 C. x2+y2-4x+2y+20=0
B. x2+y2+4x-2y-20=0 D. x2+y2-4x+2y-20=0
______15. What figure is formed when points A(3, 7), B(11,10), C(11, 5), and D(3, 2) are connected?
A. parallelogram C. square
B. trapezoid D. rectangle
______16. Which of the following is the graph of the circle whose equation is (x-4)2+(y+3)2=22?
A. C.
B. D.
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______17. A demographer predicts that the population, P, of a town t years from now can be modelled by the
function .What is the present population of the town?
A. 2 000 C. 6 000
B. 4 000 D. 12 000
______18. If a population of a town is modelled by the function , how
many years from now when the population of the town will be 14 016?
A. 2 C. 4
B. 3 D. 5
______19. A prominent copra buyer determines that its profit, P, in thousands of pesos, can be modelled by the
function where x represents the number of kilos sold. Solve for the
profit at x = 100?
A. Php 75.28 C. Php 125,097.00
B. Php 12,959.50 D. Php 1,125,297.00
______20. The figure below shows a sketch of a circular children’s park and the different pathways from the
main road. If the distance from the main road to gate 2 is 40 m and the length of the pathway from
gate 2 to the exit is 50 m, about how far from the main road is gate 1?
A. 60 m
B. 75.65m
C. 90 m
D. 20 m
______21. In the figure on the right, m =150o and m =30o, what is m/XPY?
A. 60o C. 120o
B. 90o D. 180o
______22. Considering that sound waves travel in circular direction, a radio signal can transmit messages up to
a distance of 5 km. If the radio signal’s origin is located at a point whose coordinates are (-2,7).
What is the equation of the circle that defines the boundary up to which the messages can be
transmitted?
A. C.
B. D.
______23.Alison is jogging on a circular track that has a radius of 140 feet. He runs along the track from
point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.
A. 92° C. 94°
B. 93° D. 95°
______24. Allan and Arnold were asked to find the length of AB in the figure below. The following are their
solutions. Who do you think would arrive at the correct answer and why?
Allan:7x = 9(10) A
x B
.x 7
Arnold:7(x+7) = 9(9+10) E 10
x D9 C
x
x
3
x
A. Allan. He used the theorem “If two secant segments are drawn to a circle from an exterior
point, then product of the lengths of one secant segment and its external secant segment is
equal to the product of the lengths of the other secant segment and its external secant
segment.”
B. Allan. He used the theorem “If two secant segments are drawn to a circle from an interior
point, then product of the lengths of one secant segment and its internal secant segment is
equal to the product of the lengths of the other secant segment and its internal secant
segment.”
C. Arnold. He used the theorem “If two secant segments are drawn to a circle from an exterior
point, then product of the lengths of one secant segment and its external secant segment is
equal to the product of the lengths of the other secant segment and its external secant
segment.”
D. Arnold. He used the theorem “If two secant segments are drawn to a circle from an interior
point, then product of the lengths of one secant segment and its internal secant segment is
equal to the product of the lengths of the other secant segment and its internal secant
segment.”
______25. In what points do the graph of will pass through?
A. (-1, 0), (2, 0), and (3, 0) C. (1, 0), (-2, 0), and (3, 0)
B. (-1, 0), (-2, 0), and (3, 0) D. (-1, 0), (2, 0), and (-3, 0)
______ 26. The coordinates of the vertices of a square are H(3, 8), I(15, 8), J(15, -4), and K(3, -4). What is the
length of a diagonal of the square?
A. 4 C. 12
B. 8 D.
______27. Which of the following statements shows that X(1,-1) is the midpoint of the segment with endpoints
A(4,1) and B(-2,-3) ?
A. AX = , BX = since AX=BX, therefore, X is the midpoint of AB.
B. AX = , BX = since AX=BX, therefore, X is the midpoint of AB.
C. AX = , BX = since AX=BX, therefore, X is the midpoint of AB.
D. AX = , BX = since AX=BX, therefore, X is the midpoint of AB.
______28. 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 Isidro is 20 km away from San Rafael.
Which of the following could be the coordinates of the point corresponding to San Isidro?
A. (17, 16) C. (9, 10)
B. (17, 10) D. (-15, 16)
______29. On a grid map of a province, the coordinate that corresponds to the location of a cellular phone
tower is (-2, 8) and it can transmit signals up to a 12 km radius. What is the equation that
represents the transmission boundaries of the tower?
2 2
A. x +y -4x+16y-76=0 C. x2+y2-4x-16y+76=0
B. x2+y2+4x-16y-76=0 D. x2+y2+4x-16y+76=0
______30. A new Globe tower will be put up midway between two existing towers. On a map drawn on a
coordinate plane, the coordinates of the first existing tower are (-5, -3) and the coordinates of the
second existing tower are (9, 13). What are the coordinates of the point where the new tower will be
placed?
A. (2, 5) C. (4, 10)
B. (7, 8) D. (14, 16)
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______31. A tracking device in a car indicates that it is located at a point whose coordinates are (17, 14). In the
tracking device, each unit on the grid is equivalent to 5 km. How far is the car from its starting point
whose coordinates are (1, 2)?
A. 20 km C. 60 km
B. 40 km D. 100 km
______32. A radio signal can transmit messages up to a distance of 3 km. If the radio signal’s origin is located
at a point whose coordinates are (4,9), what is the equation of the circle that defines the boundary up
to which the messages can be transmitted?
A. x2 + y2 + 8x +18y + 88 = 0 C. x2 + y2 -8x – 18y -88 = 0
B. x2 + y2 -8x – 18y + 88 = 0 D. x2 + y2 + 8x +18y- 88 = 0
For numbers 33-34, refer to the figure on the right. In Circle R,
______33. .
A.
B.
C.
D.
______34. ̸ BCD
A. . ̸ CAB
B. . ̸ DAC
C. . ̸ ABD
D. ̸ ABC
for numbers 35-38, refer to the figure below.
In circle E,
, , , and are chords.
______35. If m ̸ A = 40, then m ̸ C= ______.
A. 40 C. 80
B. 140 D. 320
______36. If m ̸ B= 15, then m ̸ D= _____.
A. 15 C. 60
B. 30 D. 165
______37. If m =150, then m ̸ A=_____.
A.30 C. 150
B. 75 D. 210
______38. If m ̸ C= 80, then m = ______.
A. 40 C. 100
B. 80 D. 160
______39. If you are to design a pendant which is a regular octagon set in a circle and suppose the opposite
vertices are connected by line segments and meet at the center of the circle, what will be the
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measure of each angle formed at the center?
A. 22.5° C. 67.5°
B. 45° D. 135°
______40. Given: ○E ○I
̸ SET ̸ BIG
Prove:
Statement Reason
1. ○E ○I
̸ ̸ SET ̸ BIG
2. m ̸ SET = m ̸ BIG
3. is the intercepted arc of ̸SET.
is the intercepted arc of ̸ BIG
4. m = m ̸ SET
m = m ̸ BIG
5. Transitivity
6.
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MATH 10 QUARTER 2 EXAM
KEY ANSWER
1. B 21. A
2. D 22. C
3. C 23. C
4. C 24. C
5. B 25. A
6. C 26. D
7. D 27. A
8. C 28. C
9. C 29. B
10. C 30. A
11. B 31. D
12. D 32. B
13. C 33. B
14. B 34. D
15. A 35. A
16. D 36. A
17. D 37. B
18. C 38. D
19. C 39. B
20. A
For number 40. (Constructed Response Item)
Statement Reason
1. ○E ○I Given
̸ ̸ SET ̸ BIG
2. m ̸ SET = m ̸ BIG Definition of congruent angles.
Definition of intercepted arc.
3. is the intercepted arc of ̸SET.
is the intercepted arc of ̸ BIG
The measure of the intercepted arc is equal to the
4. m = m ̸ SET
measure of the central angle intercepting it.
m = m ̸ BIG
Transitivity
5. =m
Definition of congruent arcs.
6.
Marking Scheme :1 point for each correct response.
0.5 for each incomplete response.
