Republic of the Philippines
Department of Education
Region I
SCHOOLS DIVISION OFFICE I PANGASINAN
Dasol District
FIRST QUARTERLY ASSESSMENT
School Year: 2022-2023
PRE-CALCULUS 1
Learning Area
Name: _____________________________________________________ Score: _________________
Grade and Section: ____________________________________ Date: __________________
MULTIPLE CHOICE
Directions: Read the following statements and choose the letter of the correct answer.
Write your answer on the space provided.
______1. What type of conic section can you create if you slice the nappes like what the
figure the below?
a. circle
b. parabola
c. hyperbola
d. ellipse
______2. It is the simplest, best known and special type of conic section that is the
intersection of a plane perpendicular to the cone’s axis.
a. circle b. parabola c. hyperbola d. ellipse
______3. What is the center of the circle with the standard form of (x−2)2+( y −1)2=4 ?
a. (2,1) b. (1,2) c. (-2,-1) d. (-1,-2)
______4. Evaluate the standard form of the equation of a circle whose center is at (2,1)
and whose radius is 2.
a. (x +2)2 +( y +1)2=4 c. ( x +1)2 +( y +2)2=4
b. ( x−2)2+( y −1)2=4 d. ( x−1)2+( y−2)2=4
______5. Evaluate the standard form of the equation of a circle whose center is at (3,2)
and whose diameter is 6.
a. ( x +3)2+( y +2)2=3 c. ( x−3)2 +( y −2)2 =3
b. (x +3)2+( y +2)2=9 d. (x−3)2 +( y −2)2 =9
______6. It is the locus of all points in the plane whose distances from a fixed-point F and
a line l (not passing through F) are the same.
a. circle b. parabola c. hyperbola d. ellipse
______7. How many orientations are there in parabola?
a.1 b. 2 c. 3 d. 4
______8. Which of the following is true about parabola?
a. The directrix is c units below or above the vertex.
b. The focus and directrix are units above and below the vertex.
c. The vertex is the point midway between the focus and the directrix.
d. all of the above
______9. How many units are the latus rectum of the parabola y 2=20 x ?
a. 10 b. 20 c. 30 d. 40
For number 10-11.
I II III IV
______10. In the figure above, which of the following has the graph y 2=4 ax ?
a. I b. II c. III d. IV
______11. Which of the following has the graph x 2=4 ay
a. I b. II c. III d. IV
______12. It is the locus of all points (x,y) such that the sum of the distances from P to
two fixed points, F 1 and F 2 called the foci, is a constant.
a. circle b. parabola c. hyperbola d. ellipse
______13. The ellipse has 2 axis. What do you call on the longest axis?
a. major axis b. minor axis c. conjugate axis d. transverse axis
______14. How many latus rectum are there in an ellipse?
a.1 b. 2 c. 3 d. 4
2 2
( x−h) ( y−k )
______15. What is the graph of the ellipse with a standard form of + =1?
a2 b2
a. horizontal b. vertical c. slant horizontal d. slant vertical
2 2
( x−h) ( y−k )
______16. What is the graph of the ellipse with a standard form of + =1?
b2 a2
a. horizontal b. vertical c. slant horizontal d. slant vertical
2 2
x y
______17. In + =1, evaluate its vertex.
4 36
a. 2 b. 4 d. 6 d. 36
______18. It is the set of all points where the difference between their distances from two
fixed points (the foci) is constant.
a. circle b. parabola c. hyperbola d. ellipse
______19. What kind of axis in hyperbola pass in the points of vertex and focus?
a. major axis b. minor axis c. conjugate axis d. transverse axis
______20. What kind of axis in hyperbola pass in the points of vertex and focus?
a. major axis b. minor axis c. conjugate axis d. transverse axis
x2 y 2
______21. What is the orientation of a hyperbola with a standard form of, − =1?
a2 b2
a. horizontal b. vertical c. slant horizontal d. slant vertical
______22. What is the orientation of a hyperbola with a standard form of,
2 2
(x−h) ( y −k )
2
− 2
=1?
a b
a. horizontal b. vertical c. slant horizontal d. slant vertical
2 2
( x−3) ( y +2)
______23. What is the center of the hyperbola with a standard form of − =1 ?
16 4
a. (-3,2) b. (3,-2) c. (2,-3) d. (-2,3)
______24. The general form of hyperbola is 5 x 2−4 y 2+50 x +16+29=0. Create a standard
form of the hyperbola.
2 2 2 2 2 2
( x +5) ( y−2) ( x−5) ( y +2) ( x +5) ( y−2)
a. − =1 b. − =1 c. − =1 d.
16 20 16 20 20 16
( x−5)2 ( y +2)2
− =1
20 16
______25. If center is (h,k), what do you think is the center of your answer in number 24?
a. (-5,2) b. (-5,-2) c. (2,5) d. (-2,-5)
______26. From your answer on number 24, what do you think is the measurement in
unit of covertex?
a. -4 b. -16 c. 4 d. 16
______27. How can you determine the vertex and the covertex of ellipses and hyperbolas?
a. vertex is lesser than covertex c. vertex is greater than covertex
b. covertex is equal to vertex d. covertex is greater than vertex
______28. Applying the formula of latus rectum, how many units are the latus rectum of
( x +2)2 ( y −3)2
− =1 ?
16 9
a. 2 b. 2.25 c. 2.5 d. 2.75
______29. How can you determine the foci of ellipse and hyperbolas?
a. √ ❑ b. √ ❑ c. √ ❑ d. √ ❑
2 2
( x−5) ( y +3)
For number 30-34. − =1
9 16
______30. If center is (h,k), what is the center of the hyperbola above?
a. (-5,3) b. (-5,-3) c. (5,3) d. (5,-3)
______31. How many units are the vertices of the hyperbola?
a. 3 b. 4 c. 9 d. 16
______32. How many units are the covertices of the hyperbola?
a. 3 b. 4 c. 9 d. 16
______33. How many units are the focus of the hyperbola?
a. 3 b. 4 c. 5 d. 6
______34. What do you think is the orientation of the hyperbola?
a. horizontal b. vertical c. slant horizontal d. slant vertical
______35. Which of the following numbers can we apply arithmetic series?
1 1 1
a. 3,7,11,.. 10th? b. 2,6,18,..10th c. 3,6,12,..10th d. , , ,..10th
2 4 8
______36. Which of the following numbers can we apply geometric series?
1 1
a. , 1,1 , 2 b. 3,6,12,..10th c. 3,7,11,.. 10th? d. 3,8,13,..10th
2 2
______37. In 3,6,12,..10th, what do you think is the common ratio?
a. 2 b. 3 c. 4 d. 5
______38. What do you call if you add up the terms of an arithmetic sequence?
a. arithmetic series c. geometric series
b. arithmetic sequence d. geometric sequence
______39. What do you call if you add up the terms of an geometric sequence?
a. arithmetic series c. geometric series
b. arithmetic sequence d. geometric sequence
______40. Evaluate the geometric series 1,2,4,8,…10th.
a. 1,020 b. 1,021 c. 1,022 d. 1,023
______41. It is used as a convenient shorthand notation for the summation of terms.
a. Cigma notation b. Sigma notation c. Xigma notation d. Zigma notation
______42. How can you write 3 4+ 35 +36 in sigma notation?
6 6 6 6
a. ∑ x3 b. ∑ 33 c. ∑ 3x d. ∑ 3 x3
x=3 x=3 x= 4 x=3
______43. How can you write ¿ in sigma notation?
6 6 5 6
a. ∑ ( x + 4)x
b. ∑ (3+ x) x
c. ∑ (x +3) x
d. ∑ (3+ x )x
x= 4 x= 4 x= 4 x=2
6 x
______44. How can you write ∑ 3x in expanded form?
x= 4
34 3 5 36 4 4 55 66 34 3 5 36 33 33 33
a. + + b. + + c. + + d. + +
4 5 6 4 5 6 3 3 3 4 5 6
3
______45. How can you write ∑ 4 x +2 in expanded form?
x=1
a. ( 41+2 )+ ( 42+2 ) + ( 43+2 ) c. ( 4 +2 ) + ( 4 +2 ) + ( 4 +2 )
b. ( 4(1)+2 ) + ( 4 (2)+2 ) + ( 4 (3)+2 ) d. ( 1+2 ) + ( 2+2 ) + ( 3+2 )
3
______46. Evaluate ∑ x +2.
x=1
a. 10 b. 11 c. 12 d. 13
10
______47. Evaluate ∑ x.
x=2
a. 22 b. 33 c. 44 d. 55
5
______48. Evaluate ∑ x 2.
x=2
a. 50 b. 52 c. 53 d. 54
3
______49. Evaluate ∑ 2 x +2.
x=1
a. 12 b. 14 c. 16 d. 18
3
______50. Evaluate ∑ x 3 +2.
x=1
a. 42 b. 44 c. 46 d. 48
Answer Key
1. c 21. a 41. b
2. a 22. b 42. c
3. a 23. b 43. b
4. b 24. a 44. a
5. d 25. a 45. b
6. b 26. c 46. c
7. d 27. c 47. c
8. d 28. b 48. d
9. b 29. c 49. d
10. a 30. d 50.
11. c 31. b
12. d 32. a
13. a 33. c
14. d 34. b
15. a 35. a
16. b 36. b
17. a 37. 2
18. c 38. a
19. d 39. c
20. c 40. d
