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    Precal Midterm

    Uploaded by

    Mary Lyd Tiu
    This document appears to be a test for a pre-calculus class covering topics related to conic sections such as circles, parabolas, ellipses, and hyperbolas. It contains 38 multiple choice questions testing students on properties and equations of different conic sections, solving systems of equations, finding distances and lengths related to conic sections, and identifying specific conic section graphs based on given equations. The test covers key concepts about the shapes, equations, centers, foci, vertices and other properties of circles, parabolas, ellipses and hyperbolas.

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    © All Rights Reserved
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    Precal Midterm

    Uploaded by

    Mary Lyd Tiu
    216 views4 pages
    This document appears to be a test for a pre-calculus class covering topics related to conic sections such as circles, parabolas, ellipses, and hyperbolas. It contains 38 multiple choice questions testing students on properties and equations of different conic sections, solving systems of equations, finding distances and lengths related to conic sections, and identifying specific conic section graphs based on given equations. The test covers key concepts about the shapes, equations, centers, foci, vertices and other properties of circles, parabolas, ellipses and hyperbolas.

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    Midterm Exam

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    precal midterm

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    This document appears to be a test for a pre-calculus class covering topics related to conic sections such as circles, parabolas, ellipses, and hyperbolas. It contains 38 multiple choice questions testing students on properties and equations of different conic sections, solving systems of equations, finding distances and lengths related to conic sections, and identifying specific conic section graphs based on given equations. The test covers key concepts about the shapes, equations, centers, foci, vertices and other properties of circles, parabolas, ellipses and hyperbolas.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    216 views4 pages

    Precal Midterm

    Uploaded by

    Mary Lyd Tiu
    This document appears to be a test for a pre-calculus class covering topics related to conic sections such as circles, parabolas, ellipses, and hyperbolas. It contains 38 multiple choice questions testing students on properties and equations of different conic sections, solving systems of equations, finding distances and lengths related to conic sections, and identifying specific conic section graphs based on given equations. The test covers key concepts about the shapes, equations, centers, foci, vertices and other properties of circles, parabolas, ellipses and hyperbolas.

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    Republic of the Philippines

    Department of Education
    Division of Malaybalay City
    CASISANG NATIONAL HIGH SCHOOL
    First Quarter Examination
    PreCalculus
    S.Y 2022-2023

    Name:_________________________________________ Score:__________________
    Year&Section:___________________________________

    Direction: Solve the given problem and write the letter of the best answer before the number.

    1. It is a set of all points P(x,y) in a plane such that it is equidistant to the fixed point and a fixed line. The
    conic formed is __________.
    a. Circle b. Parabola c. Ellipse d. Hyperbola
    2 2
    2. In the equation 7 x + 7 y =49 ,the radius is ____________.
    a. √ 7 b. 6 c. 7 d. 49
    2
    3. The equation of a parabola is y −6 x=0. The opening of the graph is _______________.
    a. Left b. Right c. Upward d. Downward
    4. The fixed line of the parabola is ____________.
    a. Directix b. Axis of symmetry c. Latus rectum d. Locus
    5. The fixed point of the parabola is _________________.
    a. Directrix b. Locus c. Focus d. Center
    6. It is a set of all points P(x,y) in a plane such that the sum of the distances from the fixed points is
    constant.
    a. Circle b. Parabola c. Ellipse d. Hyperbola
    2 2
    7. Which type of conic section is defined by the equation 4 x + 4 y =16 ?
    a. Circle b. Parabola c. Ellipse d. Hyperbola
    8. It is formed when the cutting plane is parallel to the base of the conic section.
    a. Circle b. Parabola c. Ellipse d. Hyperbola
    9. In the equation 2 x2 +2 y 2=50 , what are the coordinates of the center?
    a. (0,0) b. (0,5) c. (5,0) d. (50,0)
    10. Which of the following is the x-intercept of the equation 6 x +3 y=12 ?
    a. 2 b. 12 c. 6 d. 3
    11. It is a set of all points P(x,y) in a plane such that the difference of its distances from the two fixed points
    is constant.
    a. Circle b. Parabola c. Ellipse d. Hyperbola
    2 2
    12. What is the center of the circle defined by the equation x + y −6 x+ 4 y =3 ?
    a. (3,2) b. (-3,2) c. (-3,-2) d. (3,-2)
    13. What is the vertex of the parabola x 2−6 x−6 y =3 ?
    a. (3,2) b. (-3,2) c. (-3,-2) d. (3,-2)
    14. Which of the following represents the vertex of the parabola defined by the equation
    2
    x −8 x−16 y−16=0 ?
    a. (4,2) b. (-4,-2) c. (4,-2) d. (-4,2)
    15. What is the equation of the directrix of a parabola x 2−20 x=0 ?
    a. y=5 b. y=−5 c. x=5 d. x=−5
    16. What are the coordinates of the center of an ellipse represented by the equation
    2 2
    4 x +9 y −8 x −54 y +49=0 ?
    a. (-1,-3) b. (1,-3) c. (-1,3) d. (1,3)
    17. It is a line segment passing through the center and is connecting the points.
    a. Conjugate Axis b. Latus rectum c. transverse axis d. Assymptotes
    18. Find the distance between the points A(-4,6) and B(2,3).
    a. 3 √ 5 b. 9 √ 5 c. 5 √ 3 d. √ 46

    19. Solve the system of equation: {22x−x+3y=−5


    y =7

    a. (1,-3) b. (0,5) c. (-3,1) d. (-1,3)


    20. What is the radius of a circle whose equation is defined by x 2+ y 2−8 x+ 2 y +8=0 ?
    a. 9 b. 8 c. 3 d. 2 √2
    21. What is the length of foci of an ellipse with major and minor axes at 18 and 12 respectively?
    a. √ 45 b. 3 √ 5 c. 6 √ 5 d. 10
    22. Determine the length of the latus rectum of the parabola represented by the equation
    2
    x + 6 x−8 y +17=0.
    a. 2 b. 4 c. 6 d. 8
    23. Which of the following represents the center of the hyperbola 4 x2 −16 y 2−16 x−64 y −112=0 ?
    a. (2,2) b. (-2,2) c. (-2,-2) d. (2,-2)
    2 2
    24. The graph of an equation 16 x −9 y =144 is a/an ____________.
    a. circle b. parabola c. ellipse d. hyperbola

    25. Solve the system of equation: {32xx−2+ y=6


    y =2
    a. (3,-2) b. (2,-3) c. (2,2) d. (-1,3)
    26. What is the length of the radius of a circle with endpoints of its diameter at (5,7) and (-1,-3)?
    a. √ 30 b. √ 32 c. √ 34 d.√ 35
    27. Which of the following represents the opening of the parabola 4 x=8 ¿
    a. Upward b. Downward c. Left d. Right
    28. What is the length of the major axis of an ellipse defined by the equation
    2 2
    9 x + 16 y −18 x−64 y−71=0 ?
    a. 6 b. 8 c. 9 d. 16
    29. What is the length of the transverse axis of the equation x 2−4 y 2−4 x−8 y−16=0 ?
    b. 2 b. 4 c. 8 d. 16
    2
    30. The equation y −8 x +6 y +25 represents ______________.
    a. Circle b. Ellipse c. Parabola d. Hyperbola

    31. What is the solution to the system of equation: { y=2 x−1


    y=−x +5
    a. (-2,-3) b. (-3,2) c. (3,2) d. (-1,3)
    32. Jules is asked to solve the system below by elimination. Which of the following steps would be the best
    way to begin?
    a. Multiply equation 1 by 2 and multiply equation 2 by 3.
    b. Multiply equation 2 by 2.
    c. Multiply equation 1 by 2.
    d. Multiply equation 2 by 2 and multiply equation 1 by 3.
    33. Find the distance between the centers of the circles defined by the equations
    x 2+ y 2−16=0∧x 2 + y 2−8 x−10 y +25=0.
    a. √ 41 b. √ 42 c. √ 43 d. √ 44
    34. Which of the following is the equation of a parabola with vertex at (2,-3) and the focus at (4, -3)?
    a. y 2−8 x−6 y+ 25=0 c. y 2−8 x−6 y−25=0
    b. y 2−8 x +6 y +25=0 d. y 2 +8 x+ 6 y−25=0
    35. What is the equation of a parabola with vertex at (2,5), passing through the point (4,1), and with axis of
    symmetry at vertical axis?
    a. ( y−5)2=8( x−2) c. ( y−5)2=−8(x−2)
    b. ( x−2)2=8( y−5) d. (x−2)2=−8 ( y +5)
    c 4
    36. Find the equation of an ellipse with center at (1,3), one vertex is at (1, 8), and = .
    a 5
    2 2 2 2
    ( y−3) (x−1) ( y−1) ( x−3)
    a. + =1 c. + =1
    25 9 25 9
    ( y−3 )2 ( x−1 )2 ( y−1 )2 ( x−3 )2
    b. + =1 d. + =1
    9 25 9 25
    37. Find the standard equation of a hyperbola with center at (0,0), the transverse axis at the x-axis, the focal
    distance is 12 units, and the distance between the directrices is 2 units.
    x2 y 2 x2 y2
    a. − =1 c. − =1
    6 30 30 6
    x2 y 2 x2 y2
    b. + =1 d. + =1
    6 30 30 6
    38. For which system is (-3,5) the solution?

    a. {2x+2
    x + y=−1
    y=7
    c. {42x−3 y =−27
    x+ 4 y =12
    b. {52xx−3 y=12
    +3 y=18
    d. {63x−4
    x +2 y=1
    y=2
    39. For which system is (-2,6) the solution?

    {
    a . x +3 y=16
    4 x +4 y=16
    c. {2xx+2+4y=−2
    y=−4

    b . {x +3 y=17 d. {2xx++yy=−2
    2 x + y=15 =16
    40. For which system is (4,-2) the solution?

    a. {4 x−2
    x+ 4 y=15
    y=−17
    c. {−24xx++4y=14
    y=−16

    b . { 2 x+ 4 y=4 d. {2xx+4+4y=4
    −2 x + y=14 y=8

    Trust yourself. You survived a lot and you’ll survive whatever is to come -unknown
    God Bless!
    Prepared by:
    MARY LYD B. TIU

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