PRELIM-EXAM-PRECALCULUS.pdf

Semester: Score MOONWALK NATIONAL HIGH SCHOOL PARAÑAQUE...

Semester: Score MOONWALK NATIONAL HIGH SCHOOL PARAÑAQUE FIRST SEMESTER Senior High School Type of test: S.Y. 2024 - 2025 1ST QUARTER PRELIM EXAM Subject: PRECALCULUS Name: Grade & Section: Date of Exam: Direction: Read each test item carefully and select the letter of the correct answer. 1. Let (𝑥𝑥 − ℎ)2 + (𝑦𝑦 − 𝑘𝑘)2 = 𝑟𝑟 2 be the equation of 7. When the radius is equal to zero, what will circle. Which of the following ordered pair happen to the graph of the circle? represents the center of circle 𝐶𝐶? a. The graph is a single point. (not a a. (ℎ, 𝑘𝑘) circle) b. (𝑥𝑥, ℎ) b. The graph is still the same. c. (𝑥𝑥, 𝑦𝑦) c. There is no graph since the radius is d. (𝑦𝑦, 𝑘𝑘) imaginary. d. The graph is out of round. 2. Find the standard form of the equation of the parabola given that the vertex is at (−3, −1) and 8. What is the equation of the parabola whose 3 the directrix is 𝑦𝑦 = −. vertex is at the center of 𝑥𝑥 2 + 𝑦𝑦 2 − 10𝑥𝑥 + 4𝑦𝑦 − 4 5 = 0 and whose focus is on the y-axis? a. (𝑥𝑥 + 1)2 = −(𝑦𝑦 + 3) a. (𝑦𝑦 + 2)2 = −20(𝑥𝑥 + 5) b. (𝑥𝑥 + 3)2 = −(𝑦𝑦 + 1) 3 b. (𝑦𝑦 + 2)2 = 20(𝑥𝑥 − 5) c. (𝑥𝑥 − 1)2 = − (𝑦𝑦 + 1) c. (𝑦𝑦 + 2)2 = −20(𝑥𝑥 − 5) 4 3 d. (𝑥𝑥 + 3)2 = (𝑦𝑦 − 1) d. (𝑦𝑦 − 5)2 = −20(𝑥𝑥 + 2) 4 3. What is the line segment joining the vertices of a 9. What is the midpoint between the focus and the directrix? hyperbola? a. Circle a. Conjugate axis b. Vertex b. Transverse axis c. Latus rectum c. Major axis d. Intercept d. Minor axis 10. What is TRUE about hyperbolas? 4. Find the equation of an ellipse with center at (1, a. A hyperbola is asymmetric along the 2), horizontal major axis, focal distance of length transverse axis. 20 units, and minor axis of length 42 units. b. The vertices of the hyperbola are along (𝑥𝑥−2)2 (𝑦𝑦−1)2 the conjugate axis. a. + =1 c. Hyperbolas do not have latus rectum. 841 441 (𝑥𝑥−1)2 (𝑦𝑦−2)2 d. The pair of straight lines drawn parallel b. + =1 841 441 to the hyperbola is called the (𝑥𝑥−1)2 (𝑦𝑦−2)2 c. + =1 asymptote. 441 841 (𝑥𝑥−2)2 (𝑦𝑦−1)2 d. + =1 441 841 11. What is the line segment in a hyperbola that passes through the center and is perpendicular 5. What is the distance from the center of a vertex to the transverse axis whose length is 2b? (𝑥𝑥−5)2 of the hyperbola given by the equation − a. Conjugate axis 16 (𝑦𝑦−3)2 b. Transverse axis = 1? c. Major axis 9 a. a = 16 units d. Minor axis b. a = 3 units 12. What is formed when the plane intersects one c. a = 4 units cone at an angle other than 90°? d. a = 9 units a. Circle b. Ellipse 6. What is the distance from the center to a focus of c. Hyperbola a hyperbola? d. Parabola a. Vertex b. Focus c. Intercept d. Focal distance 13. Which of the following describes an ellipse? 21. What is the equation of an ellipse with a a. A plane intersects one nappe of a horizontal major axis centered at (h, k)? double napped cone at an angle of 75°. (𝑥𝑥−ℎ)2 (𝑦𝑦−𝑘𝑘)2 a. + =1 b. A plane is parallel to the axis of 𝑎𝑎2 𝑏𝑏2 (𝑥𝑥−ℎ)2 (𝑦𝑦−𝑘𝑘)2 revolution. b. − =1 𝑎𝑎2 𝑏𝑏2 c. A plane is parallel to the generating line (𝑥𝑥−ℎ)2 (𝑦𝑦−𝑘𝑘)2 c. + =1 of one cone. 𝑏𝑏2 𝑎𝑎2 (𝑥𝑥−ℎ)2 (𝑦𝑦−𝑘𝑘)2 d. A plane is perpendicular to the axis of d. − =1 𝑏𝑏2 𝑎𝑎2 revolution. 22. Which conic section is defined as the set of all 14. What type of conic is represented by 𝑥𝑥 2 − points where the distance from a fixed point 4𝑥𝑥𝑥𝑥 + 3𝑦𝑦 + 5 = 0. (focus) to any point on the curve is constant? a. Parabola a. Circle b. Ellipse b. Ellipse c. Hyperbola c. Hyperbola d. Circle d. Parabola 15. The circle x2 + y2 + 4x – k passes through the 23. What is the focus-directrix definition of a conic point (3, 2). What is the value of k? section? a. 23 a. A conic section is the set of all points b. 32 where the distance from a fixed point c. 25 (focus) to any point on the curve is d. 52 constant. b. A conic section is the set of all points 16. _______________ are obtained from the equidistant from two fixed points (foci) intersection between a double-napped cone and the distance to the directrix is and a plane. constant. a. Asymptotes c. A conic section is the set of all points b. Tractrices where the distance from the directrix c. Simple curves to any point on the curve is constant. d. Conic sections d. A conic section is the set of all points on a straight line. 17. What is generated when the plane cuts through the double-napped cone parallel to the line of 24. Which of the following is NOT a conic section? curve? a. Parabola a. Circle b. Circle b. Parabola c. Line c. Ellipse d. Ellipse d. Hyperbola 25. Which parameter determines the size and 18. If a tree was chopped in the middle, which shape of an ellipse? conic section will be formed? a. Eccentricity a. a circle b. Radius b. an ellipse c. Major Axis c. two intersecting lines d. Semi-major axis d. a single line 26. In the equation of a parabola, what does 'c' 19. A circle is formed when a plane _______________ to represent? the axis intersects a double-napped cone. a. The slope of the parabola a. perpendicular b. The distance between the vertex and b. parallel the focus c. adjacent c. The distance between the vertex and d. coincident the directrix d. The length of the major axis 20. What is the general equation of a conic section? a. y = ax 2 + bx + c 27. What happens to the eccentricity of an ellipse b. x 2 + y 2 = r 2 as it becomes more elongated (less circular)? a. The eccentricity increases. c. Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 b. The eccentricity decreases. d. x = a2 + b2 c. The eccentricity remains constant. d. The eccentricity becomes undefined. 28. Suppose the length of the radius of circle A is 34. The arch of a tunnel is in the form of a semi- 10 units and its center is located 3 units below ellipse. The distance between the bases of the the origin along the y -axis. What is the arch is 20 meters. The height of the tunnel at equation of circle A? the center is 8meters. Can a truck that is 7 a. x 2 + (y + 3)2 = 100 meters high and 8 meters wide pass through b. x 2 + (y − 3)2 = 100 c. (x + 3)2 + y 2 = 100 the tunnel? d. (x − 3)2 + y 2 = 100 a. Yes, because the height of the vehicle is less than 7.33 meters. 29. Find the equation of an ellipse with center at b. Yes, because the height is 8 meters. the origin, major axis of length 26 units long on c. No, because the focal distance is 6 m. the 𝑥𝑥-axis, and minor axis of length 24 units. d. No, because the truck will hit the arch. 𝑥𝑥 2 𝑦𝑦 2 a. + =1 26 2 24 2 35. In the equation of a parabola, which term 𝑥𝑥 𝑦𝑦 b. + = 1 determines the direction (up or down for 144 169 c. 𝑥𝑥 2 + 𝑦𝑦 2 = 1 vertical, left or right for horizontal) of the 169 144 parabolic curve? 𝑥𝑥 2 𝑦𝑦 2 d. + =1 a. The coefficient of x 676 576 b. The coefficient of y 30. What is the vertex of the parabola given by the c. The sign of the constant term equation (𝑦𝑦 + 1)2 = −8𝑥𝑥? d. The sign of the linear term a. (0, -1) b. (-1, 0) 36. Which of the following values of B will make c. (1, 0) the equation 4𝑥𝑥 2 − 𝐵𝐵𝑦𝑦 2 = 1 a circle? d. (0, 1) a. -4 b. -1 31. An electricity-generating dish uses a parabolic c. 4 reflector to concentrate sunlight onto a high- d. 2 frequency engine located at the focus of the reflector. If the engine is located 4.5mm above 37. What conic section is represented by the the vertex, what is the equation that represents equation (𝑦𝑦 + 3)2 − (𝑥𝑥 + 1)2 = −𝑥𝑥 2 ? the cross-section of the dish with its vertex at a. parabola (0,0)? b. ellipse a. 𝑥𝑥 2 = 18𝑦𝑦 c. hyperbola b. y 2 = 18x d. circle c. 𝑥𝑥 2 = 4.5𝑦𝑦 d. 𝑦𝑦 2 = 4.5𝑥𝑥 38. Which of the following conic sections is an ellipse? 32. The _____________ of the distances from any point a. 5𝑦𝑦 2 − 𝑥𝑥 − 12𝑦𝑦 − 15 = 0 on an ellipse to its foci is constant. b. 7𝑥𝑥 2 + 7𝑦𝑦 2 + 9𝑥𝑥 − 3𝑦𝑦 + 1 = 0 a. Difference c. 5𝑥𝑥 2 + 5𝑦𝑦 2 − 12𝑥𝑥 − 4𝑦𝑦 − 31 = 0 b. Sum d. 5𝑥𝑥 2 + 2𝑦𝑦 2 − 6𝑥𝑥 + 3𝑦𝑦 − 5 = 0 c. Product d. Quotient 39. What is the number of foci in a hyperbola? a. 1 33. In a circle, what is the relationship between the b. 2 radius and the distance between the center and c. 0 a point on the circle? d. 3 a. The radius is equal to the distance. 40. Which type of conic section has no foci or b. The radius is less than the distance. directrices? c. The radius is greater than the distance. a. ellipse d. The radius is irrelevant. b. circle c. hyperbola d. Parabola