Pre-calculus - First Semester (1st Quarter)
68 Questions
2 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following is the standard equation of the circle with center (0, -3) and radius 58?

  • $x^2 + (y + 3)^2 = 58$ (correct)
  • $x^2 + (y - 3)^2 = 29$
  • $x^2 + (y - 3)^2 = 58$
  • $x^2 + (y + 3)^2 = 29$

Which of the following is the standard equation of a circle with center (3, -2) and radius 2?

  • $(x + 3)^2 + (y - 2)^2 = 4$
  • $(x - 3)^2 + (y + 2)^2 = 4$
  • $(x - 3)^2 + (y + 2)^2 = 2$ (correct)
  • $(x + 3)^2 + (y - 2)^2 = 2$

Which of the following is the standard equation of a circle with center (5, 6) that is tangent to the x-axis?

  • $(x + 5)^2 + (y + 6)^2 = 36$
  • $(x - 5)^2 + (y + 6)^2 = 36$ (correct)
  • $(x + 5)^2 + (y - 6)^2 = 36$
  • $(x - 5)^2 + (y - 6)^2 = 36$

Which of the following is the standard equation of a circle with the center at the origin and a diameter of 6?

<p>$x^2 + y^2 = 36$ (C)</p> Signup and view all the answers

Which of the following is the center and radius of the circle with the equation $x^2 + y^2 + 10x - 14y + 70 = 0$?

<p>Center: (-5, 7), Radius: 5 (A)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, 0) and radius 11?

<p>$x^2 + y^2 = 121$ (A), $x^2 + y^2 = 121$ (B), $x^2 + y^2 = 121$ (C)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (3, -2) and radius 2?

<p>$(x - 3)^2 + (y + 2)^2 = 4$ (C)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (5, 6) that is tangent to the x-axis?

<p>$(x - 5)^2 + (y + 6)^2 = 36$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, -3) and radius 58?

<p>$x^2 + (y + 3)^2 = 58$ (B)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (3, -2) and radius 2?

<p>$(x - 3)^2 + (y + 2)^2 = 4$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (5, 6) that is tangent to the x-axis?

<p>$(x - 5)^2 + (y + 6)^2 = 36$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (3, -4) and focus (3, -2)?

<p>$y = -2(x - 3)^2 - 4$ (C)</p> Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (-2, 5) and directrix y = 9?

<p>$y = - rac{1}{4}(x + 2)^2 + 5$ (B)</p> Signup and view all the answers

Which of the following is the equation of the axis of symmetry for the parabola with equation $y = 2x^2 + 4x + 3$?

<p>$x = -1$ (A)</p> Signup and view all the answers

Which of the following is the equation of the latus rectum for the parabola with equation $y = rac{1}{4}x^2 - 2x + 1$?

<p>$x = 4$ (A)</p> Signup and view all the answers

Which of the following is the general equation of a parabola with focus (2, -1) and directrix x = -3?

<p>$x^2 = 8y + 6x - 13$ (C)</p> Signup and view all the answers

Which of the following is the equation of the axis of symmetry for a parabola with vertex (2, -5)?

<p>$x = 2$ (B)</p> Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (0, 0) and directrix y = -4?

<p>$y^2 = -8x$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (-3, 2) and radius 5?

<p>$(x + 3)^2 + (y - 2)^2 = 25$ (B)</p> Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (2, -3) and directrix y = 5?

<p>$x^2 - 4x + 24y + 17 = 0$ (C)</p> Signup and view all the answers

Which of the following is the equation of the latus rectum for the parabola with equation $y = -3x^2 + 6x - 1$?

<p>$x = 2$ (B)</p> Signup and view all the answers

Which of the following is the equation of the axis of symmetry for the parabola with equation $y = 2x^2 - 4x + 3$?

<p>$x = -1$ (B)</p> Signup and view all the answers

Which of the following is the standard form equation of the given ellipse?

<p>$\frac{(x-0)^2}{18^2} + \frac{(y-0)^2}{15^2} = 1$ (D)</p> Signup and view all the answers

What is the maximum height of the truck?

<p>14.14 ft (A)</p> Signup and view all the answers

Which of the following is the equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

<p>$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (C)</p> Signup and view all the answers

Which of the following is the equation of an ellipse with a major axis along the y-axis and a center at (h, k)?

<p>$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$ (A)</p> Signup and view all the answers

What is the equation of the ellipse with the given standard form equation?

<p>$\frac{(x-6)^2}{18^2} + \frac{(y-n)^2}{15^2} = 1$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

<p>$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (C)</p> Signup and view all the answers

What are the coordinates of the foci of the ellipse with the equation $x^2/81 + y^2/25 = 1$?

<p>(±7, 6) (C)</p> Signup and view all the answers

What is the equation of the ellipse with the given standard form equation?

<p>$\frac{(x-4)^2}{16} + \frac{(y-2)^2}{9} = 1$ (A)</p> Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

<p>$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (C)</p> Signup and view all the answers

Which of the following is the equation of an ellipse with a major axis along the y-axis and a center at (h, k)?

<p>$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (A)</p> Signup and view all the answers

What is the maximum height of the truck?

<p>14.14 ft (D)</p> Signup and view all the answers

Which of the following is the standard form of the equation given in the text?

<p>$(x+3)^2/4 - (y+1)^2/1 = 1$ (D)</p> Signup and view all the answers

What is the value of $c$ in the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

<p>3 (B)</p> Signup and view all the answers

What is the equation of the asymptotes for the hyperbola with the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

<p>$y = 3x/5 + 4/5$ (C)</p> Signup and view all the answers

What is the value of $b^2$ in the equation $6x^2 - 5y^2 = 30$?

<p>6 (A)</p> Signup and view all the answers

What is the equation of the latus rectum for the parabola with equation $y = -3x^2 + 6x - 1$?

<p>$x = 2/3$ (A)</p> Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (600, 0) and F2 (600, 0)?

<p>$\frac{(x-600)^2}{244400} - \frac{y^2}{115600} = 1$ (C)</p> Signup and view all the answers

What is the value of $b^2$ in the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

<p>25 (D)</p> Signup and view all the answers

What are the coordinates of the center, foci, vertices, and asymptotes of the hyperbola with the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

<p>Center: (4, -3), Foci: (4±√40, -3), Vertices: (4±√15, -3), Asymptotes: y = ±(5/3)(x-4) - 3 (C)</p> Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (600, 0) and F2 (600, 0)?

<p>$(x-600)^2/4 - (y-0)^2/1 = 1$ (A)</p> Signup and view all the answers

What are the coordinates of the foci of the ellipse with the equation $x^2/81 + y^2/25 = 1$?

<p>(0, -5) (B)</p> Signup and view all the answers

What is the value of $c$ in the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

<p>5 (C)</p> Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

<p>$(x-h)^2/a^2 - (y-k)^2/b^2 = 1$ (B)</p> Signup and view all the answers

Which of the following is the equation of the directrix for the parabola with equation $y = 2x^2 - 4x + 1$?

<p>$y = -1$ (B)</p> Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (0, 3) and F2 (0, -3)?

<p>$y^2/a^2 - x^2/b^2 = 1$ (B)</p> Signup and view all the answers

Which of the following is the equation of the latus rectum for the parabola with equation $y = 4x^2 + 8x + 2$?

<p>$x = -2$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (3, -2) and directrix y = -6?

<p>$(x+3)^2 = 4p(y-2)$ (C)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (-3, 2) and radius 5?

<p>$(x + 3)^2 + (y - 2)^2 = 5^2$ (A)</p> Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (0, 3) and F2 (0, -3)?

<p>$x^2 - y^2 = 9$ (B)</p> Signup and view all the answers

Which of the following is the general equation of a parabola with focus (2, -1) and directrix x = -3?

<p>$(x - 2)^2 = 4p(y + 1)$ (D)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, -3) and radius 58?

<p>$x^2 + (y + 3)^2 = 58^2$ (C)</p> Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the y-axis and a center at (h, k)?

<p>$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$ (A)</p> Signup and view all the answers

What is the maximum height of the truck?

<p>16 feet (A)</p> Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, 0) and radius 11?

<p>$x^2 + y^2 = 121$ (B)</p> Signup and view all the answers

Which of the following is the standard equation of the circle with center (0, -3) and radius 58?

<p>$x^2 + (y+3)^2 = 58^2$ (A)</p> Signup and view all the answers

Which of the following equations represents a linear equation?

<p>$3x + 2y = 5$ (A)</p> Signup and view all the answers

Which of the following equations represents a non-linear equation?

<p>$x^2 + y^2 = 25$ (C)</p> Signup and view all the answers

What is the slope of the line represented by the equation $2x + 3y = 7$?

<p>$\frac{2}{3}$ (D)</p> Signup and view all the answers

What is the constant value in the linear equation $4x - 5y = 10$?

<p>10 (D)</p> Signup and view all the answers

Which of the following equations represents a non-linear equation?

<p>$x^2 + y^2 = 16$ (B)</p> Signup and view all the answers

Which of the following equations represents a linear equation?

<p>$10x = 1$ (C)</p> Signup and view all the answers

Which of the following equations represents a non-linear equation?

<p>$x^2 + 12xy + y^2 = 0$ (B)</p> Signup and view all the answers

What is the general representation of a linear equation?

<p>$y = mx + c$ (D)</p> Signup and view all the answers

Which of the following equations represents a linear equation?

<p>$4x = 3x$ (A)</p> Signup and view all the answers

Which of the following equations represents a non-linear equation?

<p>$x^2 + y^2 = 1$ (D)</p> Signup and view all the answers

What is the standard equation of a linear equation?

<p>$y = mx + c$ (B)</p> Signup and view all the answers

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser