Question 1

Which of the following is also known as a degenerate case of conic sections?

Accepted Answer

Point

Answer

Hyperbola

Answer

Circle

Answer

Ellipse

Question 2

Which of the following conic sections is defined as the set of all points in a plane that are the same distance from a given point and a given line?

Accepted Answer

Parabola

Answer

Hyperbola

Answer

Ellipse

Answer

Circle

Question 3

Which conic section is defined by the locus of points for which the distance to a given point, called the focus, is a constant ratio to the distance from a given line, the directrix, where the ratio is greater than but not equal to one?

Accepted Answer

Hyperbola

Answer

Ellipse

Answer

Circle

Answer

Parabola

Question 4

What is the mathematical definition of a circle?

Accepted Answer

A set of points in a plane that are all the same distance from a fixed point

Answer

A round shape with no corners or edges

Answer

A polygon with infinite number of sides

Answer

A set of lines that all intersect at a single point

Question 5

Which equation defines a circle with center (h,k) and radius r in a two-dimensional coordinate system?

Accepted Answer

(x-h)^2 + (y-k)^2 = r^2

Answer

$(x-h) + (y-k) = r$

Answer

$(x+h)^2 + (y+k)^2 = r^2$

Answer

$(x-h)^2 * (y-k)^2 = r^2$

Question 6

What is the radius of a circle with center at the origin (0, 0) if its equation is given as $x^2 + y^2 = 25$?

Accepted Answer

5

Answer

12.5

Answer

25

Answer

50

Question 7

What is the standard form of the equation of a circle with a center at (2,-3) and a radius of 4?

Accepted Answer

(x - 2)² + (y + 3)² = 16

Answer

(x + 2)² + (y + 3)² = 16

Answer

(x + 2)² + (y - 3)² = 16

Answer

(x - 2)² + (y - 3)² = 16

Question 8

What is the standard form of the equation of a circle with a center at (-5,4) and a radius of 7?

Accepted Answer

(x + 5)² + (y - 4)² = 49

Answer

(x - 5)² + (y + 4)² = 49

Answer

(x - 5)² + (y - 4)² = 49

Answer

(x + 5)² + (y + 4)² = 49

Question 9

What is the standard form of the equation of a circle with a center at (3,-2) and a radius of 5?

Accepted Answer

(x - 3)² + (y + 2)² = 25

Answer

(x + 3)² + (y - 2)² = 25

Answer

(x - 3)² + (y - 2)² = 25

Answer

(x + 3)² + (y + 2)² = 25

Question 10

Which one of these is a correct definition of a parabola?

Accepted Answer

A parabola is a set of all points in a plane that are equidistant from a fixed point (focus) and a fixed line (directrix).

Answer

A parabola is a set of all points in a plane that are equidistant from a fixed point (focus) and a movable line (directrix).

Answer

A parabola is a set of all points in a plane that are the same distance from two fixed points.

Answer

A parabola is a curve where any point is at the same distance from a fixed point and a fixed line.

Question 11

Which of the following equations represents a parabola?

Accepted Answer

y = x^2

Answer

y = |x|

Answer

y = 2x

Answer

y = x^3

Question 12

What shape does a parabola form?

Accepted Answer

U-shaped curve

Answer

Straight line

Answer

Wavy line

Answer

Circular shape

Question 13

Given the vertex (3,2) and the focus (3,5) of a parabola, what is the standard form of its equation?

Accepted Answer

y = 1/3(x - 3)^2 + 2

Answer

y = 1/3(x - 3)^2 + 3

Answer

y = (x - 3)^2 + 2

Answer

y = (x - 3)^2 + 5

Question 14

Given a parabola's vertex (2,-3) and directrix y = -5, what is its standard form equation?

Accepted Answer

y = 1/2(x - 2)^2 - 3

Answer

y = 1/2(x + 2)^2 - 3

Answer

y = 2(x + 2)^2 - 3

Answer

y = 2(x - 2)^2 - 3

Question 15

What is the standard form equation of a parabola with a focus at (3,2) and a directrix x = 1?

Accepted Answer

(x - 3)^2 = 4(y - 2)

Answer

(x + 3)^2 = 4(y + 2)

Answer

(x - 2)^2 = 4(y - 3)

Answer

(y - 2)^2 = 4(x - 3)

Question 16

Which of the following best describes an ellipse?

Accepted Answer

A set of points where the sum of the distances from any point on the ellipse to two fixed points is constant

Answer

A set of all points where the difference of the distances from any point on the curve to two fixed points is constant

Answer

A set of points equidistant from a common center

Answer

A type of parabola which opens either upward or downward

Question 17

In the equation of an ellipse (x-h)²/a² + (y-k)²/b² = 1, what does 'a' represent?

Accepted Answer

Semi-major axis length

Answer

Semi-minor axis length

Answer

Distance from the center to the foci

Answer

Length of the latus rectum

Question 18

What is the foci of an ellipse?

Accepted Answer

Two fixed points inside the ellipse

Answer

The highest and lowest points of the ellipse

Answer

The points where the ellipse intersects with the axis

Answer

The center point of the ellipse

Question 19

What is the standard form of the equation of an ellipse with a major axis on the x-axis, center at the origin, and radii 3 and 2?

Accepted Answer

x^2/9 + y^2/4 = 1

Answer

x^2/2 + y^2/3 = 1

Answer

x^2/4 + y^2/9 = 1

Answer

x^2/3 + y^2/2 = 1

Question 20

What is the standard form of the equation of an ellipse with a major axis on the y-axis, center at the origin, and radii of 5 and 7?

Accepted Answer

x^2/49 + y^2/25 = 1

Answer

x^2/5 + y^2/7 = 1

Answer

x^2/25 + y^2/49 = 1

Answer

x^2/7 + y^2/5 = 1

Question 21

What is the standard form of the equation of an ellipse centered at (0,0) with a horizontal major axis of length 6 and a minor axis of length 4?

Accepted Answer

x^2/9 + y^2/4 = 1

Answer

x^2/6 + y^2/4 = 1

Answer

x^2/4 + y^2/9 = 1

Answer

x^2/4 + y^2/6 = 1

Question 22

Which of the following best defines a hyperbola?

Accepted Answer

A set of all points in a plane such that the difference of the distances from two fixed points, called foci, is constant.

Answer

A set of all points in a plane such that the sum of the distances from two fixed points, called foci, is constant.

Answer

A curve that is reflected symmetry in two lines intersects at a right angle.

Answer

A curve where any point is at an equal distance from a fixed point, called the focus, and a fixed line, called the directrix.

Question 23

Which one of the following best represents the general equation of a hyperbola?

Accepted Answer

(x-h)²/a² - (y-k)²/b² = 1

Answer

(y-k)²/b² - (x-h)²/a² = 1

Answer

(x-h)²/a² * (y-k)²/b² = 1

Answer

(x-h)²/a² + (y-k)²/b² = 1

Question 24

What do we call the line that passes through the foci of the hyperbola?

Accepted Answer

Transverse axis

Answer

Asymptote

Answer

Conjugate axis

Answer

Directrix

Question 25

Which of the following is the standard form of the equation of a hyperbola with its center at origin?

Accepted Answer

x^2/a^2 - y^2/b^2 = 1

Answer

(x-h)²/a² - (y-k)²/b² = 1

Answer

(x-h)²/a² + (y-k)²/b² = 1

Answer

x^2/a^2 + y^2/b^2 = 1

Question 26

Determine the standard form equation of a hyperbola that has a horizontal transverse axis, with its center at (0,0), a = 5 and b = 3.

Accepted Answer

x^2/25 - y^2/9 = 1

Answer

x^2/25 + y^2/9 = 1

Answer

x^2/9 + y^2/25 = 1

Answer

x^2/9 - y^2/25 = 1

Question 27

What is the standard form of the equation for a hyperbola?

Accepted Answer

$(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1$

Answer

$y = mx + b$

Answer

$a^2x^2 + b^2y^2 = 1$

Answer

$(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1$

Question 28

Which of the following equations represents a parabola?

Accepted Answer

$y = a(x - h)^2 + k$

Answer

$(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1$

Answer

$x^2 + y^2 = r^2$

Answer

$(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1$

Question 29

A small factory which manufactures candy cones uses parabolic molds for their products. If the diameter of the base is 6 cm and the height is 9 cm, find the equation of the parabola that can represent the shape of the cone.

Accepted Answer

y = -1/6x^2 + 9

Answer

y = -1/3x^2 + 9

Answer

y = -1/4x^2 + 9

Answer

y = -1/2x^2 + 9

Question 30

A satellite dish has a parabolic shape with a diameter of 10 meters and a depth of 2 meters. Find the equation of the parabola.

Accepted Answer

y = 1/20x^2

Answer

y = 1/10x^2

Answer

y = 1/30x^2

Answer

y = 1/15x^2

Question 31

A golf course's fairway design is in the form of an ellipse and is given by the equation 4x^2 + y^2 = 900. What is the semi-major axis of this elliptical fairway?

Accepted Answer

15

Answer

30

Answer

90

Answer

45

Question 32

Which of the following is an example of a series?

Accepted Answer

3 + 6 + 9 + 12 + ...

Answer

√2, √3, √4, √5, ...

Answer

y = mx + b

Answer

2x - 5 = 7

Question 33

What is the sum of the arithmetic series 2 + 4 + 6 + 8 + ... + 50?

Accepted Answer

676

Answer

680

Answer

668

Answer

656

Question 34

What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ...?

Accepted Answer

2

Answer

1

Answer

1.5

Answer

2.5

Question 35

Which of the following options correctly differentiates a sequence from a series in terms of mathematical concepts?

Accepted Answer

A sequence is an ordered list of numbers while a series is the sum of a sequence.

Answer

A sequence is the product of numbers while a series is a sequence in reverse.

Answer

A sequence represents addition while a series represents multiplication.

Answer

A sequence and a series share the exact same definition.

Question 36

Which of the following statements is true regarding sequences and series?

Accepted Answer

A sequence is a list of numbers in a particular order, but a series is the sum of terms of a sequence.

Answer

A sequence and a series are exactly the same thing.

Answer

A series is a list of numbers in a specific order, while a sequence is the sum of terms of a series.

Answer

A series is an equation, while a sequence is a biographical data.

Question 37

Which of the following best describes the difference between a series and a sequence?

Accepted Answer

A sequence is an arrangement of numbers in a particular order, whereas a series is the summation of numbers in a sequence.

Answer

Both a series and a sequence refer to an equation involving variables.

Answer

A series is an arrangement of numbers in a specific order, whereas a sequence is the summation of numbers in a series.

Answer

A sequence and a series are the same thing.

Question 38

What is the sum of the series represented by the sigma notation Σ from i=1 to 5 of (2i)?

Accepted Answer

30

Answer

35

Answer

25

Answer

20

Question 39

What does the sigma notation Σ from n=3 to 5 of n represent?

Accepted Answer

12

Answer

14

Answer

15

Answer

10

Question 40

What is the sum of the series represented by the sigma notation Σ from i=1 to 4 of (3i)?

Accepted Answer

30

Answer

28

Answer

24

Answer

32

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