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# Pre-Calculus

Is an advanced level math course that prepares students for college-level calculus and covers topics such as functions, trigonometry, and complex numbers.

## mathematics

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (Large 100x^2 + 100y^2 - 100x + 400y + 409 =0 )

• Circle

Use the Binomial Theorem to expand and simplify the expression. (x2/3 - y1/3)3

• a. X2 – 3x2/3y2/3 + 3x4/3y1/3 – y
• b. X2 – 3x4/3y1/3 + 3x2/3y2/3 – y
• c. X2 + 3x4/3y1/3 - 3x2/3y2/3 – y
• d. X4 – 3x4/3y1/3 + 3x2/3y2/3 + y

Convert the angle in radians to degrees. Round to two decimal places. -3.97 radians

• a. -227.46°
• b. -227.06°
• c. 0.07°
• d. 0.06°

Where is the center of the circle? (x-h)2+(y-k)2=r

• a. (k,r)
• b. (-h,-k)
• c. (h,r)
• d. (h,k)

Find the standard form of the equation of the parabola with the given characteristics: Vertex: (5, 2); focus: (3, 2)

• (Large (y-2)^2 =-8(x+5))
• (Large (y+2)^2 =-8(x+5))
• (Large (y-2)^2 =8(x-5))
• (Large (y-2)^2 =-8(x-5))

Give the coordinates of the center, foci, and covertices of the ellipse with equation 41x2 + 16y2 + 246x - 192y + 289 = 0. Only vertices are given. Enclose the coordinates in parentheses. For example, (6, 4)

• (-3, 6)(-3, 1)(-7, 6)(-3, 11)(1, 6)

Solve the system by the method of elimination and check any solutions algebraically.X + 2y = 4 X – 2y = 1

• (12, 2)
• (8, 2)
• (2, 0)
• (3, 4)

The shape of this conic section is a bounded curve which looks like a flattened circle.

• circle
• hyperbola
• parabola
• ellipse

Find the standard form of the equation of the ellipse with the given characteristics: Center: (0, 4), a = 2c; vertices:

• (Large frac {x^2} {16} + frac {(y+4)^2}{-12} = 1)
• (Large frac {x^2} {16} + frac {(y-4)^2}{12} = 1)
• (Large frac {x^2} {12} + frac {(y-4)^2}{16} = 1)
• (Large frac {x^2} {-16} + frac {(y-4)^2}{12} = 1)

Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. ( 4 cos^2x - 1 = 0)

• a. ( frac{pi}{3} + 2npi, frac{2pi}{3} + pi, frac{4pi}{3} + 2npi, frac{5pi}{3} + 2npi), where n is any integer
• b. .9 + 2nπ, 2.3 + 2nπ, 3.6 + 2nπ, 5.8 + 2nπ, where n is any integer
• c. ( frac{pi}{3} + 2npi, frac{2pi}{3} + 2npi, frac{4pi}{3} + 2npi, frac{5pi}{3} + 2npi), where n is any integer
• d. ( frac{pi}{3} + 2npi, pi + 2npi, frac{5pi}{3} + 2npi), where n is any integer
• e. 1 + π, 2.3 + 2nπ, 3.3 - 2nπ, 5.8 + 2nπ, where n is any integer

Use the Binomial Theorem to expand and simplify the expression. (x2 + y2)4

• a. x8 + 6x6y2 + 4x4y4 + 4x2y6 + y8
• b. x8 + 6x6y2 + 4x4y4 + 6x2y6 + y8
• c. x8 + 4x6y2 + 6x4y4 + 4x2y6 + y8
• d. 3x8 + 2x6y2 + 9x4y4 + 4x2y6 + 2y8

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (Large y^2 -4x^2 +4x -2y -4 =0)

• hyperbola

A truck that is about to pass through the tunnel from the previous item is 10 ft wide and 8.3 ft high. Will this truck be able to pass through the tunnel?

• No
• Yes

Expand the expression in the difference quotient and simplify.

• a. 1x+h−−−−√+x−−√ ,h ≠0
• b. 1x+h−−−−√−x−−√ ,h =0
• c. 1x+h−−−−√−x−−√ ,h ≠0
• d. 1x−h−−−−√+x−−√ ,h ≠0

Find the exact value of the tangent of the angle by using a sum or difference formula. -165°

• −2√4(3–√−1
• tan (-165)° = −2√4(3–√+1
• 2√4(1−3–√
• 2−3–√

Convert the polar equation to rectangular form. r = 62−3sinθ

• a. y = 4
• b. (x2 + y2)2 = 6x2y – 2y3
• c. X2 + 4y – 4 = 0
• d. 4x2 – 5y2 – 36y – 36 = 0
• e. X2 + y2 – x2/3 = 0

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (large 25x^2-10x-200y-119=0)

• Parabola

Find the exact value of the cosine of the angle by using a sum or difference formula.

• −2√4(3–√−1)
• 2√4(3–√+1)
• cos 195° = 2√4(1−3–√)
• −2√4(3–√+1)

Find the exact value of the trigonometric function given that sin u=−725

• 3/5

Find the standard form of the equation of the parabola with the given characteristics: Focus: (2, 2); directrix: x = -2

• (y+2)2=−8x
• (y−2)2=−8x
• (y+2)2=8x
• (y−2)2=8x

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2−4x−8y+2=0

• Parabola

Solve each equation for exact solutions over the interval [00, 3600]. ( (tan theta - 1)( costheta - 1) = 0 )

• a. {300, 2000, 3100}
• b. {900, 2100, 3300}
• c. {300, 2100, 2400, 3000}
• d. {150, 1300, 4300}
• e. {00, 450, 2250}

Use the Binomial Theorem to expand and simplify the expression. (x + 1)4

• X4 + 4x3 + 6x2 + 4x + 1
• X4 + 16x3 + 3x2 + 4x + 1
• X4 + 2x3 + 3x2 + 2x + 1
• X4 - 4x3 + 6x2 + 4x - 1

Expand the binomial by using Pascal's Triangle to determine the coefficients. (x - 2y)5

• 2x5 + 20x4y + 80x3y2 + 80x2y3 + 40xy4 + 32y5
• x5 + 10x4y + 40x3y2 + 80x2y3 + 80xy4 + 32y5
• x5 + 10x4y + 40x3y2 + 80x2y3 + 40xy4 + 16y5
• 32x5 + 10x4y + 40x3y2 + 80x2y3 + 40xy4 + 16y5

Find the standard form of the equation of the ellipse with the given characteristics: Vertices: (0, 2), (4, 2); endpoints of the minor axis: (2, 3), (2, 1)

• (x−2)24+(y−2)21=1
• (x−2)24+(y+2)21=1
• (x−2)22+(y−2)21=1
• (x−2)24−(y−2)21=1

Solve the system by the method of elimination and check any solutions algebraically:

• a. (4, -1)
• b. (-7, 3)
• c. (5, -1)
• d. (5, -2)

Solve the equation for exact solutions over the interval [0, 2π]. 2–√cos2x=−1

• {π12,5π12,13π12,17π12}
• {π17,7π17,13π17,19π17,25π17,31π17}
• {π18,7π18,13π18,19π18,25π18,31π18}
• {0,π3,2π3,π,4π3,5π3}
• {3π8,5π8,11π18,13π18}

Give all exact solutions over the interval [00, 3600].

• 22.5° + 360°n, 112.5° + 360°n, 202.5° + 360°n, 292.5° + 360°n, where n is any integer.
• 0° + 360°n, 60° + 360°n, 180° + 360°, 300° + 360°n, where n is any integer.
• 11.8° + 360°n, 78.2° + 360°n, 191.8° + 360°n, 258.2° + 360°n, where n is any integer
• 30° + 360°n, 90° + 360°n, 150° + 360°n, 210° + 360°n, 270° + 360°n, 330° + 360°n, where n is any integer.

Write the first five terms of the sequence. Assume that n begins with 1.

• 0
• , Answer
• 6
• 24
• 60

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes.

• d.

Find the standard equation of the hyperbola which satisﬁes the given conditions:

• a. (x−7)255−(y−8)226=12
• b. (x−3)225−(y−8)256=1
• c. (x+5)228−(y−8)216=6
• d. (x+6)220−(y−12)216=1

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. b. xy – 2y – 4x = 0

• [No Answer]

What is the quadrant or axis on which the point is located? (-10, -16)

• II
• IV
• III
• I

Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. 3sin2x−sinx−1=0

• .9 + 2nπ, 2.3 + 2nπ, 3.6 + 2nπ, 5.8 + 2nπ, where n is any integer
• π3+2nπ,π+2nπ,5π3+2nπ
• 1 + π, 2.3 + 2nπ, 3.3 - 2nπ, 5.8 + 2nπ, where n is any integer
• π3+2nπ,2π3+2nπ,4π3+2nπ,5π3+2nπ

The term _________ is both used to refer to a segment from center C to a point P on the circle, and the length of this segment.

• a. parabola
• b. radius
• c. diameter
• d. point

Find a polar equation of the conic with its focus at the pole.

• r=11−cosθ
• r=12+sinθ
• r=103+2cosθ
• r=21−sinθ
• r=101−cosθ
• r=21+2cosθ

Find the standard form of the equation of the ellipse with the given characteristics: Foci: (0, 0), (0, 8); major axis of length 16

• x248+(y+4)264=1
• x248+(y−4)264=1
• x248+(y−4)264=−1

Convert the rectangular equation to polar form. Assume a > 0. x2 + y2 - 2ax = 0

• r=−23cosθ−sinθ
• r=2acosθ
• r = a
• r2=16secθcscθ=32csc2θ
• r=41−cosθor−41+cosθ

Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. (2 cos^2 + cos x =1)

• a. (frac{pi}{3} + 2npi, frac{2pi}{3} + 2npi, frac{4pi}{3} + 2npi,frac{5pi}{3} + 2npi), where n is any integer
• b. (frac{pi}{3} + 2npi, pi + 2npi,frac{5pi}{3} + 2npi), where n is any integer
• c. .9 + 2nπ, 2.3 + 2nπ, 3.6 + 2nπ, 5.8 + 2nπ, where n is any integer
• d. (frac{pi}{3} + 2npi, frac{2pi}{3} +pi, frac{4pi}{3} + 2npi,frac{5pi}{3} + 2npi), where n is any integer
• e. 1 + π, 2.3 + 2nπ, 3.3 - 2nπ, 5.8 + 2nπ, where n is any integer

Find the sum.

• 30

Give the coordinates (enclose the coordinates in parentheses) of the foci, vertices, and covertices of the ellipse with equation

• (-12, 0)(-13, 0)(0, -5)(12, 0)(13, 0)(0, 5)

What is the quadrant or axis on which the point is located? (13, -14)

• II
• I
• x-axis
• IV

Convert the polar equation to rectangular form. r=4cscθ

• a. 4x2 – 5y2 – 36y – 36 = 0
• b. (x2 + y2)2 = 6x2y – 2y3
• c. X2 + 4y – 4 = 0
• d. X2 + y2 – x2/3 = 0
• e. y = 4

An airplane flying into a headwind travels the 1800-mile flying distance between Pittsburgh, Pennsylvania and Phoenix, Arizona in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

• a. 1050 miles per hour, 50 miles per hour
• b. 500 miles per hour, 100 miles per hour
• c. 750 miles per hour, 25 miles per hour
• d. 550 miles per hour, 50 miles per hour

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2−y2−4x−3=0

• hyperbola

Write the expression as the sine, cosine, or tangent of an angle. cos 25° cos 15° - sin 25° sin 15°

• cos 40
• °

Solve the equation for exact solutions over the interval [0, 2π]. sin 3x = 0

• {π18,7π18,13π18,19π18,25π18,31π18}
• {π12,5π12,13π12,17π12}
• {π17,7π17,13π17,19π17,25π17,31π17}
• {3π8,5π8,11π18,13π18}
• {0,π3,2π3,π,4π3,5π3}

Using the equation for the circle find its radius: x2 + y2 + 6x + 2y + 6 = 0.

• a. r = 1
• b. r = 2
• c. r = 3
• d. r = 4

A type of Conic where the plane is horizontal.

• a. parabola
• b. circle
• c. hyperbola
• d. ellipse

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

• a. -5 radians
• b. 1/5 radians
• 5
• radians
• c. 5°
• d. 5 radians

Solve the system by the method of substitution. Check your solution graphically. -2x + y = -5 X2 + y2 = 25

• a. (0, -5), (4, 3)
• b. (2, -1), (5, -5)
• c. (2, -1), (5, 3)
• d. (9, -3), (6, 2)

What is the quadrant or axis on which the point is located? (7,7)

• IV
• I
• II
• III

Solve each equation for exact solutions over the interval [00, 3600]. (tanθ−1)(cosθ−1)=0

• {300, 2100, 2400, 3000}
• {150, 1300, 4300}
• {300, 2000, 3100}
• {00, 450, 2250}
• {900, 2100, 3300}

Convert the rectangular equation to polar form. Assume a > 0. y2 - 8x - 16 = 0

• r2=16secθcscθ=32csc2θ
• r=41−cosθor−41+cosθ
• r=2acosθ
• r = a
• r=−23cosθ−sinθ

Solve the system by the method of elimination and check any solutions algebraically. 0.05x – 0.03y = 0.21 0.07x + 0.02y = 0.16

• [No Answer]

Solve the system by the method of substitution: -x + 2y = 2 3x + y = 15

• a. (8, 1)
• b. (0, -3)
• c. (4, 3)
• d. (-2, 3)

Convert π/18 to Degrees.

• a. 20°
• b. 18°
• c. 10°
• d. 15°

What are the coordinates of the figure below: A

• A(4, 5); B(-5, 5)
• A(4, 5); B(5, -5)
• A(4, 5); B(5, 5)
• A(5, 24); B(5, -5)

Classify the angle as acute, right, obtuse, or straight: 2π/3

• a. right
• b. obtuse
• c. straight
• d. acute

Convert the polar equation to rectangular form. ( r = 2 sin 3 theta )

• a. (x2 + y2)2 = 6x2y – 2y3
• b. X2 + 4y – 4 = 0
• c. y = 4
• d. 4x2 – 5y2 – 36y – 36 = 0
• e. X2 + y2 – x2/3 = 0

Convert the polar equation to rectangular form.

• 3–√x+y=0
• x2+y2=16
• x2+y2−4y=0
• x2+y2−2y=0

Use the Binomial Theorem to expand and simplify the expression.

• a. X2 + 6x3/2 + 22x + 54x1/2 + 40
• b. X2 + 6x3/2 + 26x + 54x1/2 + 9
• c. X2 + 12x3/2 + 54x + 108x1/2 + 81
• d. X2 + 28x3/2 + 50x - 108x1/2 + 80

Solve the system by the method of elimination and check any solutions algebraically.

• [No Answer]

Determine the quadrant in which the angle lies. 349°

• a. Quadrant III
• b. Quadrant IV
• c. Quadrant I
• d. Quadrant II

Write the expression as the sine, cosine, or tangent of an angle. sin 3 cos 1.2 - cos 3 sin 1.2

• sin 1.8

Convert the rectangular equation to polar form. Assume a > 0. 3x - y + 2 = 0

• r = a
• r2=16secθcscθ=32csc2θ
• r=41−cosθor−41+cosθ
• r=2acosθ
• r=−23cosθ−sinθ

Solve the equation for exact solutions over the interval [0, 2π]. 23–√sin2x=3–√

• {3π8,5π8,11π8,13π8}
• {π18,7π18,13π18,19π18,25π18,31π18}
• {π17,7π17,13π17,19π17,25π17,31π17}
• {π12,5π12,13π12,17π12}
• {0,π3,2π3,π,4π3,5π3}

Solve the system by the method of substitution. Check your solution graphically.

• a. (2, -1), (5, -5)
• b. (9, -3), (6, 2)
• c. (0, -5), (4, 3)
• d. (2, -1), (5, 3)

What does r refer to in the following equation? (x-h)2+(y-k)2=r

• a. The center of a circle.
• b. The focus of a parabola.
• c. The square of the radius of a circle.
• d. The distance between the vertex and the focus of a parabola.

First six terms:

• 3, 1, -2, -6, -11, -17

Find the standard form of the equation of the ellipse with the given characteristics:

• (x+2)21+(y−1)23=1
• (x+2)21+(y+3)29=1
• (x−2)21+(y+3)29=1
• (x−2)21+(y−3)29=1

A parabola has focus F(-2, -5) and directrix x = 6. Find the standard equation of the parabola.

• (y - 5)2 = 16(x - 4)
• (y + 10)2 = 16(x - 4)
• (y - 5)2 = -16(x + 2)
• (y + 5)2 = -16(x - 2)

What are the coordinates of the given figure below:a

• A(5, -5); B(1, -2)
• A(5, 5); B(0, 2)
• A(-5, 5); B(0, 2)
• A(5, 5); B(0, -2)

Find the center point of the following circle x2 + y2 + 8x + 4y - 3 = 40.

• a. (2, 4)
• b. (4, 2)
• c. (-2, -4)
• d. (-4, -2)

Choose an expression for the apparent nth term of the sequence. Assume that n begins with 1.

• n+12n−1
• (−1)n(n+1)n+2
• an = (-1)n + 1
• 1n
• 1n2

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (Large 4x^2+3y^2+8x-24y+51 =0 )

• ellipse

Expand the binomial by using Pascal's Triangle to determine the coefficients. (2t - s)5

• 32t5 - 20t4s + 40t3s2 - 40t2s3 + 10ts4 - s5
• 32t5 - 80t4s + 40t3s2 + 80t2s3 + 20ts4 - s5
• 16t5 + 40t4s + 80t3s2 - 80t2s3 + 10ts4 - s5
• 32t5 - 80t4s + 80t3s2 - 40t2s3 + 10ts4 - s5

Find a quadratic model for the sequence with the indicated terms.

• [No Answer]

Use the Binomial Theorem to expand and simplify the expression. (y - 4)3

• Y3 +12y2 - 48y - 64
• Y3 + 16y2 - 48y + 64
• Y3 - 12y2 + 48y - 64
• Y3 - 16y2 + 48y - 64

A type of Conic where the plane intersects only on one cone to form an anbounded curve.

• a. circle
• b. hyperbola
• c. ellipse
• d. parabola

Find the standard equation of the parabola which satisﬁes the given condition:

• a. (y - 3)2 = -10(x + 8)
• b. (y - 3)2 = 10(x + 8)
• c. (y - 3)2 = 10(x - 8)
• d. (y + 3)2 = 10(x + 8)

Give the coordinates (enclose the coordinates in parentheses) of the foci, vertices, and covertices of the ellipse with equation .

• (-12, 0)(-13, 0)(0, -5)(12, 0)(13, 0)(0, -5)

Convert the polar equation to rectangular form. (theta = frac{2pi}{3} )

• a. (x^2 + y^2 = 16)
• b. (sqrt{3}x + y = 0 )
• c. (x^2 + y^2 - 4y = 0)
• d. (x^2 + y^2 - 2y = 0)

In order to graph a circle one must graph all the points that are equidistant from:

• a. a single point outside the circle.
• b. two points, one inside and one outside the circle.
• c. one point and one line, like a parabola.
• d. a single point at the center.

Use the Binomial Theorem to expand and simplify the expression. (3a - 4b)5

• a. 243a5 + 1620a4b - 4320a3b2 + 6540a2b3 + 3230ab4 - 1024b5
• b. 115a5 + 1620a4b - 4320a3b2 - 5760a2b3 + 3840ab4 - 1024b5
• c. 243a5 - 1620a4b + 4320a3b2 - 5760a2b3 + 3840ab4 - 1024b5
• d. 215a5 - 1620a4b + 2320a3b2 + 5760a2b3 - 3840ab4 - 5344b5

What is the standard form of the equation of the circle x2 + 14x + y2 - 6y - 23 = 0?

• a. (x + 7)2 + (y + 3)2 = 92
• b. (x + 7)2 + (y - 3)2 = 92
• c. (x - 7)2 + (y + 3)2 = 92
• d. (x - 7)2 + (y - 3)2 = 92

Find the exact value of each expression.

• −2√−6√4
• 12

Write the expression as the sine, cosine, or tangent of an angle. tan2x+tanx1−tan2xtanx

• tan 3x

Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. 5x2 – 6xy + 5y2 – 12 = 0

• [No Answer]

Find the exact value of the trigonometric function given that sinu=513

• -(63/65)

Give all exact solutions over the interval [0°, 360°].

• 22.5° + 360°n, 112.5° + 360°n, 202.5° + 360°n, 292.5° + 360°n, where n is any integer
• 0° + 360°n, 60° + 360°n, 180° + 360°, 300° + 360°n, where n is any integer.
• 11.8° + 360°n, 78.2° + 360°n, 191.8° + 360°n, 258.2° + 360°n, where n is any integer.
• 30° + 360°n, 90° + 360°n, 150° + 360°n, 210° + 360°n, 270° + 360°n, 330° + 360°n, where n is any integer.

An orbit of a satellite around a planet is an ellipse, with the planet at one focus of this ellipse. The distance of the satellite from this star varies from 300,000 km to 500,000 km, attained when the satellite is at each of the two vertices. Find the equation of this ellipse, if its center is at the origin, and the vertices are on the x-axis. Assume all units are in 100,000 km.

• (Large frac {x^2}{16} - frac{y^2}{15} =-1 )
• (Large frac {-x^2}{16} + frac{y^2}{15} =-1 )
• (Large frac {x^2}{16} + frac{y^2}{15} =1 )
• (Large frac {x^2}{16} - frac{y^2}{15} =1 )

A whispering gallery has a semielliptical ceiling that is 9 m high and 30 m long. How high is the ceiling above the two foci?

• a. 6.5 m
• b. 5.6 m
• c. 4.5 m
• d. 5.4 m

Solve the system by the method of substitution:

• a. (0, -3)
• b. (8, 1)
• c. (-2, 3)
• d. (4, 3)

Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. ( 3 sin^2 x - sin x - 1 = 0 )

• a. (frac{pi}{3} + 2npi, frac{2pi}{3} + 2npi, frac{4pi}{3} + 2npi, frac{5pi}{3} + 2npi), where n is any integer.
• b. .9 + 2nπ, 2.3 + 2nπ, 3.6 + 2nπ, 5.8 + 2nπ, where n is any integer
• c. (frac{pi}{3} + 2npi, pi + 2npi, frac{5pi}{3} + 2npi), where n is any integer.
• d. 1 + π, 2.3 + 2nπ, 3.3 - 2nπ, 5.8 + 2nπ, where n is any integer

Use the Binomial Theorem to approximate the quantity accurate to three decimal places.

• 1.172

Find the standard form of the equation of the parabola with the given characteristics: Vertex: (0, 4); directrix: y = 2

• (Large x^2=-8(y-4) )
• (Large x^2=8(y+4) )
• (Large x^2=2(y-4) )
• (Large x^2=8(y-4) )

A type of Conic where the plane is tilted and intersects only on one cone to form a bounded curve.

• circle
• parabola
• ellipse
• hyperbola

Expand the binomial by using Pascal’s Triangle to determine the coefficients.

• a. X5 + 10x4y + 30x3y2 + 80x2y3 + 40xy4 + 32y5
• b. X5 + 10x4y + 40x2y3 + 80x4y + 80xy5 + 32y5
• c. X5 + 10x4y + 40x3y2 + 80x2y3 + 80xy4 + 32y5
• d. X5 + 5x4y + 20x3y2 + 40x2y3 + 40xy4 + 16y5

Solve the equation for exact solutions over the interval [0, 2π]. cos2x=−12

• {π2,3π12}
• {π2,7π6,11π6}
• {0,π4,π2,3π4,π,5π4,3π27π4}
• {π12,11π12,13π12,23π12}
• {π13,2π3,4π3,5π3}

Convert the rectangular equation to polar form. Assume a > 0. y = 4

• R = 6
• R = 4 csc θ
• R = 3 sec θ
• R = 4

Find the standard form of the equation of the parabola with the given characteristics:

• y2=−4(x+4)
• y2=4(−x+4)
• y2=4(x−4)
• y2=4(x+4)

First differences:

• -2, -3, -4, -5, -6

Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. 2cos2+cosx=1

• π3+2nπ,2π3+π,4π3+2nπ,5π3+2nπ
• π3+2nπ,π+2nπ,5π3+2nπ
• π3+2nπ,2π3+2nπ,4π3+2nπ,5π3+2nπ
• .9 + 2nπ, 2.3 + 2nπ, 3.6 + 2nπ, 5.8 + 2nπ, where n is any integer
• 1 + π, 2.3 + 2nπ, 3.3 - 2nπ, 5.8 + 2nπ, where n is any integer

The ______ is the point midway between the focus and the directrix.

• a. parabola
• b. equation
• c. vertex
• d. graph

Solve the equation for exact solutions over the interval [0, 2π]. (sin 3x = -1)

• a. (Big{0,frac{pi}{4},frac{pi}{2},frac{3pi}{4},pi,frac{5pi}{4},frac{3pi}{2}frac{7pi}{4}Big})
• b. (Big{frac{pi}{2},frac{7pi}{6},frac{11pi}{6}Big})
• c. (Big{frac{pi}{2},frac{3pi}{12}Big})
• d. (Big{frac{pi}{13},frac{2pi}{3},frac{4pi}{3},frac{5pi}{3}Big})
• e. (Big{frac{pi}{12},frac{11pi}{12},frac{13pi}{12},frac{23pi}{12}Big})

Find a formula for the sum of the first n terms of the sequence.

• [No Answer]

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2+16y2−4x−32y+1=0

• Ellipse

A ___________ has a shape of paraboloid, where each cross section is a parabola.

• a. curve
• b. dish circle
• c. curve parabola
• d. satellite dish

Solve the system by the method of substitution.

• a. (4, -2)
• b. (2, -1)
• c. (1, 1)
• d. (-1, -2)

A point in polar coordinates is given. Convert the point to rectangular coordinates.

• 2√2,2√2
• 2√2,−2√2
• −2√2,2√2
• 2√3,2√3

The orbit of a planet around a star is described by the equation where the star is at one focus, and all units are in millions of kilometers. The planet is closest and farthest from the star, when it is at the vertices. How far is the planet when it is closest to the sun? How far is the planet when it is farthest from the sun?

• a. 900 million km, 700 million km
• b. 700 million km, 900 million km
• c. 800 million km, 900 million km
• d. 640 million km, 700 million km

What are the coordinates of the figure below:a

• G(6, -6); H(-2, -7)
• G(6, -2); H(-6, -2)
• G(-6, 28); H(-2, -7)
• G(6, -6); H(-7, -2)

Solve the equation for exact solutions over the interval [0, 2π]. cos 2x = 3√2

• {π3,2π3,4π3,5π3}
• {π2,7π6,11π6}
• {π12,11π12,13π12,23π12}
• {π2,3π2}
• {0,π4,π2,3π4,π,5π43π2,7π4}

Plot the point given in polar coordinates and find two additional polar representations of the point, using -2π < θ < 2π.

• [No Answer]

Find the standard form of the equation of the ellipse with the given characteristics: Vertices: (0, 4), (4, 4); minor axis of length 2

• (x+2)24+(y−4)21=1
• (x+2)24+(y+4)21=1
• (x−2)24+(y−4)21=1
• (Large frac {(x-2)^2}{4} + frac {(y+4)^2}{1} =1)

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. a. x2 – 2xy + y2 – 1 = 0

• [No Answer]

Solve the equation for exact solutions over the interval [0, 2π]. cot3x=3–√

• {0,π3,2π3,π,4π3,5π3}
• {3π8,5π8,11π18,13π18}
• {π18,7π18,13π18,19π18,25π18,31π18}
• {π12,5π12,13π12,17π12}
• {π17,7π17,13π17,19π17,25π17,31π17}

What is the quadrant or axis on which the point is located? (-15, 0)

• IV
• y-axis
• x-axis
• II

A big room is constructed so that the ceiling is a dome that is semielliptical in shape. If a person stands at one focus and speaks, the sound that is made bounces off the ceiling and gets reﬂected to the other focus. Thus, if two people stand at the foci (ignoring their heights), they will be able to hear each other. If the room is 34 m long and 8 m high, how far from the center should each of two people stand if they would like to whisper back and forth and hear each other?

• a. 17 m
• b. 15 m
• c. 24 m
• d. 16 m

Use the Binomial Theorem to expand and simplify the expression. 2(x - 3)5 + 5(x - 3)2

• 2x4 – 12x3 + 25x2 – 220x + 207
• 2x4 + 24x3 - 113x2 + 246x + 207
• 2x4 + 24x3 - 113x2 + 246x - 207
• 2x4 – 24x3 + 113x2 – 246x + 207

Second differences:

• -1, -1, -1, -1

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2+y2−6x+4y+9=0

• Circle

Solve each equation for exact solutions over the interval [00, 3600]. ((cottheta - sqrt{3})(2sintheta + sqrt{3}) = 0)

• a. {00, 450, 2250}
• b. {150, 1300, 4300}
• c. {900, 2100, 3300}
• d. {300, 2100, 2400, 3000}
• e. {300, 2000, 3100}

Determine the vertex of the parabola with the equation x2 - 6x + 5y = -34. Enclose your answers in parentheses.

• (3, -5)

What kind of symmetry does a circle have?

• a. All of the answer choices are correct.
• b. Horizontal
• c. Radial
• d. Vertical

Which answer choice shows the center of the circle with the equation x2 + y2 -8x +14y +57.

• a. (-7, 4)
• b. (7, 4)
• c. (-4, 7)
• d. (4, -7)

A satellite dish in the shape of a paraboloid is 10 ft across, and 4 ft deep at its vertex. How far is the receiver from the vertex, if it is placed at the focus? Round off your answer to 2 decimal places.

• [No Answer]

Solve the equation for exact solutions over the interval [0, 2π]. sinx2=2–√−sinx2

• {π13,2π3,4π3,5π3}
• {π12,11π12,13π12,23π12}
• {0,π4,π2,3π4,π,5π4,3π27π4}
• {π2,3π12}
• {π2,7π6,11π6}

Use the Binomial Theorem to expand and simplify the expression. 2(x - 3)4 + 5(x - 3)2

• a. x4 + 24x3 + 98x2 - 113x - 207
• b. 2x4 - 12x3 - 96x2 + 232x + 207
• c. 2x4 + 12x3 - 94x2 + 246x - 153
• d. 2x4 - 24x3 + 113x2 - 246x + 207

Find the equation in standard form of the ellipse whose foci are F1 (-8,0) and F2 (8,0), such that for any point on it, the sum of its distances from the foci is 20.

• [No Answer]

What is the standard form of the equation of the circle x2 + y2 + 10x - 4y - 7 = 0?

• a. (x + 5)2 + (y - 2)2 = 62
• b. (x + 5)2 + (y + 2)2 = 62
• c. (x - 5)2 + (y - 2)2 = 62
• d. (x - 5)2 + (y + 2)2 = 62

Find Pk+1 for the given Pk.

• [No Answer]

Find the specified nth term in the expansion of the binomial.

• a. 30x8y2
• b. 60x7y3
• c. 120x7y3
• d. 120x3y7

Convert the angle in degrees to radians. Express answer as a multiple of π. 144°

• a. 3π/4 radians
• 3π/5 radians
• 5π/6
• radians
• d.
• 4π/5

Expand the binomial by using Pascal’s Triangle to determine the coefficients. (x + 2y)5

• a. X5 + 5x4y + 20x3y2 + 40x2y3 + 40xy4 + 16y5
• b. X5 + 10x4y + 40x3y2 + 80x2y3 + 80xy4 + 32y5
• c. X5 + 10x4y + 30x3y2 + 80x2y3 + 40xy4 + 32y5
• d. X5 + 10x4y + 40x2y3 + 80x4y + 80xy5 + 32y5

Find the standard equation of the ellipse which satisﬁes the given conditions.

• (x+4)249+(y−6)240=1
• (x+4)249−(y−6)240=−1
• (x+4)249+(y−6)240=−1
• (x−4)249−(y−6)240=−1

What are the coordinates of the center of the circle given by the equation x2+y2-16x-8y+31=0?

• (8,4)
• (-8,4)
• (-8,-4)
• (8,-4)

What Quadrant does 294° belongs to?

• a. Quadrant III
• b. Quadrant IV
• c. Quadrant I
• d. Quadrant II

Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.

• [No Answer]

Solve the equation for exact solutions over the interval [0, 2π]. (cos2x = -frac{1}{2} )

• a. (Big{frac{pi}{12},frac{11pi}{12},frac{13pi}{12},frac{23pi}{12}Big})
• b. (Big{0,frac{pi}{4},frac{pi}{2},frac{3pi}{4},pi,frac{5pi}{4},frac{3pi}{2}frac{7pi}{4}Big})
• c. (Big{frac{pi}{13},frac{2pi}{3},frac{4pi}{3},frac{5pi}{3}Big})
• d. (Big{frac{pi}{2},frac{3pi}{12}Big})
• e. (Big{frac{pi}{2},frac{7pi}{6},frac{11pi}{6}Big})

A circle can be centered anywhere in the coordinate plane.

• True
• False

Solve the system by the method of elimination and check any solutions algebraically. 3x + 2y = 10 2x + 5y = 3

• (2, 8)
• (4, -1)
• (8, -1)
• (-4, 2)

Solve the equation for exact solutions over the interval [0, 2π]. (sinfrac{x}{2} = sqrt{2} - sinfrac{x}{2})

• a. (Big{frac{pi}{12},frac{11pi}{12},frac{13pi}{12},frac{23pi}{12}Big})
• b. (Big{frac{pi}{2},frac{7pi}{6},frac{11pi}{6}Big})
• c. (Big{0,frac{pi}{4},frac{pi}{2},frac{3pi}{4},pi,frac{5pi}{4},frac{3pi}{2}frac{7pi}{4}Big})
• d. (Big{frac{pi}{2},frac{3pi}{12}Big})
• e. (Big{frac{pi}{13},frac{2pi}{3},frac{4pi}{3},frac{5pi}{3}Big})

Convert the polar equation to rectangular form. r = 4

• a. x2+y2=16
• b. 3–√x+y=0
• c. x2+y2−4y=0
• d. x2+y2+2y=0

Solve the equation for exact solutions over the interval [0, 2π]. tan 4x = 0

• a. (Big{0,frac{pi}{4},frac{pi}{2},frac{3pi}{4},pi,frac{5pi}{4},frac{3pi}{2}frac{7pi}{4}Big})
• b. (Big{frac{pi}{13},frac{2pi}{3},frac{4pi}{3},frac{5pi}{3}Big})
• c. (Big{frac{pi}{12},frac{11pi}{12},frac{13pi}{12},frac{23pi}{12}Big})
• d. (Big{frac{pi}{2},frac{3pi}{12}Big})
• e. (Big{frac{pi}{2},frac{7pi}{6},frac{11pi}{6}Big})

What Quadrant does 144° belongs to?

• a. Quadrant I
• b. Quadrant III
• c. Quadrant IV
• d. Quadrant II

Use any method to solve the system.

• a. (2, 1)
• b. (0, 2)
• c. (4, 1)
• d. (8, 2)

Solve each equation for exact solutions over the interval [00, 3600]. 2sinθ−1=cscθ

• {00, 450, 2250}
• {300, 2000, 3100}
• {150, 1300, 4300}
• {900, 2100, 3300}
• {300, 2100, 2400, 3000}

A structure of ellipse that have the origin as their centers.

• a. diagonal
• b. horizontal
• c. vertical
• d. center

r=21−cosθ

• PARABOLA

Find the sum using the formulas for the sums of powers of integers.

• [No Answer]

Two control towers are located at points Q(-500, 0) and R(500, 0), on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds) before the message from R.

• a. x2212000−y269700=7(leftbranch)
• b. x2202500−y247500=1(leftbranch)
• c. x2204500−y257500=1(leftbranch)
• d. x2217500−y237700=12(leftbranch)

Find the standard equation of the hyperbola which satisﬁes the given condition:

• a. (x−4)226−(y−8)264=1
• b. (x−5)236−(y−7)264=1
• c. (x−6)240−(y−4)22=4
• d. (x+2)216−(y−4)220=8

Convert 2π into degrees.

• a. 300°
• b. 144°
• c. 360°
• d. 280°

Convert the angle in radians to degrees. 5π/ 4

• a. 450°
• b. 225°
• c. 144π°
• d. 144°

Solve the equation for exact solutions over the interval [0, 2π]. 3tan3x=3–√

• {π12,5π12,13π12,17π12}
• {3π8,5π8,11π18,13π18}
• {π17,7π17,13π17,19π17,25π17,31π17}
• {0,π3,2π3,π,4π3,5π3}
• {π18,7π18,13π18,19π18,25π18,31π18}

The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system. a.Θ = 90o, (0, 3)

• a. (3, 0)
• b. (-3, 0)
• c. (-3, 0)
• d. (0, -3)
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