Pre-Calculus

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}

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

• circle
• parabola
• ellipse
• hyperbola

Use any method to solve the system.

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

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

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)

What Quadrant does 144° belongs to?

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

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

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.

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

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 system by the method of substitution.

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

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)

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

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)

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

• circle
• hyperbola
• parabola
• ellipse

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)

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°

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})

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

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

• IV
• I
• II
• III

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

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

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

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)

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

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

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

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 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

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 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 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

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}

r=21−cosθ

• PARABOLA

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)

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)

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}

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

• hyperbola

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.

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

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

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

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

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}

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

• Circle

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

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

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) )

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

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)

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

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)

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

• IV
• y-axis
• x-axis
• II

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

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

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))

First differences:

• -2, -3, -4, -5, -6

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)

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

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

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

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

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}

Convert π/18 to Degrees.

• a. 20°
• b. 18°
• c. 10°
• d. 15°

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.

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 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}

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

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

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

Find the exact value of each expression.

• −2√−6√4
• 12

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

• II
• IV
• III
• I

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.

Find Pk+1 for the given Pk.

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 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

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

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)

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

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 )

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)

Second differences:

• -1, -1, -1, -1

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

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)

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

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

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

A type of Conic where the plane is horizontal.

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

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

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

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.

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

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

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 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 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}

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

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

• II
• I
• x-axis
• IV

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)

Determine the quadrant in which the angle lies. 349°

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

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

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

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.

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

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

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

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

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

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})

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

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

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

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)

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

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

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–√

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)

First six terms:

• 3, 1, -2, -6, -11, -17

Convert 2π into degrees.

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

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}

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

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

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

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

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

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

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

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 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

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

A circle can be centered anywhere in the coordinate plane.

• True
• False

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

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)

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}

What Quadrant does 294° belongs to?

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}

Find the sum.

• 30

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

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

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)

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

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})

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

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}

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 substitution:

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

Convert the polar equation to rectangular form.

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

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.

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

• Parabola

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

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

• Ellipse

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

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

• 3/5

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

What kind of symmetry does a circle have?

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

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

• tan 3x

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

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

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

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)

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