40 Algebra multiple choice questions

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Question 1 of 40

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x - 2y + z = 0 y - 3z = -1 2y + 5z = -2

A. {(-1, -2, 0)}

B. {(-2, -1, 0)}

C. {(-5, -3, 0)}

D. {(-3, 0, 0)}

Question 2 of 40

Use Gaussian elimination to find the complete solution to each system.

x - 3y + z = 1 -2x + y + 3z = -7 x - 4y + 2z = 0

A. {(2t + 4, t + 1, t)}
B. {(2t + 5, t + 2, t)}
C. {(1t + 3, t + 2, t)}
D. {(3t + 3, t + 1, t)}
Question 3 of 40

Use Cramer’s Rule to solve the following system.

4x - 5y = 17 2x + 3y = 3

A. {(3, -1)}
B. {(2, -1)}
C. {(3, -7)}
D. {(2, 0)}
Question 4 of 40

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 2y = z - 1 x = 4 + y - z x + y - 3z = -2

A. {(3, -1, 0)}
B. {(2, -1, 0)}
C. {(3, -2, 1)}
D. {(2, -1, 1)}
Question 5 of 40

Use Cramer’s Rule to solve the following system.

x + 2y + 2z = 5 2x + 4y + 7z = 19 -2x - 5y - 2z = 8

A. {(33, -11, 4)}
B. {(13, 12, -3)}
C. {(23, -12, 3)}
D. {(13, -14, 3)}
Question 6 of 40

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

w - 2x - y - 3z = -9 w + x - y = 0 3w + 4x + z = 6 2x - 2y + z = 3

A. {(-1, 2, 1, 1)}
B. {(-2, 2, 0, 1)}
C. {(0, 1, 1, 3)}
D. {(-1, 2, 1, 1)}
Question 7 of 40

Use Gauss-Jordan elimination to solve the system.

-x - y - z = 1 4x + 5y = 0 y - 3z = 0

A. {(14, -10, -3)}
B. {(10, -2, -6)}
C. {(15, -12, -4)}
D. {(11, -13, -4)}
Question 8 of 40

Find values for x, y, and z so that the following matrices are equal.

2x z

y + 7 4

-10 6

13 4

A. x = -7; y = 6; z = 2
B. x = 5; y = -6; z = 2
C. x = -3; y = 4; z = 6
D. x = -5; y = 6; z = 6
Question 9 of 40

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12

A. {(3 - 3t, 2 + t, t)}
B. {(6 - 3t, 2 + t, t)}
C. {(5 - 2t, -2 + t, t)}
D. {(2 - 1t, -4 + t, t)}
Question 10 of 40

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

2x - y - z = 4 x + y - 5z = -4 x - 2y = 4

A. {(2, -1, 1)}
B. {(-2, -3, 0)}
C. {(3, -1, 2)}
D. {(3, -1, 0)}
Question 11 of 40

Use Cramer’s Rule to solve the following system.

2x = 3y + 2 5x = 51 - 4y

A. {(8, 2)}
B. {(3, -4)}
C. {(2, 5)}
D. {(7, 4)}
Question 12 of 40

Use Cramer’s Rule to solve the following system.

x + y = 7 x - y = 3

A. {(7, 2)}
B. {(8, -2)}
C. {(5, 2)}
D. {(9, 3)}
Question 13 of 40

Use Cramer’s Rule to solve the following system.

x + y + z = 0 2x - y + z = -1 -x + 3y - z = -8

A. {(-1, -3, 7)}
B. {(-6, -2, 4)}
C. {(-5, -2, 7)}
D. {(-4, -1, 7)}
Question 14 of 40

Use Cramer’s Rule to solve the following system.

3x - 4y = 4 2x + 2y = 12

A. {(3, 1)}
B. {(4, 2)}
C. {(5, 1)}
D. {(2, 1)}
Question 15 of 40

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1

A. {(0, -1, -2)}
B. {(2, 0, 2)}
C. {(1, -1, 2)}
D. {(4, -1, 3)}
Question 16 of 40

Solve the system using the inverse that is given for the coefficient matrix.

2x + 6y + 6z = 8 2x + 7y + 6z =10 2x + 7y + 7z = 9

The inverse of:

2 2 2

6 7 7

6 6 7

7/2 -1 0

0 1 -1

-3 0 1

A. {(1, 2, -1)}
B. {(2, 1, -1)}
C. {(1, 2, 0)}
D. {(1, 3, -1)}
Question 17 of 40

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

3x + 4y + 2z = 3 4x - 2y - 8z = -4 x + y - z = 3

A. {(-2, 1, 2)}
B. {(-3, 4, -2)}
C. {(5, -4, -2)}
D. {(-2, 0, -1)}
Question 18 of 40

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

2w + x - y = 3 w - 3x + 2y = -4 3w + x - 3y + z = 1 w + 2x - 4y - z = -2

A. {(1, 3, 2, 1)}
B. {(1, 4, 3, -1)}
C. {(1, 5, 1, 1)}
D. {(-1, 2, -2, 1)}
Question 19 of 40

Give the order of the following matrix; if A = [aij], identify a32 and a23.

1 0 -2

-5 7 1/2

∏ -6 11

e -∏ -1/5

A. 3 * 4; a32 = 1/45; a23 = 6
B. 3 * 4; a32 = 1/2; a23 = -6
C. 3 * 2; a32 = 1/3; a23 = -5
D. 2 * 3; a32 = 1/4; a23 = 4
Question 20 of 40

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

3x1 + 5x2 - 8x3 + 5x4 = -8 x1 + 2x2 - 3x3 + x4 = -7 2x1 + 3x2 - 7x3 + 3x4 = -11 4x1 + 8x2 - 10x3+ 7x4 = -10

A. {(1, -5, 3, 4)}
B. {(2, -1, 3, 5)}
C. {(1, 2, 3, 3)}
D. {(2, -2, 3, 4)}
Question 21 of 40

Find the vertices and locate the foci of each hyperbola with the given equation. x2/4 - y2/1 =1

A. Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)
B. Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)
C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)
D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)
Question 22 of 40

Find the solution set for each system by finding points of intersection.

x2 + y2 = 1 x2 + 9y = 9

A. {(0, -2), (0, 4)}
B. {(0, -2), (0, 1)}
C. {(0, -3), (0, 1)}
D. {(0, -1), (0, 1)}
Question 23 of 40

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola. y2 - 2y + 12x - 35 = 0

A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9
B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6
C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6
D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8

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Question 24 of 40

Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length = 10 Length of minor axis = 4 Center: (-2, 3)

A. (x + 2)2/4 + (y - 3)2/25 = 1
B. (x + 4)2/4 + (y - 2)2/25 = 1
C. (x + 3)2/4 + (y - 2)2/25 = 1
D. (x + 5)2/4 + (y - 2)2/25 = 1
Question 25 of 40

Find the vertex, focus, and directrix of each parabola with the given equation. (x - 2)2 = 8(y - 1)

A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1
B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1
C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1
D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1
Question 26 of 40

Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: (7, 9) and (7, 3) Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)2/6 + (y - 6)2/7 = 1
B. (x - 7)2/5 + (y - 6)2/6 = 1
C. (x - 7)2/4 + (y - 6)2/9 = 1
D. (x - 5)2/4 + (y - 4)2/9 = 1
Question 27 of 40

Locate the foci of the ellipse of the following equation. 25x2 + 4y2 = 100

A. Foci at (1, -√11) and (1, √11)
B. Foci at (0, -√25) and (0, √25)
C. Foci at (0, -√22) and (0, √22)
D. Foci at (0, -√21) and (0, √21)
Question 28 of 40

Locate the foci of the ellipse of the following equation. x2/16 + y2/4 = 1

A. Foci at (-2√3, 0) and (2√3, 0)
B. Foci at (5√3, 0) and (2√3, 0)
C. Foci at (-2√3, 0) and (5√3, 0)
D. Foci at (-7√2, 0) and (5√2, 0)
Question 29 of 40

Convert each equation to standard form by completing the square on x and y. 9x2 + 25y2 - 36x + 50y - 164 = 0

A. (x - 2)2/25 + (y + 1)2/9 = 1
B. (x - 2)2/24 + (y + 1)2/36 = 1
C. (x - 2)2/35 + (y + 1)2/25 = 1
D. (x - 2)2/22 + (y + 1)2/50 = 1
Question 30 of 40

Find the focus and directrix of each parabola with the given equation. y2 = 4x

A. Focus: (2, 0); directrix: x = -1
B. Focus: (3, 0); directrix: x = -1
C. Focus: (5, 0); directrix: x = -1
D. Focus: (1, 0); directrix: x = -1
Question 31 of 40

Convert each equation to standard form by completing the square on x and y. 4x2 + y2 + 16x - 6y - 39 = 0

A. (x + 2)2/4 + (y - 3)2/39 = 1
B. (x + 2)2/39 + (y - 4)2/64 = 1
C. (x + 2)2/16 + (y - 3)2/64 = 1
D. (x + 2)2/6 + (y - 3)2/4 = 1
Question 32 of 40

Convert each equation to standard form by completing the square on x and y. 9x2 + 16y2 - 18x + 64y - 71 = 0

A. (x - 1)2/9 + (y + 2)2/18 = 1
B. (x - 1)2/18 + (y + 2)2/71 = 1
C. (x - 1)2/16 + (y + 2)2/9 = 1
D. (x - 1)2/64 + (y + 2)2/9 = 1
Question 33 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -6), (0, 6) Asymptote: y = 2x

A. y2/6 - x2/9 = 1
B. y2/36 - x2/9 = 1
C. y2/37 - x2/27 = 1
D. y2/9 - x2/6 = 1
Question 34 of 40

Find the vertex, focus, and directrix of each parabola with the given equation. (y + 1)2 = -8x

A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2
B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3
C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1
D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5
Question 35 of 40

Locate the foci and find the equations of the asymptotes. x2/100 - y2/64 = 1

A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x
B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x
C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x
D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x
Question 36 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (-4, 0), (4, 0) Vertices: (-3, 0), (3, 0)

A. x2/4 - y2/6 = 1
B. x2/6 - y2/7 = 1
C. x2/6 - y2/7 = 1
D. x2/9 - y2/7 = 1
Question 37 of 40

Find the focus and directrix of each parabola with the given equation. x2 = -4y

A. Focus: (0, -1), directrix: y = 1
B. Focus: (0, -2), directrix: y = 1
C. Focus: (0, -4), directrix: y = 1
D. Focus: (0, -1), directrix: y = 2
Question 38 of 40

Find the vertex, focus, and directrix of each parabola with the given equation. (y + 3)2 = 12(x + 1)

A. Vertex: (-1, -3); focus: (1, -3); directrix: x = -3
B. Vertex: (-1, -1); focus: (4, -3); directrix: x = -5
C. Vertex: (-2, -3); focus: (2, -4); directrix: x = -7
D. Vertex: (-1, -3); focus: (2, -3); directrix: x = -4
Question 39 of 40

Locate the foci of the ellipse of the following equation. 7x2 = 35 - 5y2

A. Foci at (0, -√2) and (0, √2)
B. Foci at (0, -√1) and (0, √1)
C. Foci at (0, -√7) and (0, √7)
D. Foci at (0, -√5) and (0, √5)
Question 40 of 40

Find the vertices and locate the foci of each hyperbola with the given equation. y2/4 - x2/1 = 1

A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)
B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)
C. Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)
D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)

40 Algebra multiple choice questions

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