math test 5

Decide whether the given sequence is finite or infinite.

-4, -3, -2, -1

		Finite
		Infinite

2.1 points

Question 2

1. 
   
   Evaluate the expression.

   (10
   2)

   		1,814,400
   		22
   		5
   		45

2.1 points

Question 3

1. 
   
   Evaluate the series, if it converges.

   9 – + – + . . .

   		– 1
   		8
   		Does not converge

2.1 points

Question 4

1. 
   
   Evaluate the sum.

   

   		218
   		173
   		124
   		162

2.1 points

Question 5

1. 
   
   Evaluate the sum. Round to the nearest hundredth, if necessary.

   

   		42
   		20
   		44
   		54

2.1 points

Question 6

1. 
   
   Evaluate the terms of the sum using the given information.

   x ₁ = 4, x ₂ = 1, x ₃ = 0, and x ₄ = -1
   

   		12 – 3 + 4 + 5
   		-20 – 5 – 4 – 5
   		-12 + 5 – 4 + 5
   		-20 + 3 – 4 – 3

2.1 points

Question 7

1. 
   
   Find a general term an for the geometric sequence.

   a ₁ = 3, r = 3

   		an = 6n
   		an = 3n
   		an= 3 + 6(n – 1)
   		an = 3n-1 + 2

2.1 points

Question 8

1. 
   
   Find a rectangular equation for the plane curve defined by the parametric equations.

   x = , y = 2t + 5, for t in (0, ∞)

   		y = 2 + 5, x in (0, ∞)
   		y = 2×2 + 5, x in (0, ∞)
   		y = 2 – 5, x in (0, ∞)
   		y = 2×2 – 5, x in (0, ∞)

2.1 points

Question 9

1. 
   
   Find an equation for the conic. If the conic is a parabola, assume that the vertex is at the origin. If the conic is an ellipse or hyperbola, assume that it is centered at the origin.

   Focus at (0, -6) and e = 1

   		y = – x2
   		x = – y2
   		y = x2
   		y = – x2

2.1 points

Question 10

1. 
   
   Find an equation for the parabola with vertex at the origin.

   Through (9, 8), opening to the right

   		y = x2
   		x = – y2
   		x = y2
   		x = y2

2.1 points

Question 11

1. 
   
   Find an equation of a parabola that satisfies the given conditions.

   Vertex (3, -10), focus (3, -8)

   		8(y – 10) = (x + 3)2
   		(y + 10)2 = 8(x – 3)
   		(x – 3)2 = 8(y + 10)
   		y – 10 = 8(x + 3)2

2.1 points

Question 12

1. 
   
   Find an equation of the ellipse.

   An ellipse with center at origin, length of major axis 6 and y-intercepts

   		+ = 1
   		+ = 1
   		+ = 1
   		+ = 1

2.1 points

Question 13

1. 
   
   Find an equation of the hyperbola.

   Vertices at (0, 3), (0, -3); foci at (0, 9), (0, -9)

   		– = 1
   		– = 1
   		– = 1
   		– = 1

2.1 points

Question 14

1. 
   
   Find the center and radius of the circle.

   x 2 + y 2 + 12x – 2y = -1

   		(1, -6), r = 6
   		(6, -1), r = 36
   		(-1, 6), r = 36
   		(-6, 1), r = 6

2.1 points

Question 15

1. 
   
   Find the center-radius form for the circle having the given endpoints of a diameter.

   ( -3, -5) and (7, 7)

   		(x + 2)2 + (y + 1)2 = -11
   		(x + 2)2 + (y + 1)2 = 61
   		(x – 2)2 + (y – 1)2 = -11
   		(x – 2)2 + (y – 1)2 = 61

2.1 points

Question 16

1. 
   
   Find the center-radius form of the equation of the circle satisfying the given conditions.

   Center ( -10, 0), radius 1

   		(x + 10)2 + y2 = 1
   		x2 + (y – 10)2 = 1
   		(x – 10)2 + y2 = 1
   		x2 + (y + 10)2 = 1

2.1 points

Question 17

1. 
   
   Find the common difference for the arithmetic sequence.

   3, 5, 7, 9, …

   		2
   		0.02
   		-2
   		6

2.1 points

Question 18

1. 
   
   Find the common ratio r for the given infinite geometric sequence.

   4, -12, 36, -108, 324, …

   		-3
   		3
   		-16
   		–

2.1 points

Question 19

1. 
   
   Find the coordinates of the vertex and the direction of opening of each parabola.

   y = (x + 2) 2 + 7

   		(-7, 2) opens upward
   		(7, -4) opens downward
   		(7, -2) opens downward
   		(-2, 7) opens upward

2.1 points

Question 20

1. 
   
   Find the eccentricity of the ellipse or hyperbola.

   x 2 – y 2 = 49

   		1
   		0

2.1 points

Question 21

1. 
   
   Find the first six terms of the sequence.

   a 1 = -9, a n = 5 ∙ a n-1

   		-9, -45, -225, -1125, -5625, -28,125
   		-9, -45, -40, -35, -30, -25
   		-45, -225, -1125, -5625, -28,125, -140,625
   		0, 5, -45, -40, -35, -30

2.1 points

Question 22

1. 
   
   Find the sum of the arithmetic series using a formula.

   1 + 3 + 5 + … + 515

   		66,049
   		66,822
   		66,564
   		67,081

2.1 points

Question 23

1. 
   
   Find the sum of the first n terms of the following arithmetic sequence.

   a 1 = -10, d = -2; n = 4.

   		-40
   		-10
   		-52
   		-18

2.1 points

Question 24

1. 
   
   Find the sum of the geometric series.

   

   		-156
   		-7710
   		-2460
   		244

2.1 points

Question 25

1. 
   
   Find a_nand a₆ for the following arithmetic sequence.

   -1, 1, 3, 5, 7

   		an = 3n – 2; a6 = 16
   		an = n + 2; a6 = 8
   		an = 2n – 3; a6 = 9
   		an = -1(2)n-1; a6 = -32

2.1 points

Question 26

1. 
   
   For the given parabola, give the coordinates of the vertex, the axis, the domain, and the range.

   x = (y – 8) ² + 6

   		vertex: (-6, 8); axis: y = 8; domain: [-6, ∞) range: (-∞, ∞);
   		vertex: (8, 6); axis: y = 6; domain: [8, ∞) range: (-∞, ∞);
   		vertex: (-6, -8); axis: y = -8; domain: [-6, ∞) range: (-∞, ∞);
   		vertex: (6, 8); axis: y = 8; domain: [6, ∞) range: (-∞, ∞);

2.1 points

Question 27

1. 
   
   Give the focus, directrix, and axis for the parabola.

   – x 2 = y

   		(0, -3), y = 3, y-axis
   		(0, 3), y = -3, y-axis
   		(-6, 0), x = 3, x-axis
   		(0, -3), y = 3, x-axis

2.1 points

Question 28

1. 
   
   Graph the circle if possible.

   (x – 1) 2 + (y – 3) 2 = 16

   

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