31 pre calc questions

1. Solve the triangle.

A = 48°, a = 32, b = 27 (1 point)

Cannot be solved
B = 38.8°, C = 113.2°, c ≈ 34.4
B = 38.8°, C = 93.2°, c ≈ 43
B = 38.8°, C = 93.2°, c ≈ 25.8
2. State whether the given measurements determine zero, one, or two triangles.

A = 80°, a = 24, b = 50 (1 point)

Zero
Two
One
Three
3. Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 55°, a = 12, b = 14 (1 point)

B = 72.9°, C = 52.1°, c = 12.5; B = 107.1°, C = 17.9°, c = 12.5
B = 72.9°, C = 52.1°, c = 11.6; B = 107.1°, C = 17.9°, c = 4.5
B = 17.1°, C = 107.9°, c = 10.3; B = 162.9°, C = 72.1°, c = 10.3
B = 17.1°, C = 107.9°, c = 13.9; B = 162.9°, C = 72.1°, c = 13.9
4. Solve the triangle.

A = 51°, b = 11, c = 7 (1 point)

a ≈ 12.8, C ≈ 39.1, B ≈ 89.9
a ≈ 8.5, C ≈ 39.1, B ≈ 89.9
No triangles possible
a ≈ 12.8, C ≈ 43.1, B ≈ 85.9
5. Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

B = 104°, a = 11 cm, c = 18 cm (1 point)

192.12 cm2
96.06 cm2
23.95 cm2
99 cm2
6. Given that P = (-5, 11) and Q = (-6, 4), find the component form and magnitude of vector QP . (1 point)
<-11, 7>, square root of 38
<-1, -7>, square root of 50
<1, 7>, 50
<1, 7>, square root of 50
7. Let u = <5, 6>, v = <-2, -6>. Find -2u + 5v. (1 point)
<-20, -42>
<-20, 0>
<0, 18>
<-6, 0>
8. Find the dot product, a • b.

a = 6i + 5j, b = -5i + 4j (1 point)

50
<1, 9>
-10
<-30, 20>
9. Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <7, 2>, v = <21, 6> (1 point)

Neither
Orthogonal
Parallel
None of these
10. Find the first six terms of the sequence.

a1 = -3, an = 2 • an-1 (1 point)

-6, -12, -24, -48, -96, -192
-3, -6, -12, -24, -48, -96
0, 2, -6, -4, -2, 0
-3, -6, -4, -2, 0, 2
11. Determine whether the sequence converges or diverges. If it converges, give the limit.

11, 22, 44, 88, … (1 point)

Converges; 341
Converges; 165
Converges; 77
Diverges
12. Find an explicit rule for the nth term of the sequence.

2, -8, 32, -128, … (1 point)

an = 2 • 4n+1
an = 2 • (-4)n
an = 2 • 4n-1
an = 2 • (-4)n-1
13. Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively. (1 point)
an = 9 • 4n+1
an = 9 • 4n+3
an = 9 • 4n-1
an = 9 • 4n-2
14. Write the sum using summation notation, assuming the suggested pattern continues.

5 – 15 + 45 – 135 + … (1 point)

summation of 5 times 3 to the power of n from n equals 0 to infinity
summation of 5 times negative 3 to the power of the quantity n minus 1 from n equals 0 to infinity
summation of 5 times 3 to the power of the quantity n plus 1 from n equals 0 to infinity
summation of 5 times negative 3 to the power of n from n equals 0 to infinity
15. Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6. (1 point)
y equals 1 divided by 24 x squared
y2 = 6x
y2 = 24x
y equals 1 divided by 6 x squared
16. A radio telescope has a parabolic surface, as shown below.

A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 9 meters and its width from left to right is 12 meters.

If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex? (1 point)

4 m
3 m
1 m
9 m
17. Find the center, vertices, and foci of the ellipse with equation. (1 point)

x squared divided by 81 plus y squared divided by 225 equals 1

Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9)
Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0)
Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)
18. Find the center, vertices, and foci of the ellipse with equation 2x2 + 7y2 = 14. (1 point)
Center: (0, 0); Vertices: (-7, 0), (7, 0); Foci: Ordered pair negative 3 square root 5 comma 0 and ordered pair 3 square root 5 comma 0
Center: (0, 0); Vertices: Ordered pair negative square root 7 comma 0 and ordered pair square root 7 comma 0 ; Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0
Center: (0, 0); Vertices: Ordered pair 0 comma negative square root 7 and ordered pair 0 comma square root 7 ; Foci: Ordered pair 0 comma negative square root 5 and ordered pair 0 comma square root 5
Center: (0, 0); Vertices: (0, -7), (0, 7); Foci: Ordered pair 0 comma negative 3 square root 5 and ordered pair 0 comma 3 square root 5
19. A satellite is to be put into an elliptical orbit around a moon.

A vertical ellipse is shown surrounding a spherical object labeled moon

The moon is a sphere with radius of 959 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 357 km to 710 km. (1 point)

x squared divided by 357 plus y squared divided by 710 equals 1
x squared divided by 1669 squared plus y squared divided by 1316 squared equals 1
x squared divided by 1316 squared plus y squared divided by 1669 squared equals 1
x squared divided by 710 plus y squared divided by 357 equals 1
20. Find the vertices and foci of the hyperbola with equation. (1 point)

quantity x minus 3 squared divided by 81 minus the quantity of y plus 5 squared divided by 144 equals 1

Vertices: (-5, 15), (-5, -9); Foci: (-5, -9), (-5, 15)
Vertices: (12, -5), (-6, -5); Foci: (-12, -5), (18, -5)
Vertices: (-5, 12), (-5, -6); Foci: (-5, -12), (-5, 18)
Vertices: (15, -5), (-9, -5); Foci: (-9, -5), (15, -5)
21. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and asymptotes at y = ± 3 divided by 5x x. (1 point)
y squared over 36 minus x squared over 25 equals 1
y squared over 100 minus x squared over 36 equals 1
y squared over 25 minus x squared over 9 equals 1
y squared over 36 minus x squared over 100 equals 1
22. Find all polar coordinates of point P where P = ordered pair 3 comma negative pi divided by 3 . (1 point)
(3, negative pi divided by 3 + 2nπ) or (-3, negative pi divided by 3 + (2n + 1)π)
(3, negative pi divided by 3 + 2nπ) or (-3, negative pi divided by 3 + 2nπ)
(3, negative pi divided by 3 + 2nπ) or (3, negative pi divided by 3 + (2n + 1)π)
(3, negative pi divided by 3 + (2n + 1)π) or (-3, negative pi divided by 3 + 2nπ)
23. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 3 – 4 sin θ (1 point)

y-axis only
No symmetry
Origin only
x-axis only
24. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 3 cos 5θ (1 point)

x-axis, y-axis
x-axis, y-axis, origin
y-axis only
x-axis only
25. Find the derivative of f(x) = negative 10 divided by x at x = -12. (1 point)
72 divided by 5
5 divided by 72
6 divided by 5
5 divided by 6
26. Find the limit of the function by using direct substitution. (1 point)

limit as x approaches zero of quantity x squared plus four

Does not exist
4
0
-4
27. Find the limit of the function algebraically. (1 point)

limit as x approaches negative four of quantity x squared minus sixteen divided by quantity x plus four

1
-8
Does not exist
-4
28. Use the given graph to determine the limit, if it exists.

A coordinate graph is shown with a horizontal line coming from the left crossing the y axis at four and ending at the open point 2,4, a closed point at 2,1, and a horizontal line starting at the open point 2, negative 4 and continuing to the right

Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x . (1 point)

Font Family
Font Size
29. Use graphs and tables to find the limit and identify any vertical asymptotes of the function. (1 point)

limit of 1 divided by the quantity x minus 10 as x approaches 10 from the left

Font Family
Font Size
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