31 pre calc questions
1.  Solve the triangle.
A = 48Â°, a = 32, b = 27 (1 point) 


2.  State whether the given measurements determine zero, one, or two triangles.
A = 80Â°, a = 24, b = 50 (1 point) 


3.  Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
A = 55Â°, a = 12, b = 14 (1 point) 


4.  Solve the triangle.
A = 51Â°, b = 11, c = 7 (1 point) 


5.  Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.
B = 104Â°, a = 11 cm, c = 18 cm (1 point) 


6.  Given that P = (5, 11) and Q = (6, 4), find the component form and magnitude of . (1 point)  

7.  Let u = <5, 6>, v = <2, 6>. Find 2u + 5v. (1 point)  

8.  Find the dot product, a â€¢ b.
a = 6i + 5j, b = 5i + 4j (1 point) 


9.  Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <7, 2>, v = <21, 6> (1 point) 


10.  Find the first six terms of the sequence.
a_{1} = 3, a_{n} = 2 â€¢ a_{n1} (1 point) 


11.  Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 22, 44, 88, … (1 point) 


12.  Find an explicit rule for the nth term of the sequence.
2, 8, 32, 128, … (1 point) 


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)  

14.  Write the sum using summation notation, assuming the suggested pattern continues.
5 – 15 + 45 – 135 + … (1 point) 


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)  

16.  A radio telescope has a parabolic surface, as shown below.
If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex? (1 point) 


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

18.  Find the center, vertices, and foci of the ellipse with equation 2x^{2} + 7y^{2} = 14. (1 point)  

19.  A satellite is to be put into an elliptical orbit around a 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) 


20.  Find the vertices and foci of the hyperbola with equation. (1 point)  

21.  Find an equation in standard form for the hyperbola with vertices at (0, Â±6) and asymptotes at y = Â± x. (1 point)  

22.  Find all polar coordinates of point P where P = . (1 point)  

23.  Determine if the graph is symmetric about the xaxis, the yaxis, or the origin.
r = 3 – 4 sin Î¸ (1 point) 


24.  Determine if the graph is symmetric about the xaxis, the yaxis, or the origin.
r = 3 cos 5Î¸ (1 point) 


25.  Find the derivative of f(x) = at x = 12. (1 point)  

26.  Find the limit of the function by using direct substitution. (1 point)  

27.  Find the limit of the function algebraically. (1 point)



28.  Use the given graph to determine the limit, if it exists.
Find and . (1 point) 


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