Precalc Final Questions
The vertex of (y - 3)^2 = -8(x + 2) is
(-2, 3)
what point do all conics of the form x^2 = 4py have in common?
(0,0)
The center of 4x^2 - 12y^2 - 16x -72 y - 44 = 0
(2, -3)
The focus of y^2 = 12x is
(3,0)
The center of 9x^2 + 4y^2 - 72x -24y + 144 = 0 is
(4, 3)
Which of these is an efficient first step in proving the identity (sinx/ 1 - cos x) = (1 + cos x/ sin x)
(sin x/ 1 - cos x) = (sin x / 1 - cos x) * (1 + cos x/ 1 + cos x)
One focus of x^2 + 4y^2 = 4 is
(√3, 0)
One focus of x^2 - 4y^2 = 4 is
(√5, 0)
sin 15º =
(√6 - √2)/4
The slopes of the asymptotes of the hyperbola x^2/4 - y^2/3 = 1 are
+/- √3/2
If cos A cos B = sin A sin B, then cos (A+B) =
0
The function y = sin x cos 2x + cos x sin 2x has amplitude
1
The shortest side of a triangle with angles 50º, 60º, and 70º has length 9.0. What is the length of the longest side
11.0
The area of a triangle with sides 7, 8, and 9 is
12√5
The length of x in the triangle shown at the right is
18.1
If f(x) = sin x and g(x) = cos x, then f(2x) =
2 f(x) g(x)
Two boats start at the point and speed away along courses that form a 110º angle. If one boat travels at 24 mph and the other boat travels at 32 mph, how far apart are the boats after 30 min?
23 mi
What is the measure of the smallest angle in a triangle with sides 12, 17, and 25.
25º
The perimeter of a triangle with one vertex on the ellipse x^2/a^2 + y^2/b^2 = 1 and the other two vertices at the foci of the ellipse would be
2a + 2c
What is the area of a regular dodecagon (12-sided figure) inscribed in a circle of radius 12?
432
If f(x) = g(x) is an identity with domain validity D, which of the following must be true? I. For any x in D, f(x) is defined II. For any x in D, g(x) is defined III. For any x in D, f(x) = g(x)
I, II, and III
Which of the following three triangle parts do not necessarily determine the other three parts
SSA
If f(x) = g(x) and f(x)/g(x) = k, which of the following must be false?
f(x) = 0
A function with the property f(1 + 2) = ( f(1) + f(2) )/ ( 1 - f(1)f(2) )
f(x) = tan x
How many numbers between 0 and 2π satisfy the equation sin 2x = cos x
four
Exactly four of the six basic trigonometric functions are
odd
Which of the following curves is not a conic section?
oval
Which of the following could be an intermediate expression in a proof of the identity tan ø + sec ø = cos ø/ 1 - sin ø
sin ø + 1/ cos ø
sin 22.5 =
squareroot((2- √2)/2)
Which of the following could not be set equal to sin x as an identity?
tan x sec x
A simpler expression for (sec ø + 1)(sec ø - 1) is
tan^2ø
How many noncongruent triangles ABC can be formed if AB = 5, A = 60º, and BC = 8?
three
How many numbers between 0 and 2π solve the equation 3 cos^2 x + cos x = 2
three
The focal axis of (x - 2)^2/ 25 + (y - 3)^2/ 16 = 1
y = 3
The focal axis of (x + 5)^2/9 - (y -6)^2/16 = 1 is
y = 6
The period of the function sin^2x - cos^2x is
π
