Question 1

Which of the following is the correct equation for the circle with center at $$(-3, 4)$$ and radius $$5$$?

Accepted Answer

$$ (x + 3)^2$ + (y - 4)^2$ = 25 $$

Question 2

A satellite dish is shaped like a paraboloid. If the dish is $$4$$ meters wide and $$1$$ meter deep, what is the equation of its cross-section (parabola) if the vertex is at the origin and opens upward?

Accepted Answer

$$ x^2$ = 4y $$

Question 3

Which of the following is the standard form of the equation for an ellipse centered at the origin with a major axis of length $$10$$ along the $$x-$$axis and a minor axis of length $$6$$ along the $$y-$$axis?

Accepted Answer

$$ \frac{x^2$}{25} + \frac{y^2$}{9} = 1 $$

Question 4

Given the parametric equations $$x = 2t + 1$$ and $$y = 3t - 4$$, which of the following is the Cartesian equation relating $$x$$ and $$y$$?

Accepted Answer

$$ y = \frac{3}{2}x - \frac{11}{2} $$

Question 5

A Ferris wheel has a diameter of $$40$$ meters and is $$2$$ meters above the ground at its lowest point. If a rider boards at the lowest point and the wheel rotates counterclockwise, which of the following parametric equations describes the rider's position after $$t$$ seconds, assuming the wheel makes one revolution every $$80$$ seconds?

Accepted Answer

$$ x = 20 \cos \left( \frac{\pi t}{40} \right),\ y = 20 \sin \left( \frac{\pi t}{40} \right) + 22 $$

Question 6

Which of the following conic sections is represented by the equation $$x^2$$ - $$4y^2 = 16$?

Accepted Answer

Hyperbola

Question 7

If $$	an 	heta = 3$$ and $$	heta is in $$the second quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$ \frac{3}{\sqrt{10}} $$

Question 8

Which of the following is the polar form of the equation $$x^2$$ + $$y^2 = 4x$?

Accepted Answer

$$ r = 2 \cos 	heta $$

Question 9

A projectile is launched from the ground with an initial velocity of $$50 m/s at an $$angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the velocity?

Accepted Answer

$$ 50 \cos 30^\circ $$

Question 10

Which of the following is the correct formula for the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r 
eq 1$$?

Accepted Answer

$$ S_n = a \frac{1 - r^n}{1 - r} $$

Question 11

Given the polar equation $$r = 3 \sin 	heta$$, what is the corresponding Cartesian equation?

Accepted Answer

$$ x^2$ + y^2$ = 3y $$

Question 12

If $$\cos 	heta = -\frac{5}{13}$$ and $$	heta is in $$the third quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$ -\frac{12}{13} $$

Question 13

Which of the following is the equation of a hyperbola centered at the origin with vertices at $$(\pm 4, 0)$$ and asymptotes $$y = \pm \frac{3}{4}x$$?

Accepted Answer

$$ \frac{x^2$}{16} - \frac{y^2$}{9} = 1 $$

Question 14

A bank offers an account with interest compounded quarterly at an annual rate of $$8\%. If $$you deposit $$\1000$, what is the balance after 2$ years? (Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$)

Accepted Answer

$$ 1000 \left(1 + \frac{0.08}{4}\$$right)^{8}$$ $$

Question 15

Which of the following is the correct formula for the $$nth $$term of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$ a_n = a_1$ + (n - 1)d $$

Question 16

If $$\sin \alpha = \frac{5}{13}$$ and $$\alpha is in $$the second quadrant, what is $$\cos \alpha$$?

Accepted Answer

$$ -\frac{12}{13} $$

Question 17

Which of the following is the correct equation for a parabola with vertex at $$(2, -1)$$ and focus at $$(2, 1)$$?

Accepted Answer

$$ (x - 2)^2$ = 4(y + 1) $$

Question 18

A complex number is given by $$z = 3 - 4i. $$What is $$|z|$$?

Accepted Answer

$$ 5 $$

Question 19

Which of the following is the rectangular form of the complex number $$5 	ext{cis} \left( \frac{\pi}{3} ight)$$?

Accepted Answer

$$ \frac{5}{2} + \frac{5\sqrt{3}}{2}i $$

Question 20

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$ 17 $$

Precalculus Study Guidance: Chapter and Section Problems

Guida di studio - Domande di pratica

Study guide - Flashcard