Question 1

Given the function $f(x)=3 x^{2}+7 x-4$, find $f\left(-\frac{1}{2}\right)$.

Accepted Answer

A)  -1.25 
B)  0.25 
C)  -6.75 
D)  -8.25 
A)  -1.25 
B)  0.25 
C)  -6.75 
D)  -8.25

Question 2

Determine whether or not each relation is a function. Write its domain and range.
-  $x=7-y^{2}$

Accepted Answer

The answer of Determine whether or not each relation is...

Question 3

Name the number of petals in the rose curve $r=5 \sin 4 \theta$.

Accepted Answer

A)  10 
B)  8 
C)  4 
D)  20 
A)  10 
B)  8 
C)  4 
D)  20

Question 4

Find the coordinates of the point midway between $(-3,-5)$ and $(7,-11)$.

Accepted Answer

The answer of Find the coordinates of the point midway...

Question 5

Find the slope of the line passing through the points $(-7,-4)$ and $(-1,-9)$.

Accepted Answer

The answer of Find the slope of the line passing...

Question 6

Write the equation of the hyperbola with foci at $(0,15)$ and $(0,-15)$ and the transverse axis of length 20.

Accepted Answer

A)  $4 y^{2}-5 x^{2}=500$ 
B)  $5 y^{2}-4 x^{2}=500$ 
C)  $13 y^{2}-4 x^{2}=1300$ 
D)  $4 y^{2}-13 x^{2}=1300$ 
A)  $4 y^{2}-5 x^{2}=500$ 
B)  $5 y^{2}-4 x^{2}=500$ 
C)  $13 y^{2}-4 x^{2}=1300$ 
D)  $4 y^{2}-13 x^{2}=1300$

Question 7

Find the distance between the points (5, - 7) and (- 6, - 3). Round to three significant digits.

Accepted Answer

A)  10.2 
B)  11.7 
C)  10.0 
D)  14.9 
A)  10.2 
B)  11.7 
C)  10.0 
D)  14.9

Question 8

Find the equation of the circle with center at $(-7,-2)$ and passing through the point $(-3,6)$.

Accepted Answer

A)  $x^{2}+y^{2}-6 x+12 y-35=0$ 
B)  $x^{2}+y^{2}+6 x-12 y-35=0$ 
C)  $x^{2}+y^{2}+14 x+4 y-27=0$ 
D)  $x^{2}+y^{2}-14 x-4 y-27=0$ 
A)  $x^{2}+y^{2}-6 x+12 y-35=0$ 
B)  $x^{2}+y^{2}+6 x-12 y-35=0$ 
C)  $x^{2}+y^{2}+14 x+4 y-27=0$ 
D)  $x^{2}+y^{2}-14 x-4 y-27=0$

Question 9

Find the foci of the hyperbola $\frac{x^{2}}{121}-\frac{y^{2}}{81}=1$.

Accepted Answer

A)  $( \pm \sqrt{202}, 0)$ 
B)  $( \pm 11,0)$ 
C)  $( \pm 2 \sqrt{10}, 0)$ 
D)  $(0 \pm \sqrt{202})$ 
A)  $( \pm \sqrt{202}, 0)$ 
B)  $( \pm 11,0)$ 
C)  $( \pm 2 \sqrt{10}, 0)$ 
D)  $(0 \pm \sqrt{202})$

Question 10

$r=5+12 \sin \theta$

Accepted Answer

The answer of  $r=5+12 \sin \theta$...

Question 11

Find the equation of the circle (in standard form) with center at $(7,-8)$ and with radius 10.

Accepted Answer

A)  $(x-7)^{2}+(y+8)^{2}=100$ 
B)  $\sqrt{(x-7)^{2}+(y+8)^{2}}=100$ 
C)  $(x+7)^{2}-(y-8)^{2}=100$ 
D)  $(x+7)^{2}+(y-8)^{2}=100$ 
A)  $(x-7)^{2}+(y+8)^{2}=100$ 
B)  $\sqrt{(x-7)^{2}+(y+8)^{2}}=100$ 
C)  $(x+7)^{2}-(y-8)^{2}=100$ 
D)  $(x+7)^{2}+(y-8)^{2}=100$

Question 12

Find the equation of the ellipse with vertices at $(-20,0)$ and $(20,0)$ and foci at $(15,0)$ and $(-15,0)$.

Accepted Answer

A)  $\frac{x^{2}}{400}+\frac{y^{2}}{175}=1$ 
B)  $\frac{x^{2}}{175}+\frac{y^{2}}{400}=1$ 
C)  $\frac{x^{2}}{400}+\frac{y^{2}}{225}=1$ 
D)  $\frac{x^{2}}{225}+\frac{y^{2}}{400}=1$ 
A)  $\frac{x^{2}}{400}+\frac{y^{2}}{175}=1$ 
B)  $\frac{x^{2}}{175}+\frac{y^{2}}{400}=1$ 
C)  $\frac{x^{2}}{400}+\frac{y^{2}}{225}=1$ 
D)  $\frac{x^{2}}{225}+\frac{y^{2}}{400}=1$

Question 13

Find the equation of the parabola with vertex at (-5, - 4), focus at $(-5,1)$ and directrix $y=-9$.

Accepted Answer

A)  $(x-5)^{2}=40(y-4)$ 
B)  $(x+5)^{2}=20(y+4)$ 
C)  $(y+4)^{2}=20(x+5)$ 
D)  $(x+5)^{2}=40(y+4)$ 
A)  $(x-5)^{2}=40(y-4)$ 
B)  $(x+5)^{2}=20(y+4)$ 
C)  $(y+4)^{2}=20(x+5)$ 
D)  $(x+5)^{2}=40(y+4)$

Question 14

$r=3 \sin 5 \theta$

Accepted Answer

The answer of   $r=3 \sin 5 \theta$...

Question 15

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes.
- $\frac{x^{2}}{36}-\frac{y^{2}}{64}=1$

Accepted Answer

The answer of For the problems below, find the vertices,...

Question 16

Name the graph of the equation $4 x^{2}-9 y^{2}+8 x+36 y-68=0$. Locate the vertex if it is a parabola or the center if it is an ellipse or hyperbola.

Accepted Answer

The answer of Name the graph of the equation \(4...

Question 17

Find the length of the major axis of the ellipse $4 x^{2}+9 y^{2}=324$.

Accepted Answer

A)  2 
B)  18 
C)  $\sqrt{117}$ 
D)  9 
A)  2 
B)  18 
C)  $\sqrt{117}$ 
D)  9

Question 18

Find the equation of the parabola with focus ( $-2,7$ ) and directrix $x=4$.

Accepted Answer

A)  $y^{2}-14 y+12 x+37=0$ 
B)  $x^{2}+4 x-6 y+37=0$ 
C)  $x^{2}-4 x+22 y+37=0$ 
D)  $y^{2}+14 y+4 x+37=0$ 
A)  $y^{2}-14 y+12 x+37=0$ 
B)  $x^{2}+4 x-6 y+37=0$ 
C)  $x^{2}-4 x+22 y+37=0$ 
D)  $y^{2}+14 y+4 x+37=0$

Question 19

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse.
-  $\frac{x^{2}}{9}+\frac{y^{2}}{64}=1$

Accepted Answer

The answer of For the problems below, find the vertices,...

Question 20

Name the type of graph represented by $x^{2}-4 y 2-10 x-8 y+5=0$.

Accepted Answer

A)  ellipse 
B)  parabola 
C)  circle 
D)  hyperbola 
A)  ellipse 
B)  parabola 
C)  circle 
D)  hyperbola

Given the function $f(x)=3 x^{2}+7 x-4$ , find $f\left(-\frac{1}{2}\right)$ .

Determine whether or not each relation is a function. Write its domain and range. - $x=7-y^{2}$

Name the number of petals in the rose curve $r=5 \sin 4 \theta$ .

Find the coordinates of the point midway between $(-3,-5)$ and $(7,-11)$ .

Find the slope of the line passing through the points $(-7,-4)$ and $(-1,-9)$ .

Write the equation of the hyperbola with foci at $(0,15)$ and $(0,-15)$ and the transverse axis of length 20.

Find the distance between the points (5, - 7) and (- 6, - 3). Round to three significant digits.

Find the equation of the circle with center at $(-7,-2)$ and passing through the point $(-3,6)$ .

Find the foci of the hyperbola $\frac{x^{2}}{121}-\frac{y^{2}}{81}=1$ .

$r=5+12 \sin \theta$

Find the equation of the circle (in standard form) with center at $(7,-8)$ and with radius 10.

Find the equation of the ellipse with vertices at $(-20,0)$ and $(20,0)$ and foci at $(15,0)$ and $(-15,0)$ .

Find the equation of the parabola with vertex at (-5, - 4), focus at $(-5,1)$ and directrix $y=-9$ .

$r=3 \sin 5 \theta$

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. - $\frac{x^{2}}{36}-\frac{y^{2}}{64}=1$

Name the graph of the equation $4 x^{2}-9 y^{2}+8 x+36 y-68=0$ . Locate the vertex if it is a parabola or the center if it is an ellipse or hyperbola.

Find the length of the major axis of the ellipse $4 x^{2}+9 y^{2}=324$ .

Find the equation of the parabola with focus ( $-2,7$ ) and directrix $x=4$ .

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. - $\frac{x^{2}}{9}+\frac{y^{2}}{64}=1$

Name the type of graph represented by $x^{2}-4 y 2-10 x-8 y+5=0$ .

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Exam 1: Analytic Geometry

Given the function f(x)=3x2+7x−4f(x)=3 x^{2}+7 x-4f(x)=3x2+7x−4 , find f(−12)f\left(-\frac{1}{2}\right)f(−21​) .

Determine whether or not each relation is a function. Write its domain and range. - x=7−y2x=7-y^{2}x=7−y2

Name the number of petals in the rose curve r=5sin⁡4θr=5 \sin 4 \thetar=5sin4θ .

Find the coordinates of the point midway between (−3,−5)(-3,-5)(−3,−5) and (7,−11)(7,-11)(7,−11) .

Find the slope of the line passing through the points (−7,−4)(-7,-4)(−7,−4) and (−1,−9)(-1,-9)(−1,−9) .

Write the equation of the hyperbola with foci at (0,15)(0,15)(0,15) and (0,−15)(0,-15)(0,−15) and the transverse axis of length 20.

Find the distance between the points (5, - 7) and (- 6, - 3). Round to three significant digits.

Find the equation of the circle with center at (−7,−2)(-7,-2)(−7,−2) and passing through the point (−3,6)(-3,6)(−3,6) .

Find the foci of the hyperbola x2121−y281=1\frac{x^{2}}{121}-\frac{y^{2}}{81}=1121x2​−81y2​=1 .

r=5+12sin⁡θr=5+12 \sin \thetar=5+12sinθ

Find the equation of the circle (in standard form) with center at (7,−8)(7,-8)(7,−8) and with radius 10.

Find the equation of the ellipse with vertices at (−20,0)(-20,0)(−20,0) and (20,0)(20,0)(20,0) and foci at (15,0)(15,0)(15,0) and (−15,0)(-15,0)(−15,0) .

Find the equation of the parabola with vertex at (-5, - 4), focus at (−5,1)(-5,1)(−5,1) and directrix y=−9y=-9y=−9 .

r=3sin⁡5θr=3 \sin 5 \thetar=3sin5θ

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. - x236−y264=1\frac{x^{2}}{36}-\frac{y^{2}}{64}=136x2​−64y2​=1

Name the graph of the equation 4x2−9y2+8x+36y−68=04 x^{2}-9 y^{2}+8 x+36 y-68=04x2−9y2+8x+36y−68=0 . Locate the vertex if it is a parabola or the center if it is an ellipse or hyperbola.

Find the length of the major axis of the ellipse 4x2+9y2=3244 x^{2}+9 y^{2}=3244x2+9y2=324 .

Find the equation of the parabola with focus ( −2,7-2,7−2,7 ) and directrix x=4x=4x=4 .

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. - x29+y264=1\frac{x^{2}}{9}+\frac{y^{2}}{64}=19x2​+64y2​=1

Name the type of graph represented by x2−4y2−10x−8y+5=0x^{2}-4 y 2-10 x-8 y+5=0x2−4y2−10x−8y+5=0 .

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Given the function $f(x)=3 x^{2}+7 x-4$ , find $f\left(-\frac{1}{2}\right)$ .

Determine whether or not each relation is a function. Write its domain and range. - $x=7-y^{2}$

Name the number of petals in the rose curve $r=5 \sin 4 \theta$ .

Find the coordinates of the point midway between $(-3,-5)$ and $(7,-11)$ .

Find the slope of the line passing through the points $(-7,-4)$ and $(-1,-9)$ .

Write the equation of the hyperbola with foci at $(0,15)$ and $(0,-15)$ and the transverse axis of length 20.

Find the equation of the circle with center at $(-7,-2)$ and passing through the point $(-3,6)$ .

Find the foci of the hyperbola $\frac{x^{2}}{121}-\frac{y^{2}}{81}=1$ .

$r=5+12 \sin \theta$

Find the equation of the circle (in standard form) with center at $(7,-8)$ and with radius 10.

Find the equation of the ellipse with vertices at $(-20,0)$ and $(20,0)$ and foci at $(15,0)$ and $(-15,0)$ .

Find the equation of the parabola with vertex at (-5, - 4), focus at $(-5,1)$ and directrix $y=-9$ .

$r=3 \sin 5 \theta$

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. - $\frac{x^{2}}{36}-\frac{y^{2}}{64}=1$

Name the graph of the equation $4 x^{2}-9 y^{2}+8 x+36 y-68=0$ . Locate the vertex if it is a parabola or the center if it is an ellipse or hyperbola.

Find the length of the major axis of the ellipse $4 x^{2}+9 y^{2}=324$ .

Find the equation of the parabola with focus ( $-2,7$ ) and directrix $x=4$ .

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. - $\frac{x^{2}}{9}+\frac{y^{2}}{64}=1$

Name the type of graph represented by $x^{2}-4 y 2-10 x-8 y+5=0$ .