Question 1

Choose the equation that matches the graph.
-

Accepted Answer

A)  $(x+5)^{2}+(y-5)^{2}=9$ 
B)  $(x-5)^{2}+(y+5)^{2}=9$ 
C)  $(x+5)^{2}+(y+5)^{2}=9$ 
D)  $(x-5)^{2}+(y-5)^{2}=9$ 
A)  $(x+5)^{2}+(y-5)^{2}=9$ 
B)  $(x-5)^{2}+(y+5)^{2}=9$ 
C)  $(x+5)^{2}+(y+5)^{2}=9$ 
D)  $(x-5)^{2}+(y-5)^{2}=9$

Question 2

Evaluate the expression.
-$[[-20.7]]$

Accepted Answer

A)  -19 
B)  -21 
C)  -20 
D)  -8 
A)  -19 
B)  -21 
C)  -20 
D)  -8

Question 3

Graph the system of inequalities.
-$y \leq-x^{2} - 6x - 4$
$y \geq x^{2}+ 6x +4$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Graph the function.
-$f(x)=\sqrt{x+4}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Solve the system by the elimination method or a combination of the elimination and substitution methods.
-$xy=13$
$2y^{2}-x^{2}=13$

Accepted Answer

A)  $\{(2 \mathrm{i} \sqrt{13},-\mathrm{i} \sqrt{13}),(-2 \mathrm{i} \sqrt{13}, \mathrm{i} \sqrt{13}),(\sqrt{13}, \sqrt{13}),(-\sqrt{13},-\sqrt{13})\}$ 
B)  $\left\{\left\{-26,-\frac{1}{2}\right),(13,1)\right\}$ 
C)  $\left\{\left\{\mathrm{i} \sqrt{26},-\frac{\mathrm{i} \sqrt{26}}{2}\right),\left(-\mathrm{i} \sqrt{26}, \frac{\mathrm{i} \sqrt{26}}{2}\right),(\sqrt{13}, \sqrt{13}),(-\sqrt{13},-\sqrt{13})\right\}$ 
D)  $\left\{\left\{\left(\mathrm{i} \sqrt{26},-\frac{\mathrm{i} \sqrt{26}}{2}\right),(\sqrt{13}, \sqrt{13})\right\}\right.$ 
A)  $\{(2 \mathrm{i} \sqrt{13},-\mathrm{i} \sqrt{13}),(-2 \mathrm{i} \sqrt{13}, \mathrm{i} \sqrt{13}),(\sqrt{13}, \sqrt{13}),(-\sqrt{13},-\sqrt{13})\}$ 
B)  $\left\{\left\{-26,-\frac{1}{2}\right),(13,1)\right\}$ 
C)  $\left\{\left\{\mathrm{i} \sqrt{26},-\frac{\mathrm{i} \sqrt{26}}{2}\right),\left(-\mathrm{i} \sqrt{26}, \frac{\mathrm{i} \sqrt{26}}{2}\right),(\sqrt{13}, \sqrt{13}),(-\sqrt{13},-\sqrt{13})\right\}$ 
D)  $\left\{\left\{\left(\mathrm{i} \sqrt{26},-\frac{\mathrm{i} \sqrt{26}}{2}\right),(\sqrt{13}, \sqrt{13})\right\}\right.$

Question 6

Graph the nonlinear inequality with restrictions.
-$y^{2} - x^{2} < 9, \quad y<0$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Graph the inequality.
-$y \leq x^{2}+5 x+5$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Solve the nonlinear system.
-$3 x^{2}+2 y^{2}=48$
$x^{2}+2 y^{2}=16$

Accepted Answer

A)  $\{(-4,0),(4,0)\}$ 
B)  $\{(-4,-\sqrt{2}),(-4, \sqrt{2}),(4,-\sqrt{2}),(4, \sqrt{2})\}$ 
C)  $\{(-4 \mathrm{i}, 0),(4 \mathrm{i}, 0)\}$ 
D)  $\{(4,0)\}$ 
A)  $\{(-4,0),(4,0)\}$ 
B)  $\{(-4,-\sqrt{2}),(-4, \sqrt{2}),(4,-\sqrt{2}),(4, \sqrt{2})\}$ 
C)  $\{(-4 \mathrm{i}, 0),(4 \mathrm{i}, 0)\}$ 
D)  $\{(4,0)\}$

Question 9

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac{x^{2}}{49}+\frac{y^{2}}{16}=1$ 
B)  $\frac{y^{2}}{49}-\frac{x^{2}}{16}=1$ 
C)  $\frac{x^{2}}{16}+\frac{y^{2}}{49}=1$ 
D)  $\frac{x^{2}}{16}-\frac{y^{2}}{49}=1$ 
A)  $\frac{x^{2}}{49}+\frac{y^{2}}{16}=1$ 
B)  $\frac{y^{2}}{49}-\frac{x^{2}}{16}=1$ 
C)  $\frac{x^{2}}{16}+\frac{y^{2}}{49}=1$ 
D)  $\frac{x^{2}}{16}-\frac{y^{2}}{49}=1$

Question 10

Solve the problem.
-A railroad tunnel has the shape of half an ellipse. The height of the tunnel at the center is $52 \mathrm{ft}$ and the vertical clearance must be $26 \mathrm{ft}$ at a point $24 \mathrm{ft}$ from the center. Find an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{ft}$.

Accepted Answer

A)  $\frac{x^{2}}{768}+\frac{y^{2}}{676}=1$ 
B)  $\frac{x^{2}}{576}+\frac{y^{2}}{2704}=1$ 
C)  $\frac{x^{2}}{2704}+\frac{y^{2}}{768}=1$ 
D)  $\frac{x^{2}}{768}+\frac{y^{2}}{2704}=1$ 
A)  $\frac{x^{2}}{768}+\frac{y^{2}}{676}=1$ 
B)  $\frac{x^{2}}{576}+\frac{y^{2}}{2704}=1$ 
C)  $\frac{x^{2}}{2704}+\frac{y^{2}}{768}=1$ 
D)  $\frac{x^{2}}{768}+\frac{y^{2}}{2704}=1$

Question 11

Solve the nonlinear system.
-$y^{2}-x^{2}=18$
$x-10=y$

Accepted Answer

A)  $\left\{\left\{\left(\frac{41}{10},-\frac{59}{10}\right)\right\}\right.$ 
B)  $\left\{\left\{-\frac{59}{10},-\frac{56}{5}\right)\right\}$ 
C)  $\left\{\left\{-\frac{59}{10},-\frac{156}{5}\right)\right\}$ 
D)  $\left\{\left\{\frac{41}{10}, 6\right)\right\}$ 
A)  $\left\{\left\{\left(\frac{41}{10},-\frac{59}{10}\right)\right\}\right.$ 
B)  $\left\{\left\{-\frac{59}{10},-\frac{56}{5}\right)\right\}$ 
C)  $\left\{\left\{-\frac{59}{10},-\frac{156}{5}\right)\right\}$ 
D)  $\left\{\left\{\frac{41}{10}, 6\right)\right\}$

Question 12

Graph the system of inequalities.
-$2x + y \leq 4$
$y - 1 \leq 0$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Evaluate the expression.
-$[[5]]$

Accepted Answer

A)  4 
B)  -5 
C)  5 
D)  6 
A)  4 
B)  -5 
C)  5 
D)  6

Question 14

Which one of the following is a description of the graph of the solution set for the system below?
$$\begin{aligned}
& x^{2}+y^{2} \leq 36 \
& 4 x^{2}+9 y^{2} \leq 36
\end{aligned}$$

Accepted Answer

A)  The area inside the circle (defined by the first equation) and outside the ellipse (defined by the second equation), including both borders. 
B)  The area inside the ellipse (defined by the second equation) and outside the circle (defined by the first equation), including both borders. 
C)  The area inside the ellipse (defined by the second equation), including the border. 
D)  None of these 
A)  The area inside the circle (defined by the first equation) and outside the ellipse (defined by the second equation), including both borders. 
B)  The area inside the ellipse (defined by the second equation) and outside the circle (defined by the first equation), including both borders. 
C)  The area inside the ellipse (defined by the second equation), including the border. 
D)  None of these

Question 15

The $y$-intercepts of the ellipse with equation $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ are $(0,81)$ and $(0,-81)$.

Accepted Answer

A) True 
 B)False

Question 16

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$2 x=5 y^{2}-32$

Accepted Answer

A)  Circle 
B)  Hyperbola 
C)  Parabola 
D)  Ellipse 
A)  Circle 
B)  Hyperbola 
C)  Parabola 
D)  Ellipse

Question 17

Graph.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Graph the circle.
-$ x^{2}+y^{2}=100 $

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

Solve the system by the substitution method.
-$xy=56$
$x+y=-15$

Accepted Answer

A)  $\{(7,-8),(8,-7)\}$ 
B)  $\{(-7,8),(-8,7)\}$ 
C)  $\{(-7,-8),(-8,-7)\}$ 
D)  $\{(7,8),(8,7)\}$ 
A)  $\{(7,-8),(8,-7)\}$ 
B)  $\{(-7,8),(-8,7)\}$ 
C)  $\{(-7,-8),(-8,-7)\}$ 
D)  $\{(7,8),(8,7)\}$

Question 20

Graph the ellipse.
-$\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Choose the equation that matches the graph. -

Evaluate the expression. - $[[-20.7]]$

Graph the system of inequalities. - $y \leq-x^{2} - 6x - 4$ $y \geq x^{2}+ 6x +4$ $Graph the system of inequalities. - y \leq-x^{2} - 6x - 4 y \geq x^{2}+ 6x +4$

Graph the function. - $f(x)=\sqrt{x+4}$ $Graph the function. - f(x)=\sqrt{x+4}$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $xy=13$ $2y^{2}-x^{2}=13$

Graph the nonlinear inequality with restrictions. - $y^{2} - x^{2} < 9, \quad y<0$ $Graph the nonlinear inequality with restrictions. - y^{2} - x^{2} < 9, \quad y<0$

Graph the inequality. - $y \leq x^{2}+5 x+5$ $Graph the inequality. - y \leq x^{2}+5 x+5$

Solve the nonlinear system. - $3 x^{2}+2 y^{2}=48$ $x^{2}+2 y^{2}=16$

Choose the equation that matches the graph. -

Solve the nonlinear system. - $y^{2}-x^{2}=18$ $x-10=y$

Graph the system of inequalities. - $2x + y \leq 4$ $y - 1 \leq 0$ $Graph the system of inequalities. - 2x + y \leq 4 y - 1 \leq 0$

Evaluate the expression. - $[[5]]$

Which one of the following is a description of the graph of the solution set for the system below? +\leq36 4+9\leq36

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ are $(0,81)$ and $(0,-81)$ .

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $2 x=5 y^{2}-32$

Graph. -

Graph the circle. - $x^{2}+y^{2}=100$ $Graph the circle. - x^{2}+y^{2}=100$

Solve the system by the substitution method. - $xy=56$ $x+y=-15$

Graph the ellipse. - $\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$ $Graph the ellipse. - \frac{x^{2}}{4}+\frac{y^{2}}{49}=1$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Further Topics in Algebra

Appendices

Filters

Exam 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Choose the equation that matches the graph. -

Evaluate the expression. - [[−20.7]][[-20.7]][[−20.7]]

Graph the system of inequalities. - y≤−x2−6x−4y \leq-x^{2} - 6x - 4y≤−x2−6x−4 y≥x2+6x+4y \geq x^{2}+ 6x +4y≥x2+6x+4

Graph the function. - f(x)=x+4f(x)=\sqrt{x+4}f(x)=x+4​

Solve the system by the elimination method or a combination of the elimination and substitution methods. - xy=13xy=13xy=13 2y2−x2=132y^{2}-x^{2}=132y2−x2=13

Graph the nonlinear inequality with restrictions. - y2−x2<9,y<0y^{2} - x^{2} < 9, \quad y<0y2−x2<9,y<0

Graph the inequality. - y≤x2+5x+5y \leq x^{2}+5 x+5y≤x2+5x+5

Solve the nonlinear system. - 3x2+2y2=483 x^{2}+2 y^{2}=483x2+2y2=48 x2+2y2=16x^{2}+2 y^{2}=16x2+2y2=16

Choose the equation that matches the graph. -

Solve the nonlinear system. - y2−x2=18y^{2}-x^{2}=18y2−x2=18 x−10=yx-10=yx−10=y

Graph the system of inequalities. - 2x+y≤42x + y \leq 42x+y≤4 y−1≤0y - 1 \leq 0y−1≤0

Evaluate the expression. - [[5]][[5]][[5]]

Which one of the following is a description of the graph of the solution set for the system below? +\leq36 4+9\leq36

The yyy -intercepts of the ellipse with equation x216+y281=1\frac{x^{2}}{16}+\frac{y^{2}}{81}=116x2​+81y2​=1 are (0,81)(0,81)(0,81) and (0,−81)(0,-81)(0,−81) .

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - 2x=5y2−322 x=5 y^{2}-322x=5y2−32

Graph. -

Graph the circle. - x2+y2=100 x^{2}+y^{2}=100 x2+y2=100

Solve the system by the substitution method. - xy=56xy=56xy=56 x+y=−15x+y=-15x+y=−15

Graph the ellipse. - x24+y249=1\frac{x^{2}}{4}+\frac{y^{2}}{49}=14x2​+49y2​=1

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Further Topics in Algebra

Appendices

Filters

Evaluate the expression. - $[[-20.7]]$

Graph the system of inequalities. - $y \leq-x^{2} - 6x - 4$ $y \geq x^{2}+ 6x +4$ $Graph the system of inequalities. - y \leq-x^{2} - 6x - 4 y \geq x^{2}+ 6x +4$

Graph the function. - $f(x)=\sqrt{x+4}$ $Graph the function. - f(x)=\sqrt{x+4}$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $xy=13$ $2y^{2}-x^{2}=13$

Graph the nonlinear inequality with restrictions. - $y^{2} - x^{2} < 9, \quad y<0$ $Graph the nonlinear inequality with restrictions. - y^{2} - x^{2} < 9, \quad y<0$

Graph the inequality. - $y \leq x^{2}+5 x+5$ $Graph the inequality. - y \leq x^{2}+5 x+5$

Solve the nonlinear system. - $3 x^{2}+2 y^{2}=48$ $x^{2}+2 y^{2}=16$

Solve the nonlinear system. - $y^{2}-x^{2}=18$ $x-10=y$

Graph the system of inequalities. - $2x + y \leq 4$ $y - 1 \leq 0$ $Graph the system of inequalities. - 2x + y \leq 4 y - 1 \leq 0$

Evaluate the expression. - $[[5]]$

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ are $(0,81)$ and $(0,-81)$ .

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $2 x=5 y^{2}-32$

Graph the circle. - $x^{2}+y^{2}=100$ $Graph the circle. - x^{2}+y^{2}=100$

Solve the system by the substitution method. - $xy=56$ $x+y=-15$

Graph the ellipse. - $\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$ $Graph the ellipse. - \frac{x^{2}}{4}+\frac{y^{2}}{49}=1$