Question 1

Solve the system by the substitution method.
-$x y-x^{2}=-20$
$x-2 y=3$

Accepted Answer

A)  $\left\{(5,1),\left(-\frac{11}{2},-8\right)\right\}$ 
B)  $\left\{(-5,-1),\left(\frac{11}{2}, 8\right)\right\}$ 
C)  $\left\{(-5,-1),\left(8, \frac{11}{2}\right)\right\}$ 
D)  $\left\{(5,1),\left(-8,-\frac{11}{2}\right)\right\}$ 
A)  $\left\{(5,1),\left(-\frac{11}{2},-8\right)\right\}$ 
B)  $\left\{(-5,-1),\left(\frac{11}{2}, 8\right)\right\}$ 
C)  $\left\{(-5,-1),\left(8, \frac{11}{2}\right)\right\}$ 
D)  $\left\{(5,1),\left(-8,-\frac{11}{2}\right)\right\}$

Question 2

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

Accepted Answer

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

Question 3

Solve the system by the elimination method or a combination of the elimination and substitution methods.
-$\begin{aligned} x^{2}+2 x y+y^{2} & =9 \ x^{2}+2 x y-y^{2} & =-9\end{aligned}$

Accepted Answer

A)  $\{(0,3),(0,-3),(-6,3),(6,-3)\}$ 
B)  $\{(0,3),(0,-3),(6,3),(6,-3)\}$ 
C)  $\{(0,3),(0,-3),(-6,3),(-6,-3)\}$ 
D)  $\{(0,3),(0,-3),(6,3),(-6,-3)\}$ 
A)  $\{(0,3),(0,-3),(-6,3),(6,-3)\}$ 
B)  $\{(0,3),(0,-3),(6,3),(6,-3)\}$ 
C)  $\{(0,3),(0,-3),(-6,3),(-6,-3)\}$ 
D)  $\{(0,3),(0,-3),(6,3),(-6,-3)\}$

Question 4

The equation of a semicircle that is the upper half of the circle centered at the origin with radius 2 is $y=\sqrt{4-x^{2}}$.

Accepted Answer

A) True 
 B)False

Question 5

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$y^{2}=64-x^{2}$

Accepted Answer

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

Question 6

Graph the inequality.
-$(x+2)^{2}+(y-4)^{2} \leq 9$

Accepted Answer

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

Question 7

Find the center and radius of the circle.
-$x^{2}+y^{2}+18 x+4 y+4=0$

Accepted Answer

A)  $(-9,-2) ; r=9$ 
B)  $(2,9) ; \mathrm{r}=81$ 
C)  $(9,2) ; \mathrm{r}=81$ 
D)  $(-2,-9) ; \mathrm{r}=9$ 
A)  $(-9,-2) ; r=9$ 
B)  $(2,9) ; \mathrm{r}=81$ 
C)  $(9,2) ; \mathrm{r}=81$ 
D)  $(-2,-9) ; \mathrm{r}=9$

Question 8

Graph the system of inequalities.
-$ \begin{array}{c}3 x+2 y \leq-6 \ x-1 \geq 0\end{array} $

Accepted Answer

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

Question 9

The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution.
- 
$$y=\frac{1}{3} x^{2}-3$$
$x+y=3$

Accepted Answer

A)  $(0,-3)$ 
B)  $(-3,0)$ 
C)  $(0,3)$ 
D)  $(3,0)$ 
A)  $(0,-3)$ 
B)  $(-3,0)$ 
C)  $(0,3)$ 
D)  $(3,0)$

Question 10

The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution.
- 
$$y=-x^{2}+4$$
$x-y=2$

Accepted Answer

A)  $(-5,-3)$ 
B)  $(-3,-5)$ 
C)  $(3,5)$ 
D)  $(0,2)$ 
A)  $(-5,-3)$ 
B)  $(-3,-5)$ 
C)  $(3,5)$ 
D)  $(0,2)$

Question 11

Choose the inequality that matches the graph.
-

Accepted Answer

A) $y>x^{2}+3 x+6$ B) $y< x^{2}+3 x+6$ C) $y \geq x^{2}+3 x+6$ D) $y \leq x^{2}+3 x+6$ A) $y>x^{2}+3 x+6$ B) $y< x^{2}+3 x+6$ C) $y \geq x^{2}+3 x+6$ D) $y \leq x^{2}+3 x+6$

Question 12

Graph the system of inequalities.
-$ \begin{array}{c}x+2 y \geq 2 \ x-y \leq 0\end{array} $

Accepted Answer

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

Question 13

Solve the system by the substitution method.
-$y=3 x^{2}+6 x$
$\mathrm{y}=\mathrm{x}^{2}-4 \mathrm{x}+12$

Accepted Answer

A)  $\{(1,9),(-6,72)\}$ 
B)  $\{(2,0),(-3,9)\}$ 
C)  $\{(-2,0),(-3,9)\}$ 
D)  $\{(2,0),(3,45)\}$ 
A)  $\{(1,9),(-6,72)\}$ 
B)  $\{(2,0),(-3,9)\}$ 
C)  $\{(-2,0),(-3,9)\}$ 
D)  $\{(2,0),(3,45)\}$

Solve the system by the substitution method. - $x y-x^{2}=-20$ $x-2 y=3$

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

Solve the system by the elimination method or a combination of the elimination and substitution methods. - +2xy+ =9 +2xy- =-9

The equation of a semicircle that is the upper half of the circle centered at the origin with radius 2 is $y=\sqrt{4-x^{2}}$ .

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $y^{2}=64-x^{2}$

Graph the inequality. - $(x+2)^{2}+(y-4)^{2} \leq 9$ $Graph the inequality. - (x+2)^{2}+(y-4)^{2} \leq 9$

Find the center and radius of the circle. - $x^{2}+y^{2}+18 x+4 y+4=0$

Graph the system of inequalities. - 3x+2y\leq-6 x-1\geq0 $Graph the system of inequalities. - \begin{array}{c}3 x+2 y \leq-6 \\ x-1 \geq 0\end{array}$

Choose the inequality that matches the graph. -

Graph the system of inequalities. - x+2y\geq2 x-y\leq0 $Graph the system of inequalities. - \begin{array}{c}x+2 y \geq 2 \\ x-y \leq 0\end{array}$

Solve the system by the substitution method. - $y=3 x^{2}+6 x$ $\mathrm{y}=\mathrm{x}^{2}-4 \mathrm{x}+12$

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

Solve the system by the substitution method. - xy−x2=−20x y-x^{2}=-20xy−x2=−20 x−2y=3x-2 y=3x−2y=3

Which one of the following is a description of the graph of the solution set for the system below? x2+y2≥36x^{2}+y^{2} \geq 36x2+y2≥36 4x2+9y2≥364 x^{2}+9 y^{2} \geq 364x2+9y2≥36