Nonlinear Equations and Functions Questions for Tests and Worksheets

Select All Questions

Grade 11 Nonlinear Equations and Functions

What are the coordinates of the center of an ellipse defined by the equation

$16x^2+25y^2+160x-200y+400=0$ ?

(-5, 4)
(5, -4)
(5, 4)
(-5, -4)

Grade 11 Nonlinear Equations and Functions

Identify the following conic:

$x^2-4x-4y^2+8y=4$ .

Parabola
Circle
Hyperbola
Ellipse

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

This question is a part of a group with common instructions. View group »

Let

$(a,0)$ be the right vertex of the hyperbola. What is the distance between this vertex and

$F_1 ?$

$a-c$
$a+c$
$a$
$c$

Grade 11 Nonlinear Equations and Functions

This question is a part of a group with common instructions. View group »

Squaring both sides, expanding, and combing like terms, dividing by any common constants, and putting all terms without a square root on the left side of the equation results in which of the following equations?

$2cx - a = 0$
$cx pm a^2 = -2 sqrt((x-c)^2 + y^2)$
$cx - a^2 = 0$
$cx - a^2 = pm a sqrt( (x-c)^2 + y^2)$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

This question is a part of a group with common instructions. View group »

Let

$(x,y)$ be a point on the hyperbola. What is the distance,

$d_1$ , between

$F_1$ and the point

$(x,y) ?$

$d_1 = sqrt( (x+c)^2 + y^2)$
$d_1 = sqrt( (x-c)^2 + y^2)$
$d_1 = sqrt( (x^2 + y^2)$
$d_1 = sqrt( (x-c)^2 + (y-c)^2)$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

This question is a part of a group with common instructions. View group »

Substitute the equations for

$d_1, d_2$ found in the second and third questions into the equation in the previous question. After some rearranging, the result is the following equation:

$sqrt( (x+c)^2 + y^2) = pm 2a + sqrt( (x-c)^2 + y^2)$

Why is there a plus-minus sign on the

$2a$ term?

In order to remove the absolute value sign, one has to consider the case where $d_1>d_2$ and $d_1 < d_2$ .
To remove the square root from this term, one has to look at the positive and negative case.
Since it's not certain which side of the equation this term should be on, it could be either positive or negative.
This is a hyperbola and the curves can be on either the positive or negative x-axis.

Grade 11 Nonlinear Equations and Functions

TRUE or FALSE. A conic section is represented by a

$li n ear$ equation.

True
False

Grade 11 Nonlinear Equations and Functions

A(n) is defined by a set of points in a plane that are equidistant from a fixed line and a fixed point not on the fixed line.

circle
parabola
ellipse
None of the Above

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.1

This question is a part of a group with common instructions. View group »

Which of the following represents the length of the horizontal leg of the right triangle? (If need be, use the first correct answer in the first question if there were multiple correct answers.)

$3-x$
$x+3$
$|x-3|$
$(3-x)^2$

Grade 11 Nonlinear Equations and Functions

Identify the following shape.

$2x^2+3xy-y^2-10x-9y+5=0$

Circle
Hyperbola
Ellipse
Parabola

Grade 11 Nonlinear Equations and Functions

Solve

$x^3 = 216$ .

$x=9$
$x=6$
$x=81$
$x=27$

Grade 11 Nonlinear Equations and Functions CCSS: HSA-REI.A.2

Solve. Check for extraneous solutions.

$x/(x-1)=(x+3)/(-2x+2)$

$x=-1 or x=-2$
$x=-1$
$x=1$
$x=1 or x=-1$

Grade 10 Nonlinear Equations and Functions CCSS: HSA-REI.A.2

$(x-1)/x = 4$ , then

$x =$

$3$
$-3$
$-1/6$
$-1/3$

Grade 11 Nonlinear Equations and Functions

The equation

$x^2+y^2+2x+1=0$ represents

a point.
a circle.
a parabola.
an ellipse.

Grade 10 Nonlinear Equations and Functions

Find

$(2n^3)^2$ if

$(n+2)(n+3)=(4-n)(12-n)$ .

Grade 11 Nonlinear Equations and Functions

Identify the following shape.

$x^2+xy-y^2-10x-3y+5=0$

Circle
Hyperbola
Parabola
Ellipse

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.2

What is the equation of a parabola with the focus at

$(1,3)$ and a directrix of

$x=-5?$

$(x-3)^2 = 12(y+2)$
$(y-3)^2 = 12(x-1)$
$(y+3)^2 = 3(x-2)$
$(y-3)^2 = 12(x+2)$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

This question is a part of a group with common instructions. View group »

What does

$|d_1 - d_2|$ equal?

$|d_1 - d_2| = a$
$|d_1 - d_2| = c$
$|d_1 - d_2| = |a-c|$
$|d_1 - d_2| = 2a$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

This question is a part of a group with common instructions. View group »

What is the distance between

$F_2$ and the vertex

$(a,0) ?$

$c$
$a$
$c-a$
$a+c$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

This question is a part of a group with common instructions. View group »

What is the distance,

$d_2$ , between the

$F_2$ and the point

$(x,y) ?$

$d_2 = sqrt( (x-c)^2 + (y-c)^2)$
$d_2 = sqrt( x^2 + y^2)$
$d_2 = sqrt( (x+c)^2 + y^2)$
$d_2 = sqrt( (x-c)^2 + y^2)$

Share/Like This Page

Filter By Grade

Browse Questions

Arithmetic and Number Concepts

Calculus

Function and Algebra Concepts

Absolute Value

Algebraic Expressions

Complex Numbers

Direct and Inverse Variation

Exponents

Functions and Relations

Inequalities

Linear Equations

Literal Equations

Logarithms

Matrices

Nonlinear Equations and Functions

Number Properties

Polynomials and Rational Expressions

Quadratic Equations and Expressions

Radicals

Sequences and Series

Systems of Equations

Vectors

Geometry and Measurement

Mathematical Process

Statistics and Probability Concepts

Trigonometry

Nonlinear Equations and Functions Questions - All Grades