Free Practice Quiz Question List

06/10 Systems and Algebraic Equations Online Quiz Questions

Use this free practice quiz with 20 questions to review 06/10 Systems and Algebraic Equations, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

For the rational equation $\frac{x+1}{x-3}=2$ , which value must be excluded from the domain?

A
x = 0
B
x = 3
C
x = -3
D
There are no restrictions

True or false

1 point

True or false: After solving a transformed equation, every proposed value should be checked in the original equation because some operations can create extraneous solutions.

A
True
B
False

Choose one

1 point

Solve $3^{2x-1}=27$ . Select the value of $x$ .

A
x = 2
B
x = 1
C
x = 3
D
x = 4

Written response

1 point

For the equation $5^x=17$ , enter the value of $x$ rounded to three decimal places.

Choose all

1 point

Which three statements are valid logarithm properties, assuming all logarithm arguments are positive? Select all correct choices.

A
$\log_b(MN)=\log_b(M)+\log_b(N)$
B
$\log_b\left(\frac{M}{N}\right)=\log_b(M)-\log_b(N)$
C
$\log_b(M+N)=\log_b(M)+\log_b(N)$
D
$\log_b(M^p)=p\log_b(M)$

Fill in the blank

1 point

Complete the zero-product property: If $AB=0$ , then or .

True or false

1 point

True or false: The x-coordinates of the intersection points of the graphs of y = f(x) and y = g(x) solve the equation f(x) = g(x).

A
True
B
False

Choose one

1 point

What is the solution to the system $2x+y=7$ and $3x-y=8$ ?

A
(1, 3)
B
(3, -1)
C
(3, 1)
D
(5, 2)

Choose all

1 point

Which three statements correctly describe bisection or Newton's method? Select all correct choices.

A
Bisection requires a continuous function on the interval being considered.
B
Bisection works only when the two endpoint values have the same sign.
C
Newton's method uses the derivative in its iteration formula.
D
A poor starting estimate can cause Newton's method to fail or converge to an unintended root.

Fill in the blank

1 point

Two important parts of setting up a mathematical model are defining and stating .

Written response

1 point

What theorem can be used to test possible rational zeros of a polynomial equation?

Open ended

1 point

Solve $\log_2(x-1)+\log_2(x+1)=3$ over the real numbers. Explain the domain restriction and why any rejected candidate is not a solution.

Choose one

1 point

Which ordered pairs solve the nonlinear system $y=x^2$ and $y=x+2$ ?

A
Only (2, 4)
B
(2, 4) and (-1, 1)
C
Only (-1, 1)
D
(2, 2) and (-1, -1)

Choose one

1 point

What is the solution set of (x - 4)(x + 2) = 0?

A
x = 2 only
B
x = -2 or x = 4
C
x = -4 or x = 2
D
x = 0 or x = 6

True or false

1 point

True or false: In the equation (x + 1)/(x - 3) = 2, the value x = 3 must be excluded before solving.

A
True
B
False

Written response

1 point

What property justifies solving (x - 5)(x + 1) = 0 by setting x - 5 = 0 or x + 1 = 0?

Choose one

1 point

What does a discriminant of zero indicate for a quadratic equation with real coefficients?

A
Two distinct real solutions
B
No real solutions
C
One repeated real solution
D
Exactly two complex solutions and no real solution

Choose one

1 point

Solve the rational equation $\frac{2}{x}+\frac{1}{x+1}=1$ . Select the complete solution, including all domain restrictions.

A
$x=1-\sqrt{3}$ or $x=1+\sqrt{3}$ ; domain restrictions: $x\ne0$ and $x\ne-1$
B
$x=-1$ or $x=0$ ; these are the domain restrictions and the solutions
C
$x=1-\sqrt{2}$ or $x=1+\sqrt{2}$ ; domain restrictions: $x\ne0$ and $x\ne-1$
D
$x=2$ or $x=-1$ ; domain restrictions: $x\ne0$ and $x\ne-1$

Choose one

1 point

Solve 3^(2x - 1) = 27.

A
x = 1
B
x = 3/2
C
x = 4
D
x = 2

Written response

1 point

Solve log base 2 of (x - 1) plus log base 2 of (x + 1) = 3. Enter the valid value of x.