Algebra 3 Semester 1 Exam

Front

What is the result of \( (6x^{9}y^{5})^{2} \)?

Back

The result is \( 36x^{18}y^{10} \).

Front

How do you find the solution of a system of equations from a graph?

Back

Identify the point where the lines intersect. For example, the solution from the graph is \( (1, -4) \).

Front

If \( f(x) = -3x - 8 \), what is \( f(-1) \)?

Back

The value is \( f(-1) = -5 \).

Front

What is the formula to find the area of a rectangle?

Back

Area = length × width.

Front

Find the area of a rectangle with length \( (3x - 1) \) and width \( (2x + 5) \).

Back

The area is \( 6x^{2} + 13x - 5 \).

Front

What is the slope of the line represented by the equation \( y = 2x + 3 \)?

Back

The slope is 2.

Front

What is the power rule for exponents?

Back

For any real number \( a \) and integers \( m \) and \( n \), \( a^{m} \cdot a^{n} = a^{m+n} \).

Front

What is the definition of a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form \( y = mx + b \).

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the quadratic formula?

Back

The quadratic formula is \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \) for the equation \( ax^2 + bx + c = 0 \).