2024 Semester Review Part I

Front

What is the formula to calculate the total cost for a group visiting an amusement park?

Back

Total Cost = (Number of Adults * Adult Price) + (Number of Children * Child Price)

Front

How do you set up a system of equations based on a word problem?

Back

Identify variables for unknowns, translate the problem into equations using those variables, and ensure the equations represent the relationships described.

Front

What does the slope of a line represent in a linear equation?

Back

The slope indicates the rate of change of y with respect to x; it shows how much y increases or decreases as x increases by 1.

Front

How do you find the slope-intercept form of a line given a slope and a point?

Back

Use the formula y = mx + b, where m is the slope and b is the y-intercept. Substitute the point's coordinates to solve for b.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction; it is always non-negative.

Front

How do you solve an absolute value equation?

Back

Set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and will never intersect.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented by a straight line on a graph, where each point on the line is a solution to the equation.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they coincide, there are infinitely many solutions.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.