Algebra Proficiency Exam

Integers, Fractions, and Decimals: Understand the differences between these number types; integers are whole numbers, fractions represent parts of a whole, and decimals are another form of fractions.
Operations with Fractions: Master adding, subtracting, multiplying, and dividing fractions, ensuring a common denominator for addition and subtraction.
Variables and Expressions: Recognize symbols representing unknowns in mathematical expressions, differentiate between terms, coefficients, and constants.
Solving Equations: Proficiently solve one, two, and multi-step equations by isolating the variable through manipulation of both sides.
Equations with Variables on Both Sides: Learn to simplify and rearrange terms to isolate the variable, balancing both sides of the equation.
Solving for a Variable: Practice rearranging formulas to express one variable in terms of another, utilizing operations effectively.
Rates, Ratios, and Proportions: Understand relationships between quantities; be able to solve problems involving rates, ratios, and proportional reasoning.

Writing and Graphing Inequalities: Construct inequalities from word problems and graph on a number line, indicating the solution set.
Solving Inequalities Using Addition and Subtraction: Apply these operations to isolate the variable on one side of the inequality.
Inequalities with Variables on Both Sides: Similar to equations, rearrange and simplify to find the solution set, maintaining the direction of the inequality.
Multistep Inequalities: Solve inequalities involving more than one operation, taking special care with multiplication or division by negative numbers.
Compound Inequalities: Work with two or more connected inequalities to represent the solution set; understand ‘and’ vs ‘or’ conditions.

Graphing Relationships: Plotting points on a Cartesian plane to visualize the relationship between two variables.
Functions and Relations: Differentiate between functions (every input has one output) and general relations.
The Vertical Line Test: Determine if a graph represents a function by checking if any vertical line crosses the graph more than once.
Writing and Graphing Functions: Convert word problems into function notation and graph accordingly.
Connecting Tables and Graphs: Interpret data in tabular form and represent it graphically, recognizing patterns.
Scatter Plots: Create scatter plots to visualize the correlation between two quantitative variables.

Slopes and Intercepts: Understand slope as a measure of steepness and intercepts as points where the graph crosses the axes.
Linear Functions: Recognize equations that can be represented in the form y = mx + b, where m is the slope and b is the y-intercept.
Rate of Change: Calculate the rate of change as the change in y divided by the change in x between two points on a linear graph.
Slope Formula: Use the formula ( m = \frac{y_2 - y_1}{x_2 - x_1} ) to find the slope between any two points.
Slope-Intercept Form / Point-Slope Form: Use these forms to write linear equations based on known points or slopes.
Parallel and Perpendicular Lines: Identify characteristics, where parallel lines have equal slopes and perpendicular lines have negative reciprocal slopes.

Graphing Systems of Equations: Plot multiple linear equations to find the point of intersection which represents the solution.
Solving by Substitution: Replace a variable in one equation with its equivalent from another to find solutions.
Solving by Elimination: Add or subtract equations to eliminate a variable, making it easier to solve for the remaining variable.
Linear Inequalities: Solve systems that include inequalities, determining the feasible region on a graph.
Systems of Inequalities: Understand the intersection of multiple inequalities as it pertains to solution sets.

Properties of Exponents and Radicals: Familiarize with rules for multiplying, dividing, and raising powers, as well as simplifying radical expressions.
Square Roots and Rational Expressions: Solve equations involving square roots and manipulate rational expressions through factoring and simplification.