Algebra Proficiency Exam - Units 1 & 2

UNIT 1 - Solving Equations

• 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.

UNIT 2 - Solving Inequalities

• 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.

UNIT 3 - Functions

• 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.

UNIT 4 - Linear Functions

• 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.

UNIT 5 - Systems of Equations

• 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.

UNIT 6 - Exponents and Rational Expressions

• 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.

Test your algebra skills with this proficiency exam covering key concepts from Units 1 and 2. The exam includes solving equations, working with integers, fractions, and decimals, as well as inequalities. Assess your understanding of multi-step equations, rates, ratios, proportions, and graphing inequalities.