Algebra 1 Honors 1st Semester Exam Review

Algebra 1 Honors 1st Semester Exam Review

• Evaluate expressions: Substitute given values for variables to find the numerical result of the expression. For example: evaluating a - b for a = -3 and b = 4 results in -3 - 4 = -7

• Simplify expressions: Combine like terms in algebraic expressions. For example, 9x³ + 7x² + 4x² - x + 4x³ - 3x² simplifies to 13x³ - 6x² - x.

• Order of Operations: Follow the order of operations (PEMDAS/BODMAS) to evaluate expressions. Example: 10 - 2 - [3 - (3² + 2)] =10 - 2 - [3 - (9 + 2)] = 10 - 2 - [3 - 11] = 10 - 2 - (-8) = 16.

• Algebraic expressions: Represent word problems using variables. For example, the cost for n hours of bowling at $20 per hour plus a $3 shoe rental is 20n + 3.

• Solve equations: Isolate the variable to find its value. Example: 10 = 8 / 3w where w = 8 / 30

• Inequalities: Solve and graph inequalities. For example, the inequality 12 < c ≤ 14 can be graphed on a number line.

• Proportions: Solve for missing values in proportions (equal ratios). Example: 4 / 2 = x / 6.

• Percent problems: Calculate percentages of numbers, or find the number given a percentage. Example: What is 23% of 92, or 68% of what number is 64.6.

• Rate problems: Calculate speeds in different units of measure. (e.g., kilometers per hour to miles per hour). Example: 100 kilometers per hour is approximately 62 miles per hour.

• Similar triangles: Use proportional relationships to find missing side lengths in similar triangles. Example: If two triangles are similar, ratio of corresponding sides will be equal.

• Graphing inequalities: Represent inequalities graphically on a number line or coordinate plane.

• Geometric problems: Solving problems involving geometry concepts like area and circumference of circles, ratios of corresponding sides of triangles etc

• Probability/Combinations

  • : In probability theory, we assess the likelihood of various outcomes occurring within a specific experiment or scenario, employing mathematical models to help quantify uncertain events. The field encompasses various theorems and principles, including the fundamental laws of probability, which allow us to determine the probability of single or multiple events happening. Additionally, when dealing with combinations, it is essential to calculate the different possible selections of items from a given set, where the order of selection does not matter, as opposed to permutations, where order is crucial. This principle is particularly significant in combinatorics, a branch of mathematics involving counting, arrangement, and combination of objects. The applications of these concepts extend to various disciplines, such as statistics, where they help in analyzing data distributions; gaming, where probability influences game design and strategy; and decision-making processes, where it aids in assessing risks and forecasting outcomes. Understanding these principles is critical not only for theoretical knowledge but also for their practical implications in real-world scenarios.

  Data Analysis

• Mean, Median, Mode: Calculate the measures of central tendency for a set of data/numbers. Example: Given the data for ages of presidents, Calculate the mean, median, and mode of the ages

• Frequency tables: Create tables showing how often different values appear in a dataset. Example: Construct a frequency table for the ages of U.S. presidents.

• Box-and-whisker plots: Display data using a box-and-whisker plot to show the distribution of data

Additional Topics

• Equation problems Example: Solving equations for a variable x
• Solving for variables Example: Solving for variable in algebraic expressions with different operations
• Simple interest Example: Calculating simple interest for a savings account
• Percent increase/decrease Example: Finding percent increase/decrease in a monetary value (e.g. house sale)
• Error calculations Example: Calculating the percent error from different formulas
• Word problems: Translate word problems into equations or inequalities.