Math I Semester Exam Review (Unit 1)

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What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: c² = a² + b².

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Define a linear equation.

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A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = 0, where a and b are constants.

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What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x). It is often represented by the letter 'm'.

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How do you find the area of a triangle?

Back

The area of a triangle can be found using the formula: Area = 1/2 * base * height.

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What is the difference between mean, median, and mode?

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Mean is the average of a set of numbers, median is the middle value when numbers are arranged in order, and mode is the number that appears most frequently.

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What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

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Explain the concept of a variable in algebra.

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A variable is a symbol (often a letter) that represents an unknown value in mathematical expressions and equations.

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What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

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How do you solve a system of equations?

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A system of equations can be solved using methods such as substitution, elimination, or graphing to find the values of the variables that satisfy all equations.

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What is the difference between an expression and an equation?

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An expression is a combination of numbers, variables, and operations without an equality sign, while an equation states that two expressions are equal.