Algebra 1 - Q2 Project (2024)--Comprehensive Semester 1 Review

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What is the formula for calculating compound interest?

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The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

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What is the Elimination Method in solving systems of equations?

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The Elimination Method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable. This method is useful for solving systems of linear equations.

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What is exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It can be represented by the function f(x) = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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How do you solve an inequality?

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To solve an inequality, isolate the variable on one side of the inequality sign. If you multiply or divide by a negative number, reverse the inequality sign. Then, express the solution in interval notation or graph it on a number line.

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

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What is the difference between linear growth and exponential growth?

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Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster growth as time progresses.

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What does it mean for a function to be linear?

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A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line (depending on whether the inequality is strict or inclusive). Then, shade the region that satisfies the inequality.