Final Exam Review: Algebra 1

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In the classroom

Students solve exponential growth and decay word problems by identifying the initial value, rate, and number of time periods.
Students factor polynomials using the GCF, special-case patterns, and trinomial factoring.
Students solve systems of linear equations by graphing, substitution, and elimination, and interpret no-solution or infinite-solution cases.
Students apply the Pythagorean theorem and the distance formula to find missing side lengths and distances between points.
Students solve and graph one-variable, two-variable, and compound inequalities.

Assign as a multi-day take-home review before a cumulative final exam, given its breadth of 72 problems across roughly 35 named topics.
Use the answer key's worked solutions — such as the elimination and substitution walk-throughs — as a model for students who are stuck, rather than only checking final answers.
Review by topic heading (e.g. 'Factoring Trinomials,' 'Solving Systems of Equations by Elimination') since the packet is organized by named Algebra 1 skill rather than by difficulty.

Exponential growth and decay modeling — students write and evaluate equations for scenarios like a car losing 15% of its value yearly or savings growing at compound interest.
Polynomial factoring — students factor out the GCF and factor special cases and trinomials completely.
Systems of equations — students solve systems using graphing, substitution, and elimination, including cases with no solution or infinitely many solutions.
Pythagorean theorem and distance — students find missing triangle sides and the distance between two coordinate points.
Inequalities — students write, solve, and graph one-variable, two-variable, and compound inequalities from word descriptions and number-line graphs.

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Curriculum

8.G.B.8 — Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
HSA-CED.A.1 — Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions

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