Algebra 2 Final Exam Review Packet

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In the classroom

Students simplify, factor, and expand polynomial expressions of varying degree.
Students find the slope, intercepts, and equation of a line, including lines perpendicular to a given line.
Students solve quadratic equations and use the discriminant to determine the number and type of roots.
Students identify the degree, zeros, and vertex of a polynomial or parabola from its equation or graph.
Students simplify expressions involving complex numbers, including finding a complex conjugate.

Have students start with the topics they understand least, per the packet's own introduction, rather than working straight through in order.
Remind students of the exam's note-sheet policy (one handwritten 8.5-by-11 page, no photocopies) stated in the introduction, since it shapes how they should prepare.
Use the closing 'Random practice' section as open-response follow-up after students have worked through the multiple-choice items on the same topics.

Polynomial simplification and factoring — students expand, combine, and factor polynomial expressions across dozens of items.
Quadratic equation solving — students solve quadratics and use the discriminant to determine the number and nature of roots.
Complex number operations — students simplify expressions involving complex numbers and identify complex conjugates.
Linear and quadratic graph analysis — students identify slope, intercepts, vertex, and x-intercepts from equations and graphs.

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Curriculum

HSN-CN.A.3 — Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
HSA-REI.B.4 — Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
HSG-GPE.B.5 — Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

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