Part II Review

Part II Review: Algebra

This set mixes all four Part II chapters together with no chapter labels. Twenty questions test recognition across the full Algebra Part: linear equations and systems, quadratic equations, other types of equations, and absolute value. No calculator is required, though Desmos or a handheld may still help on a few.

Recognize the type first

• Linear equations and systems. Isolate the variable. Flip an inequality only when you multiply or divide by a negative. Use substitution when a variable is already isolated and elimination when both equations are in standard form. Answer the quantity asked for, such as $x + y$.
• Quadratics. Factor if you can; otherwise use $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. The discriminant $b^2 - 4ac$ tells you the number of real solutions, the vertex has $x$-coordinate $-\frac{b}{2a}$, and "exactly one real solution" means the discriminant is $0$ (keep both signs of $k$).
• Other equations. Factor out common variables or group four-term cubics, substitute a known zero to find a coefficient, rewrite exponential equations with a common base and set the exponents equal, and check every radical-equation answer for extraneous roots.
• Absolute value. Split equations into two cases. A "less than" inequality becomes one compound inequality, and a "greater than" inequality becomes two joined by "or." When a variable appears outside the bars, check each candidate.

Common traps across the set

Sign errors when moving constants, dropping a negative root, reporting $x$ when the question wants $x + y$ or $x^2 - 1$, forgetting to reverse an inequality, and accepting an extraneous solution account for most of the wrong answer choices in this review. After you solve each question, take five seconds to reread what was asked and, if possible, substitute your answer back into the original equation.