3. Strategy for the Hardest Items

At this level, process beats speed every time.

• Name both concepts. If a question hides a percent inside a finance problem, label them: "this is compound interest" and "this is a percent." Solve in that order.
• Backsolve the brutal ones. For quadratics, rational equations, or absolute-value equations, plugging the numeric choices back in is often faster and surer than solving.
• Watch 'at least one.' Compute \(1 - P(\text{none})\) instead of adding cases.
• Re-read the target. Hard items ask for the original price, the time it lands, the maximum height, the other solution -- not the first number you find.
• Flip on negatives. Multiplying or dividing an inequality by a negative reverses the sign; absolute-value inequalities split into two cases.
• Estimate as a check. A rough estimate catches a calculator slip or a misplaced decimal before it costs you the point.