3. Strategy for Mastery Items

At this level, every point is earned by disciplined process.

• Decode the layers out loud. "Markup, then tax." "Two solutions mixed to a target." Name each step before touching the calculator.
• Backsolve relentlessly. For quadratic, rational, exponent, and absolute-value equations, testing the numeric choices is often fastest -- and it exposes extraneous roots.
• Answer the exact target. Mastery traps hand you a correct intermediate value -- the cost, the time, the first root -- when the question wants the next thing.
• Use complements, conditionals, and ratios. 'At least one' is \(1 - P(\text{none})\); 'among those who…' divides by that group; area ratios are the square, volume ratios the cube, of the length ratio.
• Handle inequalities with care. Flip on a negative; split \(|x|>c\) into two outward pieces; a quadratic inequality is between or outside its roots.
• Estimate to defend the point. A quick estimate catches a misplaced decimal or a wrong sign before it costs you.