3. Strategy for Mastery-Level Items

With no easy questions, your process has to be airtight.

• Unpack the layers. Write down each concept a problem stacks: "bracket, then percent," "area, then cost," "doubling, then count the doublings."
• Backsolve the algebra. For quadratics, rational, and absolute-value equations, plugging the numeric choices back in is often the safest route -- and it catches extraneous solutions.
• Use complements and ratios. 'At least one' is \(1-P(\text{none})\); a conditional is the joint over the given.
• Re-read the exact target. Mastery traps love to ask for the original value, the other root, the leftover area, the time (not the height).
• Flip and split on inequalities. Dividing by a negative flips the sign; \(|x|>c\) splits into two pieces; a quadratic inequality needs the sign between or outside its roots.
• Estimate to sanity-check. A quick estimate flags a calculator slip before it costs the point.