No-Calculator Math: Speed, Precision, and Mental Math
The SAT No-Calculator section (paper: 20 questions in 25 minutes = 75 seconds per question; digital: included in the adaptive Math module without calculator) requires arithmetic fluency, algebraic manipulation accuracy, and estimation skills. Mental math strategies: (1) Powers and roots to memorize: perfect squares (1–20²), perfect cubes (1–10³), and common square roots (√2 ≈ 1.41, √3 ≈ 1.73, √5 ≈ 2.24). These appear frequently in No-Calculator geometry and algebra problems. (2) Fraction operations: add/subtract fractions by finding LCD, multiply numerators and denominators separately, divide by multiplying by the reciprocal. (3) Percentage calculations: 30% of 80 = 0.30 × 80 = 24. Percent change = (new − old)/old × 100%. (4) Estimation strategy: for multiple choice questions, estimate the answer before computing — eliminate answer choices that are clearly outside the estimated range, then compute precisely. This saves time by eliminating impossible choices before performing full computation. Common No-Calculator traps: (a) Not simplifying fractions before multiplying (creates unnecessarily large numbers), (b) Not distributing negatives correctly: −(a − b) = −a + b, (c) Confusing (−x)² = x² with −x² = −(x²) — the latter is negative, the former positive. Speed improvement: practice completing mental arithmetic for common SAT calculations (percentage of a number, fraction multiplication, small exponent evaluation) to automaticity — 3–4 weeks of daily 5-minute arithmetic drills measurably reduce computation time.