MathematicsStep-Marking SchemeCBSE / ICSE✏️ 5 marks
Question: Solve: 2x² + 7x + 3 = 0 using the quadratic formula. Verify your answer.
MARKING SCHEME — 5 marks Step 1 — Identify coefficients [½ mark] a = 2, b = 7, c = 3 Step 2 — State the quadratic formula [½ mark] x = (−b ± √(b² − 4ac)) / 2a Step 3 — Substitute correctly [1 mark] x = (−7 ± √(49 − 24)) / 4 x = (−7 ± √25) / 4 x = (−7 ± 5) / 4 Step 4 — Calculate both roots [1 mark] x₁ = (−7 + 5) / 4 = −2/4 = −½ x₂ = (−7 − 5) / 4 = −12/4 = −3 Step 5 — Verify by substitution (either root shown) [1 mark] For x = −½: 2(¼) + 7(−½) + 3 = ½ − 3½ + 3 = 0 ✓ Step 6 — Final statement [1 mark] Therefore x = −½ or x = −3 PARTIAL CREDIT RULES • Award Step 3 marks even if Steps 1–2 are missing, if formula is applied correctly. • Arithmetic error in Step 3: carry-forward — award Steps 4–5 if method is correct. • Verification missing: maximum 4/5. COMMON ERRORS TO FLAG (do not award mark) ✗ Forgetting ± (writing only +) ✗ Error in discriminant: b² − 4ac computed as b² + 4ac
