Core answer: Required final-exam score = (target total − current weighted points) ÷ final weight. Course grade = 40% homework + 60% final; you have 85 on homework and want 80 overall: need = (80 − 85×0.4) ÷ 0.6 = (80 − 34) ÷ 0.6 = 76.7 on the final. If the required score exceeds 100, the target is mathematically dead — renegotiate the target, not reality.
The general formula
Total = Σ (component_i × weight_i) + final × w_final
Required final = (target − Σ current weighted points) ÷ w_final
Weights must sum to 1 (or 100%); convert percentages first.
Worked examples
Example 1 — Standard case. Homework 88 (30%), midterm 72 (30%), final (40%). Target 80: current = 88×0.3 + 72×0.3 = 26.4 + 21.6 = 48.0; need = (80 − 48) ÷ 0.4 = 80.0. Doable with a week of work.
Example 2 — The dead target. Same grades, target 90: need = (90 − 48) ÷ 0.4 = 105 → impossible. Adjust to 85 (need 92.5, hard but alive) or 82 (need 85).
Example 3 — Multi-component. Attendance 95 (10%), quizzes 78 (20%), project 85 (25%), final (45%). Target 85: current = 9.5 + 15.6 + 21.25 = 46.35; need = (85 − 46.35) ÷ 0.45 = 85.9.
Example 4 — GPA-aware prioritization. Finals week, three courses needing 80/92/65 for your target grades: study time flows to the 65 (cheap points, protect the grade) and the 80 (achievable), NOT the 92 (needs near-perfection). Marginal utility per hour — study like an economist.
Example 5 — 及格线 special case. Just need 60: with current weighted 42 and final weight 50%, need = (60 − 42) ÷ 0.5 = 36 — a gentle reminder that showing up for the final is usually enough to pass, but "just pass" is a fragile plan when any component gets re-marked.
Common mistakes and myths
- Averaging components raw — 90 homework + 60 final "averages" 75 only at 50/50 weights; at 40/60 it's 72. Weights are the whole game.
- Ignoring dropped/lowest rules — "lowest quiz dropped" changes your current points; recompute after every drop policy applies.
- Forgetting curves — a curved course means your target is a PERCENTILE, not a raw score; the formula then gives a floor, not a guarantee.
- Panic-blindness — run the numbers before despairing; many students discover they need a modest 70, not a miracle.
- Single-point planning — compute three targets (floor / expected / stretch) and the required score for each; decide effort allocation with all three on the table.