How to Use This Calculator
This AP Calculus score calculator helps you predict your exam score based on your expected or actual performance. Follow these steps to get your predicted score:
Select Your Exam Type
Choose AP Calculus AB or AP Calculus BC. The score thresholds differ slightly between exams.
Enter Multiple Choice Score
Enter how many of the 45 multiple choice questions you answered correctly. There is no penalty for wrong answers.
Enter FRQ Scores
Estimate your score for each of the 6 free response questions. Each FRQ is worth 0-9 points based on the rubric.
View Your Results
See your composite score out of 108 and your predicted AP score from 1-5, along with a detailed breakdown.
Tip: Use practice exam results or past FRQ rubrics to estimate your FRQ scores. The College Board publishes scoring guidelines for all past exams.
AP Calculus Exam Structure
Both AP Calculus AB and BC exams follow the same format, lasting 3 hours and 15 minutes total. The exam is divided into two main sections, each worth 50% of your final score.
Section I: Multiple Choice (50%)
| Part | Questions | Time | Calculator |
|---|---|---|---|
| Part A | 30 questions | 60 minutes | Not Permitted |
| Part B | 15 questions | 45 minutes | Required |
Section II: Free Response (50%)
| Part | Questions | Time | Calculator |
|---|---|---|---|
| Part A | 2 questions | 30 minutes | Required |
| Part B | 4 questions | 60 minutes | Not Permitted |
Important Notes:
- No penalty for wrong answers on multiple choice
- Graphing calculator required for certain sections
- FRQs are scored 0-9 points each with partial credit available
- You can return to FRQ Part A questions during Part B time
Scoring Breakdown
Understanding how your raw scores convert to your final AP score is essential for setting realistic goals and interpreting practice test results.
Multiple Choice Scoring
Each correct answer earns 1 point. Your raw MC score (0-45) is multiplied by 1.2 to get your weighted MC score:
Weighted MC Score = (Number Correct) × 1.2Maximum weighted MC score: 45 × 1.2 = 54 points
Free Response Scoring
Each FRQ is scored from 0-9 points. Your total FRQ raw score (0-54) equals your weighted FRQ score:
Weighted FRQ Score = FRQ1 + FRQ2 + FRQ3 + FRQ4 + FRQ5 + FRQ6Maximum weighted FRQ score: 9 × 6 = 54 points
Composite Score
Your composite score is the sum of your weighted MC and FRQ scores:
Composite Score = Weighted MC Score + Weighted FRQ ScoreMaximum composite score: 54 + 54 = 108 points
AP Score Conversion
Your composite score is converted to an AP score of 1-5 using cut scores determined each year:
AP Calculus AB
- 5: 68-108 (63%+)
- 4: 52-67 (48-62%)
- 3: 39-51 (36-47%)
- 2: 27-38 (25-35%)
- 1: 0-26 (0-24%)
AP Calculus BC
- 5: 63-108 (58%+)
- 4: 51-62 (47-57%)
- 3: 39-50 (36-46%)
- 2: 27-38 (25-35%)
- 1: 0-26 (0-24%)
AP Calculus AB vs BC
Choosing between AP Calculus AB and BC is an important decision. Here is a comprehensive comparison to help you decide:
| Feature | AP Calculus AB | AP Calculus BC |
|---|---|---|
| Content Coverage | 1 semester of college calculus | 2 semesters of college calculus |
| Additional Topics | - | Parametric, polar, series, advanced integration |
| Score for 5 | ~68/108 (63%) | ~63/108 (58%) |
| Pass Rate (3+) | ~55% | ~75% |
| AB Subscore | N/A | Included |
| College Credit | Calculus I (3-4 credits) | Calculus I & II (6-8 credits) |
BC-Only Topics
- Parametric Equations: Derivatives and integrals of parametric curves
- Polar Coordinates: Polar curves, area, and arc length
- Vector-Valued Functions: Motion in the plane
- Infinite Series: Convergence tests, Taylor and Maclaurin series
- Advanced Integration: Integration by parts, partial fractions, improper integrals
- Euler's Method: Numerical solutions to differential equations
- Logistic Growth: Differential equations for population models
Which should you take? If you have strong algebra and precalculus skills and are comfortable with a faster pace, BC is often the better choice as it provides more college credit and includes an AB subscore as a backup. If you prefer a deeper understanding of fundamental concepts, AB allows more time for mastery.
How We Calculate Your Score
Our calculator uses the official College Board scoring methodology and historical cut score data to provide accurate predictions.
1. Raw Score Calculation
We first calculate your raw scores for each section:
MC Raw Score = Number of correct answers (0-45)FRQ Raw Score = Sum of all FRQ points (0-54)2. Weighted Score Conversion
Raw scores are weighted to ensure equal contribution from each section:
Weighted MC = MC Raw Score × 1.2 (max 54)Weighted FRQ = FRQ Raw Score × 1.0 (max 54)3. Composite Score
Your composite score combines both weighted scores:
Composite = Weighted MC + Weighted FRQ (max 108)4. AP Score Prediction
We map your composite score to an AP score using historical cut score thresholds:
Cut scores vary by 1-3 points each year based on exam difficulty. Our thresholds represent average historical values for reliable predictions.
Accuracy Note: Our predictions are typically within +/- 2-3 composite points of actual cut scores. The College Board adjusts cut scores annually using statistical equating to maintain consistent standards across years.
Real-World Score Examples
These scenarios show how different performance patterns translate to AP scores. Use these examples to set realistic targets and understand what it takes to achieve your desired score.
Sarah - AP Calculus AB (Score: 5)
Performance:
- Multiple Choice: 38/45 correct (84%)
- FRQ Average: 7.5/9 per question
- Total FRQ: 45/54 points
Result:
- MC Score: 38 × 1.2 = 45.6
- FRQ Score: 45.0
- Composite: 90.6/108 (84%)
- AP Score: 5
Sarah balanced strong performance across both sections. Her consistent 7-8 point FRQ scores and solid MC work put her well above the 68-point threshold for a 5.
Marcus - AP Calculus BC (Score: 5)
Performance:
- Multiple Choice: 34/45 correct (76%)
- FRQ Average: 6.5/9 per question
- Total FRQ: 39/54 points
Result:
- MC Score: 34 × 1.2 = 40.8
- FRQ Score: 39.0
- Composite: 79.8/108 (74%)
- AP Score: 5
Marcus benefited from BC's lower threshold (63 vs 68 for AB). He struggled with polar coordinates but excelled on series questions, showing how BC rewards depth in advanced topics.
James - AP Calculus AB (Score: 4)
Performance:
- Multiple Choice: 32/45 correct (71%)
- FRQ Average: 5.0/9 per question
- Total FRQ: 30/54 points
Result:
- MC Score: 32 × 1.2 = 38.4
- FRQ Score: 30.0
- Composite: 68.4/108 (63%)
- AP Score: 4 (close to 5)
James was just above the 68-point threshold but in an unstable position. Even one more wrong MC answer would drop him to a 4. This shows the importance of buffer room near cutoffs.
Emily - AP Calculus BC (Score: 3, AB Subscore: 4)
Performance:
- Multiple Choice: 27/45 correct (60%)
- FRQ Average: 4.5/9 per question
- Total FRQ: 27/54 points
- Strong on AB content, weak on series
Result:
- MC Score: 27 × 1.2 = 32.4
- FRQ Score: 27.0
- Composite: 59.4/108 (55%)
- BC Score: 3, AB Subscore: 4
Emily's BC-specific content (series, parametric equations) hurt her overall score, but her strong fundamentals earned a 4 AB subscore. This demonstrates the safety net BC provides.
Key Takeaway: Both sections matter equally. A strong MC score cannot fully compensate for weak FRQs, and vice versa. Aim for balanced preparation across all question types.
Common Mistakes to Avoid
Learn from these frequent errors that cost students points on both multiple choice and free response questions.
1. Forgetting to Apply Chain Rule
Problem:
Finding derivative of f(x) = sin(3x²) and writing f'(x) = cos(3x²), missing the chain rule entirely.
Solution:
Always identify composite functions. Correct answer: f'(x) = cos(3x²) · 6x. Write out each step to avoid missing the inner derivative.
2. Confusing Definite and Indefinite Integrals
Problem:
Evaluating ∫₀³ 2x dx and including "+ C" in the final answer, or forgetting to evaluate at bounds and leaving an antiderivative.
Solution:
Definite integrals produce numbers, not functions. Evaluate [x²]₀³ = 9 - 0 = 9. No "+ C" appears. For indefinite integrals, always include the constant.
3. Misinterpreting Derivative Notation in Context
Problem:
A problem states "v(t) = 3t² - 6t" and asks for acceleration. Student incorrectly finds position by integrating velocity instead of differentiating.
Solution:
Acceleration is the derivative of velocity: a(t) = v'(t) = 6t - 6. Memorize: position → velocity → acceleration (differentiate). Use diagrams to visualize relationships.
4. Not Justifying Answers on FRQs
Problem:
Question asks "Is f(x) continuous at x=2?" Student writes "Yes" without showing lim(x→2) f(x) = f(2) or checking all continuity conditions.
Solution:
Always show work for "justify" or "explain" prompts. Write: "lim(x→2⁻) f(x) = 5, lim(x→2⁺) f(x) = 5, f(2) = 5. Since all three match, f is continuous." Use theorem names.
Pro Tip: Read FRQ prompts carefully. Words like "justify," "explain," and "show" require written explanations with mathematical reasoning. Circle these keywords during the exam to ensure you address them.