Estimate AP Calculus BC scores quickly using sliders for MC and FRQs, showing composite out of 100 and predicted 1–5.
MC_w = (MC/45)×50;
FRQ_w = (ΣFRQ/54)×50;
Composite = MC_w + FRQ_w;
Predicted AP ≈ f(Composite)
An AP® Calculus BC Score Calculator converts your practice test performance into an estimated composite percentage and an approximate College Board–style scaled score (1–5). Simply input your correct multiple-choice (MC) answers and total items, along with your free-response (FRQ) points earned and their maximum. The calculator applies weighted formulas to show how each section contributes to your overall result. Since official raw-to-scaled conversions change each year and exam form, this tool is best used for goal setting, progress tracking, and “what-if” analysis—not as an official predictor. Clear equation previews explain every step so you can focus your study time on the most high-impact improvements.
The AP® Calculus BC exam includes both MC and FRQ sections. It assesses all Calculus AB topics—limits, derivatives, integrals, and applications—plus BC-only content such as infinite series, parametric and polar functions, and advanced integration techniques. This calculator assumes equal section weighting: \(w_{\text{MC}} = w_{\text{FRQ}} = 0.50\). It normalizes your raw scores, multiplies by these weights, and sums to produce a composite percentage. Finally, it maps that value to illustrative 1–5 score bands to help you benchmark progress. You can modify section maxima to match your test format (for example, \(\mathrm{MC\_max}=45\); \(\mathrm{FRQ\_max}=54\) across six questions). If you want to calculate an AB subscore, use the AB subset of questions—but this calculator focuses on the overall BC performance.
Section percentages: \[ p_{\text{MC}}=\frac{\mathrm{MC\_raw}}{\mathrm{MC\_max}},\qquad p_{\text{FRQ}}=\frac{\mathrm{FRQ\_raw}}{\mathrm{FRQ\_max}}. \]
Weighted composite percentage: \[ \mathrm{Composite\ \%}=100\cdot\big( w_{\text{MC}}\,p_{\text{MC}} + w_{\text{FRQ}}\,p_{\text{FRQ}} \big),\qquad w_{\text{MC}}+w_{\text{FRQ}}=1. \]
Illustrative bands (example only): \[ \begin{aligned} &\text{5: } \mathrm{Composite\ \%}\ge 80,\quad \text{4: } 66\le \mathrm{Composite\ \%}<80,\\ &\text{3: } 45\le \mathrm{Composite\ \%}<66,\quad \text{2: } 30\le \mathrm{Composite\ \%}<45,\quad \text{1: } <30. \end{aligned} \]
\(\mathrm{MC\_raw}=34/45\Rightarrow p_{\text{MC}}\approx0.7556\). \(\mathrm{FRQ\_raw}=38/54\Rightarrow p_{\text{FRQ}}\approx0.7037\). Composite \(=100\cdot(0.5\cdot0.7556+0.5\cdot0.7037)\approx72.97\%\Rightarrow\) score ≈ 4.
\(\mathrm{MC\_raw}=40/45\Rightarrow0.8889\). \(\mathrm{FRQ\_raw}=22/54\Rightarrow0.4074\). Composite \(=100\cdot(0.5\cdot0.8889+0.5\cdot0.4074)\approx64.82\%\Rightarrow\) score ≈ 3. Focus on improving FRQ technique and clarity in written explanations.
\(\mathrm{MC\_raw}=28/45\Rightarrow0.6222\). \(\mathrm{FRQ\_raw}=48/54\Rightarrow0.8889\). Composite \(=100\cdot(0.5\cdot0.6222+0.5\cdot0.8889)\approx75.56\%\Rightarrow\) score ≈ 4, nearing 5.
\(\mathrm{MC\_raw}=43/45\Rightarrow0.9556\). \(\mathrm{FRQ\_raw}=50/54\Rightarrow0.9259\). Composite \(=100\cdot(0.5\cdot0.9556+0.5\cdot0.9259)\approx94.08\%\Rightarrow\) score ≈ 5.
No. These are illustrative practice ranges. Official raw-to-scaled conversions differ each year and across exam forms.
By default, \(w_{\text{MC}}=0.50\) and \(w_{\text{FRQ}}=0.50\). You can modify them if your materials emphasize one section more heavily.
Match your specific practice set—for example, \(\mathrm{MC\_max}=45\) and \(\mathrm{FRQ\_max}=54\). Always verify totals from your test source.
No. Recent AP® Calculus BC formats have no guessing penalty. You should still aim for accuracy, but strategic guessing is safe.
Yes. You can calculate it separately using the AB subset, though this tool primarily focuses on the overall BC composite score.
For consistent tracking, round to two decimal places when comparing results across practice sessions.
Use “what-if” tests to identify whether additional MC accuracy or FRQ precision has a greater impact. Then prioritize the section that moves your composite farther.
Other calculators may use different weight ratios, section maximums, or score thresholds. Always align assumptions when comparing estimates.