AP Calculus BC Exam 2026: Study + Test Tips

Scoring high on the AP Calculus BC Exam takes solid preparation, but the numbers show that many students rise to the challenge. About 80.9% earned a 3 or higher in 2024, with nearly 69% scoring a 4 or 5. Out of 148,191 test-takers that year, the average score came out to an impressive 3.92.

Still, the AP Calculus BC Exam is far from easy. It includes all the content from Calculus AB along with extra topics. The pace is fast, and the questions can get tricky. So, this guide walks you through everything you need to know: what’s on the exam, how it’s structured, how long it is, and how to study in a way that actually works.

• AP Calculus BC Course and Exam Description
• AP Calculus BC Exam Format
• AP Calculus BC Exam Questions
• How to Study for the AP Calculus BC Exam
• AP Calculus BC Exam Test-Taking Tips
• AP Calculus BC Exam Date
• Is the AP Calculus BC Exam Hard?
• Frequently Asked Questions
• Takeaways

AP Calculus BC Course and Exam Description

The AP Calculus BC course covers all the topics from AP Calculus AB plus additional units you would normally learn in a second semester college calculus class. That includes parametric equations, polar and vector-valued functions, and infinite series.

You’ll learn how to apply calculus in a wide range of contexts. The course teaches you how to analyze graphs, estimate values using limits, take derivatives of different types of functions, compute definite integrals, and justify your answers with clear reasoning. You’ll also work on modeling problems, slope fields, and series convergence.

To do well, you’ll need strong algebra and trigonometry skills. You should be able to manipulate expressions, solve equations, graph different kinds of functions, and understand basic function behavior. Most students take this course in their senior year or after completing precalculus.

This is a college-level math course that moves quickly and builds on itself. Everything you’ll be tested on is listed in the official AP Calculus BC Course and Exam Description, so it’s the best place to start your prep.

AP Calculus BC Exam topics

The AP Calculus BC Exam pulls questions from ten major units. Each unit focuses on a specific set of skills. Here’s how the content is weighted on the exam:

These percentages reflect how much of the AP Calculus BC Exam is focused on each topic. For example, Unit 6 is a big one, so you should expect a lot of questions that ask you to compute definite integrals or apply the Fundamental Theorem of Calculus.

Units on analytical applications, parametric and polar equations, and series also carry major weight. That means you need to be confident working with L’Hôpital’s Rule, convergence tests, and setting up volume or motion problems.

Mastering the high-weight units gives you the best chance of scoring a 4 or 5. But the smaller units still matter, especially when they show up in multiple-choice questions with tricky setups. Strong foundational skills will help you move through all ten units with confidence.

AP Calculus BC Exam Format

The AP Calculus BC Exam uses a hybrid format. You’ll take Section I (Multiple Choice) in the College Board’s Bluebook app, and you’ll write Section II (Free Response) by hand in a paper booklet.

The test is split into two main sections, and each counts for 50% of your total score:

Section I – Multiple Choice

• 45 questions
• 105 minutes
• 50% of your score

This section is divided into two parts. Part A has 30 questions where calculators are not allowed. Part B has 15 questions where calculators are required.

These questions pull from every unit in the course. You’ll see a mix of stand-alone problems and grouped questions. They test how well you understand calculus concepts and how accurately you can interpret graphs, tables, or function behavior.

You’ll see topics like:

• Limits and continuity
• Derivatives of all types of functions
• Applications of differentiation
• Definite and indefinite integrals
• Graph and table analysis
• Parametric and polar functions
• Infinite series and convergence tests

Each question has four answer choices. There’s no penalty for guessing.

Section II – Free-Response

• 6 questions
• 90 minutes
• 50% of your score

Free-response tasks:

• Question 1 – Calculator Required: multi-part problem that may involve function modeling, graphical analysis, or real-world applications
• Question 2 – Calculator Required: another multi-part problem that often focuses on rate of change, accumulation, or tabular data
• Questions 3–6 – No Calculator: shorter tasks that test your algebra, derivatives, integrals, or series analysis

The two calculator-required problems come first. You’ll have 30 minutes for them. After that, you’ll have 60 minutes to complete the remaining four problems without a calculator.

Each question is worth the same amount, and each one includes multiple parts. You’ll need to justify your work, show steps clearly, and write answers in complete sentences when asked. Label your answers by part (a, b, c) to keep everything organized.

You can use your graphing calculator on the parts that allow it. For the rest, make sure you’ve practiced solving problems by hand. The better you are at managing your time and showing your thinking clearly, the more points you’ll earn.

How long is the AP Calculus BC Exam?

The AP Calculus BC exam lasts 3 hours and 15 minutes. You’ll spend 105 minutes on the multiple-choice portion and 90 minutes on the free-response portion. That includes all the time you’ll need to complete both calculator and non-calculator questions.

In the multiple-choice section, you have just over 2 minutes per question. In the free-response section, time management becomes even more important. You should plan to spend about 15 minutes on each of the six questions. The first two problems require a calculator, and the last four must be done without one.

The challenge is staying accurate while keeping pace. If you rush, your setup or explanation might be unclear. If you move too slowly, you might run out of time before finishing. Knowing how long to spend on each part helps you stay calm, think clearly, and avoid losing points on questions you actually know how to solve.

AP Calculus BC Exam Questions

Both sections of the AP Calculus BC Exam test your ability to think like a mathematician. That means applying concepts to real scenarios, solving problems from multiple angles, and justifying your reasoning clearly. Let’s break down what you can expect.

Multiple Choice Questions

Here’s an example taken from the 2012 AP Calculus BC Practice Exam published by the College Board:

The correct answer is (E).

This is a chain rule problem. The expression y = sin³(x) can be rewritten as y = (sin x)³, which is a composition of two functions: an outer cube function and an inner sine function.

To differentiate, apply the chain rule:

First, take the derivative of the outer function (something³), which gives 3(sin x)².

Then multiply it by the derivative of the inner function, which is cos x.

So:

dy/dx = 3(sin x)² * cos x = 3sin²(x)cos(x)

This matches choice (E).

This question tests your ability to correctly apply the chain rule when differentiating composite trigonometric expressions.

Free-Response Questions

The FRQs make up 50% of your exam score. You’ll answer 6 free-response questions in 1 hour and 30 minutes. This includes 2 long questions and 4 short ones, and each one requires you to show all your work clearly and justify your answers. These questions test your ability to apply calculus concepts to graphical, numerical, analytical, and verbal representations of functions.

Below are real free-response questions taken from the 2024 AP Calculus BC Exam.

Section II, Part A – Calculator required

Here’s an example of a real calculator-active free-response question from the 2024 exam:

1. The temperature of coffee in a cup at time t minutes is modeled by a decreasing differentiable function C, where C(t) is measured in degrees Celsius. For 0 ≤ t ≤ 12, selected values of C(t) are given in the table shown. (a) Approximate C′(5) using the average rate of change of C over the interval 3 ≤ t ≤ 7. Show the work that leads to your answer and include units of measure. (b) Use a left Riemann sum with the three subintervals indicated by the data in the table to approximate the value of ∫ from 0 to 12 of C(t) dt. Interpret the meaning of (1/12) ∫ from 0 to 12 of C(t) dt in the context of the problem. (c) For 12 ≤ t ≤ 20, the rate of change of the temperature of the coffee is modeled by C′(t) = (-24.55 * e^(0.01t)) / t, where C′(t) is measured in degrees Celsius per minute. Find the temperature of the coffee at time t = 20. Show the setup for your calculations. (d) For the model defined in part (c), it can be shown that C″(t) = (0.2455 * e^(0.01t) * (100 – t)) / t². For 12 < t < 20, determine whether the temperature of the coffee is changing at a decreasing rate or at an increasing rate. Give a reason for your answer. 2. A particle moving along a curve in the xy-plane has position (x(t), y(t)) at time t seconds, where x(t) and y(t) are measured in centimeters. It is known that x′(t) = 8t − t² and y′(t) = −t + √(t^1.2) + 20. At time t = 2 seconds, the particle is at the point (3, 6). (a) Find the speed of the particle at time t = 2 seconds. Show the setup for your calculations. (b) Find the total distance traveled by the particle over the time interval 0 ≤ t ≤ 2. Show the setup for your calculations. (c) Find the y-coordinate of the position of the particle at the time t = 0. Show the setup for your calculations. (d) For 2 ≤ t ≤ 8, the particle remains in the first quadrant. Find all times t in the interval 2 ≤ t ≤ 8 when the particle is moving toward the x-axis. Give a reason for your answer.

Let’s break down what a high-scoring response looks like for Questions 1 and 2 of the 2024 AP Calculus BC Free-Response section:

Question 1: Coffee temperature model

(a) To approximate C′(5), use the average rate of change from t = 3 to t = 7:

C′(5) ≈ [C(7) − C(3)] / (7 − 3) = (55 − 85) / 4 = −30 / 4 = −7.5°C/min

This represents the average rate at which the temperature is decreasing between t = 3 and t = 7.

(b) Use a left Riemann sum with the given subintervals (0 to 3, 3 to 7, 7 to 12):

 ∫₀¹² C(t) dt ≈ 3·100 + 4·85 + 5·69 = 300 + 340 + 345 = 985

The value of (1/12)∫₀¹² C(t) dt represents the average temperature of the coffee over the 12-minute period.

(c) To find the temperature at time t = 20, integrate the given C′(t):

C(20) = C(12) + ∫₁₂²⁰ C′(t) dt

C(20) = 55 + ∫₁₂²⁰ [−24.55e^(0.01t)/t] dt

Use a graphing calculator to evaluate the definite integral and solve for C(20).

(d) We are given the third derivative:

C‴(t) = [0.2455e^(0.01t)(100 − t)] / t²

Since all terms are positive for 12 < t < 20, and (100 − t) > 0 on that interval, we know C‴(t) > 0.

This means the rate of temperature change (C′) is increasing, so the temperature is decreasing at a decreasing rate.

Question 2: Particle motion in the plane

(a) To find the speed at t = 2:

x′(2) = 8(2) − (2)² = 16 − 4 = 12

y′(2) = −2 + √(2 × 1.2) + 20 ≈ −2 + √2.4 + 20 ≈ −2 + 1.55 + 20 = 19.55

Speed = √[(x′(2))² + (y′(2))²] = √[144 + 382.2] ≈ √526.2 ≈ 22.94 cm/s

(b) Total distance traveled from t = 0 to t = 2: 

∫₀² √[(x′(t))² + (y′(t))²] dt 

Plug in x′(t) = 8t − t² and y′(t) = −t + √(1.2t) + 20 into your calculator and evaluate the definite integral numerically.

(c) We’re given y(2) = 6. Use this to solve for y(0):

y(2) = y(0) + ∫₀² y′(t) dt → y(0) = y(2) − ∫₀² y′(t) dt

Set up and evaluate the integral to find the initial y-coordinate.

(d) To find when the particle is moving toward the x-axis on [2, 8], look for when y′(t) < 0. 

This means the vertical component is decreasing. Use a calculator to solve y′(t) = −t + √(1.2t) + 20 < 0 on the interval 2 ≤ t ≤ 8. 

Identify the time values when the inequality holds true.

Section II, Part B – No calculator allowed

Here is an example of a no-calculator question taken from the 2024 exam that focus on core calculus skills:

Now that you’ve seen what Question 3 looks like on the 2024 AP Calculus BC Exam, let’s break down what a high-scoring student response actually looks like:

(a) The student correctly sketches a solution curve that passes through the point (0, 4) and follows the slope field. The sketch accurately reflects the directional behavior of the field, showing that the solution curve increases slightly before leveling off.

(b) The student identifies the critical point by setting the derivative equal to zero:

dH/dt = (1/2)(H – 1)cos(t/2) = 0

This occurs when cos(t/2) = 0 → t/2 = π/2 → t = π.

They then test the sign of dH/dt before and after t = π to determine whether H is increasing or decreasing.

They conclude that t = π is a relative maximum, justifying it with sign changes and the context that H(t) > 1.

(c) The student correctly separates variables:

dH / (H – 1) = (1/2)cos(t/2) dt

They integrate both sides, apply the initial condition H(0) = 4, and solve for the particular solution. The work is shown clearly, and units are appropriately included.

Why this earns full credit:

• Every part of the question is addressed and fully developed.
• Mathematical reasoning is justified with clear steps and explanations.
• The student correctly applies separation of variables and initial conditions.
• Sketch and analysis match the context of the differential equation and graph.

High-scoring responses show reasoning, clarity, and connection to the problem’s context. Always make sure your steps are clear, your setup is justified, and your interpretations make sense with what’s being modeled.

If you want to get better at the free-response section, review past AP Calculus BC student responses and scoring guidelines from the College Board. Seeing real examples will help you understand what earns full credit and what common mistakes to avoid.

How to Study for the AP Calculus BC Exam

The AP Calculus BC Exam tests how well you understand core calculus concepts and how you apply them to different types of problems. You will need to show your reasoning, explain your steps clearly, and use the right notation to earn credit on both multiple-choice and free-response sections.

That means mastering key theorems, knowing when to apply integration or series techniques, and practicing written explanations that reflect your understanding. Here are seven study strategies that will help you prepare effectively:

1. Review the AP Calculus BC course outline.

The AP Calculus BC Course and Exam Description (CED) is your official roadmap. It outlines every topic, shows how much each unit contributes to your score, and includes the skills you are expected to demonstrate.

For example, Unit 10 on Infinite Series is unique to AP Calculus BC and is heavily tested. You should also know what the course expects when it comes to differential equations, slope fields, parametric motion, and vector-valued functions. Use the CED to keep your review focused and complete.

2. Use and analyze full-length practice tests.

Practice tests are essential for identifying your weak spots and building test-taking confidence. They help you get used to the timing, question styles, and calculator expectations.

After taking a full test, make sure to:

• Review each problem you got wrong or guessed on.
• Rework the problems without looking at the answer key.
• Check how the free-response questions are scored and read through high-scoring sample answers.
• Use pacing strategies to stay on track during each section.

Try to use real College Board exams if possible. These give you the most accurate picture of the test format and difficulty level.

3. Know your formulas and theorems inside and out.

You will get a formula sheet, but you still need to know when and how to apply each concept. The test will not tell you which formula to use or when to use a calculator.

Focus on:

• Common derivatives and integrals, including trig, exponential, and inverse functions.
• Taylor and Maclaurin series for functions like sin(x), cos(x), e^x, and ln(1+x).
• Theorems like the Mean Value Theorem, Extreme Value Theorem, and the Alternating Series Test.
• Vector and parametric motion formulas, especially for displacement and speed.
• Calculator-based strategies, like finding intersection points or using built-in derivative tools.

4. Practice written justifications for FRQs.

A correct answer without a proper explanation can still lose points. Your goal is to show what you know clearly and completely.

When practicing FRQs, make sure to:

• Answer every subpart of the question. Letters like (a), (b), and (c) are scored individually.
• Use full sentences where appropriate, especially when interpreting values or stating conclusions.
• Justify your reasoning. For example, “Since f ′ (x) changes from negative to positive at x = 3, the function has a local minimum at x = 3.”
• Write clearly and use proper math symbols and notation. A sloppy answer, even if correct, can be misread or misunderstood.
• Circle or box your final answer to make it easy to find.

5. Focus on visuals and interpretation.

You will encounter slope fields, graphs of functions, and motion in parametric or polar form. Being able to read and interpret visual information is critical.

To get better at this:

• Practice sketching slope fields and identifying solution curves.
• Interpret graphs of f, f ′ , and f ″. Know what slope and area mean in context.
• Work with parametric and polar graphs. Understand how to find position, velocity, and acceleration.
• Know what a graph is showing. For example, is it the rate of change or the original function?

6. Build retention with active recall and spaced review.

Reading your notes is not enough. To actually remember the material, you need to quiz yourself and revisit the content over time.

Use these techniques:

• Flashcards with prompts like “State the Mean Value Theorem and explain when it applies.”
• Teaching concepts aloud to someone else.
• Rewriting the steps of solving a differential equation without looking.
• Scheduling reviews for topics every few days, then once a week, then every few weeks.

For example:

• Review limits briefly the day you study them.
• Review again the next day.
• Review once more after 3 to 5 days.
• Review again after one week and again two weeks later.

This system helps move the material into long-term memory.

7. Strengthen your conceptual understanding.

You need more than just mechanical skill. Understanding the why behind each method or rule is what helps you solve unfamiliar problems under pressure.

Try to:

• Connect visual concepts to equations. For example, understand why the area under a velocity curve gives displacement.
• Use concept maps to connect related ideas like continuity, differentiability, and integrability.
• Explain tricky concepts in your own words. For example, “A Taylor polynomial approximates a function near a point using its derivatives.”

The more you understand what a process represents, the easier it is to apply that knowledge on the exam.

8. Use reliable third-party resources.

Resources like Khan Academy and Fiveable can offer extra practice and explanation. Just make sure the material is up to date with the current exam format.

Use these books for:

• Extra free-response practice.
• Alternate explanations for hard topics.
• Quick reference sheets and strategy guides.

But always pair third-party resources with official College Board materials whenever possible.

AP Calculus BC Exam Test-Taking Tips

How you approach the AP Calculus BC Exam on test day can be just as important as how you study for it. Many students lose points not because they don’t understand calculus, but because they make small mistakes, run out of time, or don’t explain their reasoning fully.

Here are strategies to help you avoid those mistakes and handle the test like a pro:

1. Scan the whole exam before jumping in.

Before answering, take a few minutes to scan through the multiple-choice and free-response sections. This helps you:

• Spot the easy wins. Start with problems you’re confident about to build momentum.
• Map dependencies. Some free-response questions build on earlier parts. Scanning ahead helps you avoid getting stuck if you’re unsure about part (a).

2. Use your time strategically.

The AP Calculus BC Exam is 3 hours and 15 minutes long, split into:

• Multiple-choice. 45 questions in 90 minutes (2 parts: calculator and no calculator)
• Free-response. 6 questions in 90 minutes (2 calculator, 4 no calculator)

Time yourself like this:

• Multiple-choice. Aim for ~2 minutes per question. If you get stuck, skip and come back.
• Free-response. Spend about 15 minutes on the two longer calculator questions and around 10–12 minutes on each of the four shorter ones.

3. Watch out for what the question is really asking.

On test day, misreading a single word can cost you a point. Stay alert:

• Underline verbs. Words like “justify,” “explain,” “approximate,” or “evaluate” have specific meanings.
• Note conditions. Watch out for “continuous,” “differentiable,” “t > 0,” or “at x = 1.”
• Don’t ignore constraints. If they say “using the function f,” don’t bring in your own work from a different part.

4. Always show your work.

Even if your final answer is wrong, you can still earn points for correct steps.

• Label everything. Especially for integrals, series, and slope fields.
• Use clear notation. f ′(x) ≠ dy/dx if they refer to different functions.
• Include setup. Write out definite integrals before computing them, and include units when appropriate.

5. Know your calculator rules (and limits).

You can only use your graphing calculator for Part A of both sections.

• Use it to save time. Plot complicated functions, evaluate definite integrals, and solve numerically.
• Don’t over-rely. You still need to write out the setup and include exact values when required.
• Be exact when needed. If a question wants an exact value, don’t round. Leave answers in terms of π, e, or ln(2), unless specified otherwise.

6. Label and organize your free-response answers.

The graders are looking for clearly labeled and organized math.

• Break your work into parts. Write (a), (b), (c), etc., for each section.
• Justify when asked. “The function is decreasing because f ′(x) < 0 on (a, b)” earns credit. Just writing “decreasing” doesn’t.
• Be precise. Avoid vague statements like “it gets bigger.” Say “the function increases because its derivative is positive.”

7. Use your full time.

Done early? Great—but don’t just sit there.

• Check your answers. Review integrals, derivatives, limits, and series carefully.
• Look for missing units or steps. One missing justification or unlabeled answer can cost points.
• Re-read the question. Make sure you actually answered what it asked.

If you want to do well on the AP Calculus BC Exam, smart test-day habits matter just as much as knowing the material. Stick to these strategies, stay calm, and trust your preparation.

AP Calculus BC Exam Date

The 2026 AP Calculus BC Exam is scheduled for Monday, May 11, 2026, at 8:00 AM (local time). Be sure to arrive at your testing location early. Most schools require check-in by 7:30 AM or earlier. You cannot take the exam at a different time unless your school arranges a makeup test.

To see other AP exam dates and registration info, check out our comprehensive guide.

AP Calculus BC Exam score release date

For 2026, AP Calculus BC Exam scores are expected to come out in early to mid-July. For reference, 2025 scores were released on July 7.

While the exact date hasn’t been confirmed, students will likely be able to access their scores through their College Board accounts in early July. Be sure to log in regularly during that period so you don’t miss the release.

Is the AP Calculus BC Exam Hard?

AP Calculus BC covers everything in Calculus AB along with extra topics like sequences and series, polar and parametric functions, and more advanced integration techniques. It is fast-paced, comprehensive, and rewards students who understand the reasoning behind the math, not just the steps.

If you’re wondering how challenging the AP Calculus BC Exam really is, here’s the 2024 score breakdown:

With a mean score of 3.92, AP Calculus BC has one of the highest pass rates among all AP exams. In 2024, almost half of all students earned a 5. That does not mean the test is easy. It simply reflects how well-prepared and confident most test takers are in their math skills.

To perform well, you need more than just formulas. The exam tests your ability to justify your reasoning, interpret graphs and tables, and apply calculus concepts to real-world scenarios. You will also need to manage your time carefully and avoid small errors that can cost you points.

Focus on mastering the core topics, reviewing your past mistakes, and practicing with real College Board questions. Success comes from deep understanding, not memorization.

If you want expert guidance, our AP tutorial services offer personalized lessons, practice drills, and strategies that can help you walk into test day with confidence.

Frequently Asked Questions

1. How hard is the AP Calculus BC Exam?

In 2024, about 80.9 percent of students earned a score of 3 or higher on the AP Calculus BC Exam, and 47.7 percent scored a 5. That’s one of the highest pass rates across all AP exams, but it does not mean the test is easy. You’ll still need to understand topics like series, parametric equations, and polar functions, along with core AB topics like limits, integrals, and derivatives.

Compared to other math-heavy APs, AP Calculus BC covers more material in the same amount of time. It moves faster than AP Calculus AB. It’s also more advanced than AP Statistics, which focuses on data analysis rather than pure math. Because of its pace and rigor, AP Calculus BC is often taken by students who are strong in math or planning to pursue STEM majors.

2. How many hours should you study for the AP Calculus BC Exam?

That depends on how confident you are with calculus topics. Most students spend between 80 and 120 hours preparing. If you’re aiming for a score of 4 or 5, plan to study around 4 to 6 hours per week for 2 to 3 months. This should include regular practice with problem sets, full-length FRQs, and consistent review of past mistakes.

Be sure to focus on mastering series convergence tests, differential equations, and parametric/polar graphing. These BC-only topics often trip up students who are otherwise strong in the AB material.

3. Do you need to memorize everything for the AP Calculus BC Exam?

No. You’ll need to memorize formulas that are not provided on the formula sheet, such as Maclaurin series or convergence conditions. But the exam focuses more on applying concepts than on pure memorization. You need to know when and how to apply theorems like the Mean Value Theorem or L’Hôpital’s Rule.

Focus on recognizing function behavior, writing out justifications using calculus language, and setting up integrals and derivatives in context.

4. Is AP Calculus BC worth taking?

If you’re planning to go into math, engineering, physics, or computer science, AP Calculus BC is one of the most valuable AP courses. It can place you out of an entire year of college calculus at many universities. Even if you don’t plan to major in STEM, it can make your college applications stand out and fulfill quantitative course requirements.

5. When do AP Calculus BC scores come out?

For 2026, AP Calculus BC scores are expected to be released in early to mid-July. While the College Board hasn’t announced the exact date yet, students should expect to access their results during that time frame.

In 2025, AP Calculus BC scores were released on July 7. You can check your scores by logging in to your College Board account. If you’re sending your scores to colleges, make sure to request them before the June deadline so they arrive on time.

Takeaways

Keep these points in mind as you finalize your study plan and head into test day:

• The AP Calculus BC Exam covers both AB and BC topics, so make sure you understand parametric equations, polar functions, and series in addition to limits, derivatives, and integrals. A strong foundation in AB content is not optional.
• Scoring a 5 on the AP Calculus BC Exam is achievable with focused preparation. In 2024, 47.7% of test takers earned the top score, showing that consistent practice and conceptual mastery go a long way.
• Practicing free-response questions under timed conditions is critical. The AP Calculus BC Exam tests your ability to communicate reasoning and apply calculus techniques clearly and precisely.
• Test-day strategy matters. Learn how to pace yourself, avoid common errors, and manage the calculator and non-calculator sections effectively. These small moves can make a big difference in your final score.
• For personalized support tailored to the AP Calculus BC Exam, consider working with a college admissions consultant. AdmissionSight helps students build exam-ready skills, review real College Board questions, and develop strategies that lead to top scores.