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AP Calculus BC practice questions: 928
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Use one Euler step of size 0.1 for dy/dx = x + 2y, starting at x = 1, y = 1. What is the approximate y-value after the step?
Euler's method gives y_new = y_old + h f(x_old,y_old). Here the slope is 1 + 2(1) = 3, so y_new = 1 + 0.1(3) = 1.3.
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SYLLABUS
Areas covered
Questions follow the published syllabus of AP Calculus BC.
- Unit 1: Limits and Continuity41 questions
- Unit 2: Differentiation: Definition and Fundamental Properties26 questions
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions26 questions
- Unit 4: Contextual Applications of Differentiation60 questions
- Unit 5: Analytical Applications of Differentiation21 questions
- Unit 6: Integration and Accumulation of Change16 questions
- Unit 7: Differential Equations16 questions
- Unit 8: Applications of Integration46 questions
- Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions26 questions
- Unit 10: Infinite Sequences and Series61 questions
- Unit 26 questions
- Unit 36 questions
- Unit 44 questions
- Unit 548 questions
- Unit 6114 questions
- Unit 728 questions
- Unit 830 questions
- Unit 939 questions
- Unit 10138 questions
- Unit 16 questions
- Differentiation: polynomial functions10 questions
- Differentiation: composite functions10 questions
- Limits: factoring and continuity10 questions
- Integration: antiderivatives and accumulation10 questions
- Integration: derivative of an accumulation function10 questions
- Differential equations: numerical approximation10 questions
- Series: convergence tests10 questions
- Parametric functions: dy/dx10 questions
- Polar functions: tangent slope10 questions
- Series: Taylor and Maclaurin polynomials10 questions
- Unit 9 (BC only)20 questions
- Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions — BC only30 questions
- Unit 3: Differentiation—Composite, Implicit, and Inverse Functions20 questions
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GUIDE
About the AP Calculus BC exam and how to study with examplat
About AP Calculus BC
AP Calculus BC is a College Board Advanced Placement course covering a full year of university single-variable calculus. It includes all the topics of AP Calculus AB (limits, differentiation, integration and their applications) and adds parametric, polar and vector-valued functions, additional integration techniques, improper integrals and infinite series including Taylor series. The course is organised into ten units.
The exam is held once a year in May and is scored from 1 to 5, with a separate AB subscore. It has multiple-choice and free-response sections, and some parts require a graphing calculator. Many universities grant credit or placement for qualifying scores, but each university sets its own policy. Check the College Board website for the current format and dates.
How to study the question types
Most free-response points are for showing a correct method: naming the theorem, setting up the integral or derivative, and justifying the result. Practise writing each step so that a reader could follow it, including the conditions of a theorem such as continuity or a nonzero derivative.
For short numerical answers, check units, signs and whether the answer is reasonable. For series, learn the standard tests and what each one can and cannot prove, and be ready to state why a test applies.
How to use examplat for AP Calculus BC
examplat holds more than 900 original practice questions: multiple-choice questions and short written-answer questions, organised by course unit. Each has an explanation, and the written ones have a model answer and a marking guide.
For written questions you type your answer (for example a value, an expression or a short justification) and examplat gives an automatic score as a guide. It checks the numbers and key terms against the model answer; it does not follow your algebra, so compare your working with the model answer yourself.
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For the written questions, yes. Type the result and key steps, and examplat gives a guide score by comparing numbers and key terms with the model answer. It does not check each step of the algebra.
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examplat is an unofficial question bank. All content is written independently by Sakakikaen Co., Ltd., is not affiliated with or endorsed by the body that runs AP Calculus BC, and does not guarantee a pass.