AP Calculus AB 2017 Exam (videos, questions, solutions) (2024)

Questions And Worked Solutions For AP Calculus AB 2017

AP Calculus AB 2017 Free Response Questions - Complete Paper (pdf)

AP Calculus AB 2017 Free Response Question 1
AP Calculus AB 2017 Exam (videos, questions, solutions) (1)

  1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by the function A, where A(h) is measured in square feet. The function A is continuous and decreases as h increases. Selected values for A(h) are given in the table above.
    (a) Use a left Riemann sum with the three subintervals indicated by the data in the table to approximate the volume of the tank. Indicate units of measure.
    (b) Does the approximation in part (a) overestimate or underestimate the volume of the tank? Explain your reasoning.
    (c) The area, in square feet, of the horizontal cross section at height h feet is modeled by the function f given byAP Calculus AB 2017 Exam (videos, questions, solutions) (2) Based on this model, find the volume of the tank. Indicate units of measure.
    (d) Water is pumped into the tank. When the height of the water is 5 feet, the height is increasing at the rate of 0.26 foot per minute. Using the model from part (c), find the rate at which the volume of water is changing with respect to time when the height of the water is 5 feet. Indicate units of measure.
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AP Calculus AB 2017 Free Response Question 2
AP Calculus AB 2017 Exam (videos, questions, solutions) (3)

(a) How many pounds of bananas are removed from the display table during the first 2 hours the store is open?
(b) Find f'(7) . Using correct units, explain the meaning of f'(7) in the context of the problem.
(c) Is the number of pounds of bananas on the display table increasing or decreasing at time t = 5? Give a reason for your answer.
(d) How many pounds of bananas are on the display table at time t = 8?

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AP Calculus AB 2017 Free Response Question 3
AP Calculus AB 2017 Exam (videos, questions, solutions) (4)

  1. The function f is differentiable on the closed interval [−6, 5] and satisfies f(−2) = 7. The graph of f', the derivative of f, consists of a semicircle and three line segments, as shown in the figure above.
    (a) Find the values of f(−6) and f(5).
    (b) On what intervals is f increasing? Justify your answer.
    (c) Find the absolute minimum value of f on the closed interval [−6, 5]. Justify your answer.
    (d) For each of f"(-5) and f “(3), find the value or explain why it does not exist.
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AP Calculus AB 2017 Free Response Question 4
AP Calculus AB 2017 Exam (videos, questions, solutions) (5)

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AP Calculus AB 2017 Free Response Question 5
5. Two particles move along the x-axis. For ≤ t ≤ 80, the position of particle P at time t is given by xP(t) = ln(t2 - 2t + 10 ), while the velocity of particle Q at time t is given by vQ = t2 - 8t + 15.
Particle Q is at position x = 5 at time t = 0.
(a) For 0 ≥ t ≥ 8, when is particle P moving to the left?
(b) For 0 ≥ t ≥ 8, find all times t during which the two particles travel in the same direction.
(c) Find the acceleration of particle Q at time t = 2. Is the speed of particle Q increasing, decreasing, or neither at time t = 2 ? Explain your reasoning.
(d) Find the position of particle Q the first time it changes direction.

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AP Calculus AB 2017 Free Response Question 6
AP Calculus AB 2017 Exam (videos, questions, solutions) (6)

  1. Let f be the function defined by f(x) = cos(2x) + esin x.
    Let g be a differentiable function. The table above gives values of g and its derivative g¢ at selected values of x.
    Let h be the function whose graph, consisting of five line segments, is shown in the figure above.
    (a) Find the slope of the line tangent to the graph of f at x = π.
    (b) Let k be the function defined by k(x) = h(f(x)). Find k'(π).
    (c) Let m be the function defined by m(x) = g(-2x) • h(x). Find m'(2).
    (d) Is there a number c in the closed interval [−5, -3] such that g'(c) = −4 ? Justify your answer.
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AP Calculus AB 2017 Exam (videos, questions, solutions) (2024)

FAQs

What is the hardest chapter in Calc AB? ›

According to the College Board's data, the Composite, Implicit, and Inverse Functions unit is considered the most challenging for students in the multiple-choice section of the AP Calculus AB exam. Approximately 11% of students received a score of zero on questions related to this unit in the AP Calculus AB exam 2022.

Is it easy to get a 5 in AP Calculus AB? ›

This common question has no easy answer. To achieve a 5 on the AP® Calculus AB exam, you will need a combination of tenacity, commitment to learning the material, and a dedicated study plan.

How many questions do you need to get right to pass the AP Calc AB exam? ›

Exam Weighting (Multiple-Choice Section)

Albert's AP® Calculus AB score calculator shows that you would need to answer at least 23 of the multiple-choice questions correctly and receive at least 27 points in the free-response portion of the exam in order to achieve a score of 3 or better.

Is AP Calc AB harder than precalc? ›

It typically requires a fair amount of time and effort, especially when it comes to understanding complex mathematical concepts and solving problems accurately. However, it's generally considered to be less challenging than, say, AP Calculus AB or BC, or AP Physics.

Is Calc BC or AB easier? ›

AP Calculus BC is more difficult than AP Calculus AB. Not only does it include additional topics, which requires an accelerated pace, but the additional units, especially Unit 10, tend to be more difficult than the Calc AB units.

Why is calculus ab so hard? ›

AP Calc AB builds on various math concepts and requires you to bring those concepts together to solve problems. On top of having a strong understanding of math, students should possess high reasoning and justification skills. You'll also need to know how to use a graphing calculator.

What is a 60% on an AP test? ›

Yes, a 60 is considered a passing grade in AP classes. In AP, the average passing rate is 60-70%.

What percent correct is a 5 on AP Calc AB? ›

Since you only need to get about 60% of available points to score a 5 on either AP Calculus exam, and since you have ample time on all sections, you can strategize the exam differently than you would almost any classroom test.

How hard is it to get a 4 on AP Calc AB? ›

Additionally, 16.18% of students scored a 4, and 19.4% of students scored a 3. Therefore, 57.97% of students scored a 3 or higher. The average score on the AP Calc AB exam was 2.99. A passing rate of 57.97% is strong, but don't wait until the day of the exam to see if you'll achieve a 3 or higher.

Which AP Calc is easiest? ›

Calculus BC

AP Calculus BC has earned a reputation as an easy AP course because many of its students master the material. Most AP Calculus BC students perform at an advanced level — at least one year ahead of their high school class in math — helping them achieve a high pass rate.

Is trig or pre-calc harder? ›

If you are more comfortable with solving algebraic equations and working with functions, you might find pre-calculus to be easier. However, if you enjoy working with spatial concepts and geometric relationships, trigonometry could be your better option.

Is Calc harder than Algebra 2? ›

We often consider calculus to be more difficult than algebra. Algebra courses explore the many operations, properties, and rules that can be used to manipulate equations. Calculus courses apply algebraic operations to functions in a more complex way.

Which is the most hard chapter in maths? ›

On the other hand, topics such as Quadratic Equations, Triangles, and Surface Areas and Volumes are often perceived as tougher. Quadratic Equations require mastery of multiple methods for solving equations, including factorization and the quadratic formula.

What is the hardest chapter in maths grade 12? ›

Chapter 8 Applications of Integrals, Chapter 11 Three dimensional Geometry & Chapter 13 Probability are the most challenging chapters in class 12 maths. These are time consuming and complex to comprehend too. However, with the help of NCERT Solutions For Class 12 Maths it can be easily understood and solved.

Which Calc class is harder? ›

In terms of difficulty, AP Calculus BC is generally considered harder than AP Calculus AB, due to the extra material and the faster pace.

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