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Sunday, October 25, 2026

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART A NO.11-15

11. A particle moves in the xy plane so that its position at any time is given by the parametric equations x(t) = t^2 - t^3 and y(t) = 9 - 6t. What is the speed of the particle at time t = 2 ?

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12. Which of the following is the solution to the differential equation dy/dx = -3y with the initial condition y(0) = 7 ?

a. y = 7e^-3x

b. y = e^-3x + 6

c. y = -3/2x^2 + 7

d. y = √(49-6x)

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13. Consider the series. Which of the following statements is true ?

a. The series converge absolutely

b. The series converge conditionally

c. The series diverges

d. It cannot be determined whether the series converges or diverges from the information given

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14. If f is a function such that lim x→∞ = 0 , which of the following could be an expressive for f(x)?

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15. ∫(x+1)/(x(x+3)) dx = …

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Friday, October 23, 2026

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART A NO.6-10

6. Let y = f(x) be the solution to the differential equation dy/dx = x + y^2 with initial condition f(1) = 2. What is the approximatation for f(1,4) , if Euler’s method is used, starting at x=1 with two steps of equal size ?

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A portion of the slope field for the differential equation dy/dx = x - y is shown in the figure, if the linear function y = f(x) is the solution to the differential equation such that f(-1) = -2 then f(3) = …

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8. If f(x) = sin (e^3x) then f ‘ (x) = …

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9. If the series converges, where A ≠ 0 and B ≠ 0 , what is the sum of the series ?

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10. Of the following series, which can be used with the comparison test to show that diverges?

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Wednesday, October 21, 2026

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART A NO.1-5

1. If g(x) = x^2 √(x+1) , then g’ (3) = …

2. ₀∫⁴ 100 e^(x/4) dx = ...

An airplane’s height above sea level is modeled by the differentiable function y=h(t) , where t is the number of minutes take off and h(t) is measured in feet. The graph of h is shown in the figure for 0≤t ≤15. Of the following, which is the best estimate of the rate at which the plane is rising above sea level, in feet per minute, at time t=9?

4. Let f be a vector valued function with f(0) = (-2,3). If the instantaneousrate of change of f with respect to t is given by (3t^2 +4t+1, 2t^3 + t -2 ) what if f(1)?