Grade 12 · Math · Calculus

12th grade Initial value problems and motion worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Initial value problems and motion

Grade 12 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

dy/dx = 3x² + 2 and y(1) = 8. Ari finds the particular solution. What is y(2)?
dy/dx = 6x² − 1 and y(1) = 5. Bo finds the particular solution. What is y(2)?
dy/dx = 3x² + 4 and y(2) = 1. Esme finds the particular solution. What is y(3)?
dy/dx = 9x² − 2 and y(1) = 0. Jun finds the particular solution. What is y(2)?
dy/dx = 3eˣ and y(0) = 5. Kira finds the particular solution. What is y(ln 2)?
dy/dx = 4eˣ and y(0) = -1. Luz finds the particular solution. What is y(ln 2)?
dy/dx = 6eˣ and y(0) = 2. Milo finds the particular solution. What is y(ln 2)?
A robot has velocity v(t) = 6t − 5 m/s and starts at s(0) = 2 m. Ren finds its position at t = 3. What is s(3), in meters?
A sled has velocity v(t) = 2t + 1 m/s and starts at s(0) = -4 m. Tala finds its position at t = 5. What is s(5), in meters?
A toy train has velocity v(t) = 8t − 3 m/s and starts at s(0) = 6 m. Zee finds its position at t = 2. What is s(2), in meters?

Initial value problems and motion. Every version has 10 questions, and the answer key prints on the second page.

I can find the particular solution through a given point.
I can solve a second-order problem with two starting values.
I can find position or amount from a rate and a start, and the highest point of a toss.

Standard: none (beyond CCSS)

initial value: A known point, such as y(0) = 5, that fixes C.

particular solution: The one curve of the family through that point.

second order: Involving y″: integrate twice, two constants.

Added where the step subtracts: C = y₀ − F(x₀).

Raised the power but did not divide by the new power.

Left out + C, so the curve cannot pass through the starting point.

What is the most common mistake with initial value problems and motion?

Added where the step subtracts: C = y₀ − F(x₀).

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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