Initial value problems and motion
Grade 12 Math Worksheet
Circle the best answer, or write your answer on the line.
y″ = 6x, with y′(0) = 2 and y(0) = 5. Ari integrates twice. What is y(2)?
y″ = 6x, with y′(0) = -3 and y(0) = 1. Bo integrates twice. What is y(3)?
y″ = 6x, with y′(0) = 5 and y(0) = -1. Esme integrates twice. What is y(2)?
A tank has dV/dt = 20 − 2t L/min and V(0) = 50 L (example data). Kira finds how much it holds at t = 5. What is V(5), in liters?
A barrel has dV/dt = 30 − 4t L/min and V(0) = 100 L (example data). Luz finds how much it holds at t = 3. What is V(3), in liters?
A sand pile has dV/dt = 12 − 2t L/min and V(0) = 20 L (example data). Milo finds how much it holds at t = 3. What is V(3), in liters?
A pool has dV/dt = 40 − 6t L/min and V(0) = 25 L (example data). Noah finds how much it holds at t = 2. What is V(2), in liters?
Ren solves dy/dx = 3x² for the curve through (2, 5). Which is it?
- y = x³ + 5
- y = x³ − 3
- y = 3x³ − 19
Tala solves dy/dx = cos x for the curve through (π/2, 4). Which is it?
- y = sin x + 4
- y = −sin x + 5
- y = sin x + 3
Zee solves dy/dx = sin x for the curve through (π, 1). Which is it?
- y = −cos x + 1
- y = −cos x
- y = cos x + 2