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Grade 12 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
A 10 m ladder's foot slides away from a wall at 3 m/s; θ is the angle at the ground. Bo finds dθ/dt, in radians per second, when the foot is 8 m out.
A 5 m ladder's foot slides away from a wall at 1 m/s; θ is the angle at the ground. Esme finds dθ/dt, in radians per second, when the foot is 4 m out.
A 25 m ladder's foot slides away from a wall at 1 m/s; θ is the angle at the ground. Jun finds dθ/dt, in radians per second, when the foot is 24 m out.
A 1 m robot rolls away from a 5 m lamp post at 3 m/s. Luz finds how fast the robot's shadow gets longer. What is it, in m/s?
A 2 m robot rolls away from a 8 m lamp post at 1.2 m/s. Milo finds how fast the robot's shadow gets longer. What is it, in m/s?
A 1 m robot rolls away from a 4 m lamp post at 1.5 m/s. Noah finds how fast the robot's shadow gets longer. What is it, in m/s?
Water drains from a cylinder of fixed radius 3 m, with V = 9πh. Pia differentiates both sides with respect to time t. Which is right?
- dV/dt = 9π
- dV/dt = 6πh · dh/dt
- V = 9π · dh/dt
- dV/dt = 9π · dh/dt
A ball of clay grows, with V = (4/3)πr³. Ren differentiates both sides with respect to time t. Which is right?
- dV/dt = 4πr²
- dV/dt = 4πr² · dr/dt
- V = 4πr² · dr/dt
- dV/dt = (4/3)πr² · dr/dt
A 10 m ladder slides, with x² + y² = 100. Tala differentiates both sides with respect to time t. Which is right?
- 2x + 2y = 0
- 2x · dx/dt + 2y · dy/dt = 100
- 2x · dx/dt + 2y · dy/dt = 20 · dL/dt
- 2x · dx/dt + 2y · dy/dt = 0
A square tile grows, with A = s². Zee differentiates both sides with respect to time t. Which is right?
- dA/dt = 2s · ds/dt
- dA/dt = 2s
- dA/dt = s · ds/dt
- A = 2s · ds/dt