70 minutes, closed notes, 100 points. A basic scientific calculator is allowed. Show setup, reasoning and units or domain checks. Questions 1, 2, 4 and 5 carry 15 points each: 5 for setup, 5 for results and 5 for interpretation. Questions 3 and 6 carry 20 points each: 5 for setup, 10 for results and 5 for interpretation. Afterward, allow 30 minutes for correction.
Find the real domain of √(9−x²)/(x+1). Explain both restrictions and endpoint inclusion.
A linear temperature sensor gives 1 V at 20 °C and 4 V at 80 °C. Find its model, output at 50 °C, and calibrated range. Is using it at 100 °C justified by these data alone?
Sketch f(x)=x² on [−2,3] , state its range and find its average rate of change from −2 to 1. Then identify the missing point in (x²−1)/(x−1).
An object loses 10¹² electrons. Calculate its net charge in C and μC using e=1.602176634 × 10⁻¹⁹ C. Explain the sign.
A reference section carries 2 C in the first 2 s and 6 C in the next 3 s. Find both interval-average currents and the overall average. Explain why the unweighted mean is wrong.
Nodes A and B are at 7 V and −1 V relative to one reference. Find VAB and the energy transferred when 0.25 C of positive charge passes from A to B through a load. Explain why an open lamp circuit may still have source voltage but no steady current.