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.
Invert f(x)=2+x² on x≥0. State inverse domain and infer the input for output 11. Explain why the negative branch is excluded.
Solve ln(x−1)+ln(x+1)=ln 15 with admissibility checks. Also find the domain of ln(16−x²).
For v(t)=10 e−t/5 V with t in seconds, find the time to reach 2 V, its time constant and its half-value time. Explain why these times differ.
Convert 220 μA to A and calculate power at 5 V. Convert 0.0047 MΩ to Ω. Explain the role of case in SI prefixes.
A 12 V equal divider uses two 10 kΩ resistors. Add a 100 kΩ voltmeter across the lower resistor. Calculate the reading and signed loading error relative to the unloaded voltage.
A 20 Ω ammeter is in series with a 1 kΩ resistor and ideal 6 V source. Find current and its percentage change from the unloaded value. Separately, find the error bound on a 3.20 V display specified as ±(1% of reading + 2 counts), with 0.01 V per count.