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 vertex, zeros and range of 3(x−2)²−12. Explain the transformations from x².
For v(t)=2+3 sin(8πt−π/2) V, give midline, amplitude, range, frequency, period, time shift and v(0). Use seconds.
Analyse r(x)=(x²−4)/(x²+x−6). State the original domain, hole, vertical and horizontal asymptotes. Convert 120° to radians.
An ideal 9 V source feeds 1.5 kΩ. Find current, power and energy dissipated in 20 s. Show unit conversion.
A 1 kΩ resistor is in series with a parallel pair of 3 kΩ and 6 kΩ across 12 V. Find equivalent resistance, source current, pair voltage and both branch currents. Check their sum.
A 1 kΩ resistor with ±10% tolerance is across an ideal 10 V source. Find maximum current and power. Compare 0.1 W and 0.25 W ratings against this calculated case, stating what a real design must still check.