MSTE

Page 1 Problem 1: Three-Cornered Duel Participants: Cardo (0.3 hit probability), Alakdan (never misses), Hipolito (0.5 hit probability). Firing Order: Cardo, Alakdan, Hipolito. Options for Cardo's first move: A. Target Alakdan B. Deliberately miss C. Target Hipolito D. Fire at himself Problem 2: Cylindrical Steam Boiler Construction Cost: P3200 per square meter. Total Budget: P1.5M. Maximum capacity options: A. 963 m³ B. 548 m³ C. 659 m³ D. 779 m³ Problem 3: Slope of Polar Curve r=4sin(2θ) Determine the slope at θ = π/6. Options: A. 2.887 B. 2.589 C. 1.039 D. 1.254 Problem 4: Expectation Calculation Given frequency distribution: x: [2, 3, 1, 1] f(x): [1/3, 1/6, ?] Options for expectation: A. 3 B. 4 C. 6 D. 8 Problem 5: Mean Score Calculation Scores: 92, 78, 86, 92, 95, 91. Find 7th score that raises mean by 1 point. Options: A. 94 B. 96 C. 97 D. 98 Problem 6: Standard Deviation Calculation Score data with frequency: 1: 14, 2: 15, 3: 14, 4: 17, 5: 10. Options for standard deviation: A. 1.768 B. 1.842 C. 1.162 D. 1.349 Problem 7: Design of Vertical Parabolic Curve Grades: 3% and -3.5%. Design parameters: velocity 60 kph, perception-reaction time 1.5 sec, friction coefficient 0.25. Options for curve length: A. 83.96 m B. 100.5 m C. 25.32 m D. 152.32 m Problem 8: Coordinate Translation Translate point (1, 2) to origin (5, 5). Options: A. (4, -3) B. (4, 3) C. (6, 7) D. (-6, -7) Problem 9: Tangent Line Equation Find tangent to x² = 6y + 10 at point (7, 5). Options: A. 4x + 3y = 43 B. 4x - 3y = 13 C. 10x + 3y = 85 D. 10x - 3y = 45 Page 2 Problem 10: Solar Time Difference Longitudes: Washington 77°04'00" W, San Francisco 122°25'45" W. Options: A. 3:01:27 B. 13:45 C. 4:32:12 D. 6:56:34 Problem 11: Impact Factor in Design Design speed: 80 kph, radius: 350 m. Options for impact factor: A. 0.00177 B. 0.155 C. 0.144 D. 0.256 Problem 12: Cone Volume Ratio Cone height: h, water depth: 2/3h. Options: A. 26/27 B. 27/26 C. 25/26 D. 26/25 Problem 13: Inscribed Circle Area Triangle sides: 13, 15, altitude: 12 to third side. Options for area: A. 50.27 B. 43.98 C. 51.85 D. 48.00 Problem 14: Job Completion by Workers A, B, C can complete job in 7, 9, 12 days. After 2 days, C finishes job. Options for days worked by C: A. 5.9 days B. 6.3 days C. 6.2 days D. 5.5 days Problem 15: Clock Angle Calculation Angle of 120° after 12 noon. Options for time: A. 21.818 min B. 32.342 min C. 22.34 min D. 41.23 min Problem 16: Investment in Different Transactions Investments: 9%, 6%, 4%. Total income: P34,000. Options for real estate investment: A. 150000 B. 180000 C. 200000 D. 125000 Problem 17: Manpower Reduction Scenario 60 men working for 72 days, decrease of 5 men. Options for completion time: A. 108 days B. 100 days C. 94 days D. 122 days Problem 18: Average Speed and Distance Calculation Daily speed: 2 kph and 3 kph with time scenarios. Options for distance: A. 2.4 km B. 2.1 km C. 1.8 km D. 2.4 km Problem 19: Paper Thickness Calculation Paper thickness: 0.05 in, folds: 12 times. Options: A. 10.24 in B. 17.10 in C. 12.34 in D. 11.25 in Problem 20: Contractor Worker Wages 28 workers, P150/day, initial completion in 60 days. Options for completion time: A. 45 days B. 55 days C. 50 days D. 60 days Problem 21: Elevator Calculation Time varies with weight and distance, power inversely. Options for required motor size: A. 42 HP B. 46 HP C. 44 HP D. 48 HP Problem 22: TV Set Selling Price Calculation Selling price is double cost, 25% profit on cost. Options for discount: A. 33.3% B. 22.33% C. 37.5% D. 42.5% Problem 23: Relative Velocity Calculation Mass A (20 kph, N 40° E) and Mass B (30 kph, S 30° W). Options for relative velocity of B w.r.t A: A. 49.12 kph B. 49.82 kph C. 48.12 kph D. 34.23 kph Problem 24: Earthquake Magnitude Calculation Ritcher scale measurement for Kobe (5.7) and Baguio (7.8). Strength comparison: A. 148 times B. 137 times C. 126 times D. 37 times Page 3 Problem 25: Tower Height Calculation Elevation angles from points A (25°) and B (56°), distance AB = 300 m. Options for tower height: A. 146.7 m B. 134.4 m C. 148.8 m D. 111.2 m Problem 26: Compressive Strength Specification Class "b" mix with strength results from tests listed. Mean strength options: A. 3311.25 psi B. 3289.6 psi C. 3414.34 psi D. 3411.22 psi Problem 27: Free Throw Probability Average 0.65 for free throws, find the probability of missing one. Options: A. 0.441 B. 0.444 C. 0.422 D. 0.451 Problem 28: Committee Formation PSME unit: 10 ME's, 8 PME's, 6 CPM's. Form committee of 3. Options: A. 260 B. 380 C. 480 D. 360 Problem 29: Hockey Games Only Calculation Viewership survey results, calculate hockey only. Options: A. 75 B. 95 Problem 30: Value of x Calculation Find x from the equation.