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Mathemania

Practice solving equations and applications in this comprehensive math review test covering identities, components, and addition of vectors.

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Mathemania

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  1. Mathemania Math 104 – Review for Test #3 Equations Applications Addition Components Identities 5 5 5 5 5 10 10 10 10 10 25 25 25 25 25 50 50 50 50 50 FINAL 100 100 100 100

  2. Identities

  3. 5 Point Question Is the following an equation or an identity? Equation Check Work Go Home

  4. 10 Point Question Verify the identity: Replace sec(x) with 1/cos(x), then multiply by (sin(x)/sin(x)). Check Work Go Home

  5. 25 Point Question Verify the identity Use cos(2x)=cos2(x)-sin2(x) and factor. Check Work Go Home

  6. 50 Point Question Verify the identity: Convert to sines and cosines, use the Pythagorean identity twice. Check Work Go Home Keep Score

  7. 100 Point Question Verify the identity: (cot(x) + cot(y)) sin(x) sin(y) = sin(x+y) Convert cot(x) to cos(x)/sin(x), cot(y) to cos(y)/sin(y), distribute, cancel and you are done. Check Work Go Home

  8. Components

  9. 5 Point Question A vector has magnitude of 6 and direction angle of 325°. Write the vector in component form. 4.91i – 3.44j Check Work Go Home Keep Score

  10. 10 Point Question Find the magnitude and direction angle for the vector 6i - 8j Magnitude = 10 Direction angle = 306.9° Check Work Go Home Keep Score

  11. 25 Point Question If u + v = 0, and u = -2i+5j, what is v? v=2i-5j Check Work Go Home Keep Score

  12. 50 Point Question Car A is traveling with velocity vector 21i + 35j. Car B is traveling wit velocity vector 40j. Which car is traveling faster? Car A Check Work Go Home Keep Score

  13. 100 Point Question Given ux= -5 and  = 120°, find uy uy = 8.66 Check Work Go Home Keep Score

  14. Equations

  15. 5 Point Question Solve: sin(x) = 1/2 X=300 +3600k or 1500 + 3600k Check Work Go Home

  16. 10 Point Question Solve the equation 5cos(x)-4=0 X=0.6435 + 2Pi k or X=-0.6435 + 2Pi k Check Work Go Home Keep Score

  17. 25 Point Question Solve the equation 3tan2x-1=0 X=300 + 1800k Or x=-300 + 1800k Check Work Go Home

  18. 50 Point Question Solve: cos(2x)-cos(x)=-1 X=900+1800k or 600 +3600k or - 600 +3600k Check Work Go Home

  19. 100 Point Question Solve: 2sin2(3x)-sin(3x)-1=0 Check Work Go Home Keep Score

  20. Applications

  21. 5 Point Question A scout travels 300 yards in the direction N40°W. Write this vector in component form. -192.8i+229.8j Check Work Go Home Keep Score

  22. 10 Point Question What third force is required to keep 2i + 3j and –4i +3j in check? 2i – 6j Check Work Go Home Keep Score

  23. 25 Point Question A boat travels S 50° W for 14 miles, then travels N 10° E for 5 miles. What course and distance must the boat travel to make it back to its starting point? 10.66 mi at N67.5°E Check Work Go Home Keep Score

  24. 50 Point Question A plane is flying at 200 miles per hour in the direction S 15° E. The wind is blowing due north at 30 miles per hour. What is the true speed and direction of the plane? 171.2 mph S17.6ºE Check Work Go Home Keep Score

  25. 100 Point Question A 200 lb weight is suspended by two cables in the drawing below. How big is the tension in each cable? 25° 25° 236.6 lbs Check Work Go Home Keep Score

  26. Addition

  27. 5 Point Question U = 2i + 3j, V = -3i + 2j - 4k Find U + V. U + V = -i + 5j – 4k Check Work Go Home Keep Score

  28. 10 Point Question Sketch the sum of the two vectors. Check Work Go Home Keep Score

  29. 25 Point Question u has a magnitude of 8 and a direction angle of 150º. v has a magnitude of 3 and a direction angle of 280°. Find u+ v. -6.407i+1.046j Check Work Go Home Keep Score

  30. 50 Point Question Find x and y if (y2i + 4xj) + (– 9i + 8j) = 0 x = -2 and y = -3 or 3 Check Work Go Home Keep Score

  31. FINAL QUESTION A 3000 lb car is parked on a 15° incline. What force is required to keep it from rolling down the incline? 776.457 lbs Check Work Go Home Keep Score

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