Mechanical Engineering Review Online

1. (∞ - 2800)/∞ = ?

a. Indeterminate

b. Infinity

c. Undefined

d. Plane

2. y to the power of 1/∞ is equal to:

a. 1

b. zero

c. Infinity

d. Indeterminate

3. Factor the expression as completely as possible: x² + 6x + 9

a. (x + 3)²

b. (x + 1)²

c. (x + 4)²

d.  (x - 3)²

4. Factor the expression as completely as possible: x⁴ - y⁴

a. (x² + y²)(x - y)

b. (x² + y²)(x + y)

c. (x² + y²)(x - y)²

d. (x² + y²)(x - y)(x + y)

5. Simplify: 3a(6b)^0.5 + (6a²b)^0.5 - (24a²b)^0.5 

a. 2(6b)^0.5

b. 3a(6b)^0.5

c. 2a(6b)^0.5

d. 4a(6b)^0.5

6. Factor the expression as completely as possible: 4x³ - 4x² - 24x

a. x(x+3)(x-2)

b. 4x(x+3)(x-2)

c. x²(x+3)(x-2)

d. 4x(x+3)(x+2)

7. Solve for x: x = [(y²-4y+16)(y²-16)]/y³+64

a. y-3

b. y-2

c. y-4

d. y-5

8. Simplify: 8^b+2 - 9(8)^b+1 + 64(8)^b-2

a. 8b

b. 8b+1

c. 8b-1

d. -8b

9. Solve for y: 2x - 3y = 10 and 3x + 2y = 6 

a. -18/13

b. 18/13

c. -13/18

d. 13/18

10. Simplify: 4(50y)^0.5 - 4(8y)^0.5

a. 10(2y)^0.5

b. 12(2y)^0.5

c. 8(2y)^0.5

d. 14(2y)^0.5

11. Solve the equation simultaneously: x+y=-6 ; x+z=1 ; 2z-3y+2x=5 

 a. (-5, -1, 6)

b. (-5, -1, 8)

c. (5, -1, -6)

d. (-5, 0, 6)

12. Solve the equation simultaneously: 5x+3y=6 and 6x-4y=-3 

a. 13/18, 51/38

b. -15/38, 51/38

c. -15/38, 51/38

d. 15/38, 51/38

13. Factor the expression completely: ax + ay - yb - bx.

a. (x-y)(a+b)

b. (x+y)(a+b)

c. (x+y)(a-b)

d. (x-y)(a-b)

14. Factor the expression completely: 27 + x³

a. (x+3)(x²-4x+10)

b. (x+3)(x²+3x+9)

c. (x+3)(x²-3x+9)

d.  (x+3)(x²+4x-10)

15. i²³ is equivalent to ____.

a. i

b. –i

c. 1

d. 0

16. Solve for x: 1/x + 1/(x+3) = 1

a. -3

b. 3

c. 1

d. -2

17. Solve for y: y⁴ - 9y² = 0

a. -3,0,-3

b. 3,-1,-3

c. 0,1,3

d. 0,-3,3

18. Solve for y: y²-5y+6=0

a. -2,3

b. 3,-1

c. 2,-3

d. 3,2

19. Solve for x: |6x + 18| = 4

a. 7/3, 11/3

b. -7/3, 11/3

c. -7/3, -11/3

d. 7/3, -11/3

20. Solve the inequality s – 3 < 1 or 0.5s ≥ 3

a. (s<4 or s≥6)

b. (s<4 or s≤6)

c. (s>4 or s≥6)

d. (s≥4 or s≤6)

21. Solve the inequality s – 8 < - 10

a. s<2

b. s>2

c. s>-2

d. s<-2

22. For f(x) =x²+5x, find f(3x)

a. 10x²-15x

b. 9x²+15x

c. 9x²-15x

d. 9x²-20x

23. Given the following vectors: A₁ = 3i - 3j + 7k; A₂ = 9i + 3j - 4k ; A₃ = 2i - 5j - 2k solve for (A₁+A₂)*A₃ 

a. 20

b. -18

c. 18

d. -25

24. Find the dot product of B₁ = 3i - 3j + 7k; B₂ = 9i + 3j - 4k  

a. 8

b. -9

c. -10

d. -8

25. What is the determinant of A:  

a. 70

b. 75

c. 80

d. 85

26. Find h(x) if h[f(x)] = (2x²-1)⁵ and f(x) = 2x²-1 

a. x⁵

b. 2x²

c. –x⁵

d. -2x⁵

27. Find the inverse of the function g(x) = 3x + 2

a. (y-1)/2

b. (y+3)/2

c. (y+2)/3

d. (y-2)3

28. Let f(x)=(x-3)^1/3 and h(x) = x³, find h[f(x)]

a. x-2

b. x-3

c. x+3

d. x-1

29. Let f(x) = (x-3)^1/3 and h(x) = x³ , find f[h(x)]

a. (x²-2)^1/3

b. (x²+2)^1/3

c. (x²-3)^1/3

d. (x²+3)^1/3

30. For f(x) = (x-2)^0.5, find f(3x)

a. (5x-2)^0.5

b. (2x-1)^0.5

c. (3x+2)^0.5

d. (3x-2)^0.5

31. For f(x) = 3x – 2, find f(2)

a. 4

b. 3

c. 5

d. 2

32. Find x: x = (7x - 10)^0.5

a. 5,2

b. 5,-3

c. 2,-5

d. 2,4

33. Solve the equation simultaneously: 2x²-3y²-14=0 and y=x-2 

a. (9,7), (3,1)

b. (10,8), (-3,2)

c. (9,-7),(3,2)

d. (9,7),(-3,-1)

34. Solve algebraically x and y: 3x²+8y²=35 and 12y²-4x²=42 

a. (1,2)

b. (±1,±2)

c. (-1,-2)

d. (-1,2)

35. Determine the value of m so that the equation 9x² + mx + 1 = 0 , will just one real solution.

a. ±6

b. ±7

c. ±5

d. ±8

36. Solve for y: y²-3y-10=0 

a. -2,-5

b. -2,5

c. 5,0

d. -2,8

37. Evaluate (3 + i)⁵

a. 12+315i

b. -12+300i

c. -12+316i

d. -10-310i

38. Express 4 + 8i in polar form.

a. 9.32 , 65.22^o

b. 10.32 , 60.22^o

c. 8.39 , 60.28^o

d. 8.94 , 63.43^o

39. What is the product of the complex numbers 5 + 8i and 7 – 3i?

a. 59+41i

b. 62+40i

c. 50+35i

d. 59+48i

40. What is the exponential form of the complex number 1 + 5i?

a. 5.1e^78.7i

b. 6.3e^75.2i

c. 4.3e^70.2i

d. 3.2e^68.7i

41. In the expansion of (x – 3y)⁷ find the y³-term, that is, the term involving y³.

a. 949x⁴y³

b. -940x⁴y³

c. -945x⁴y³

d. 900x⁴y³

42. Find the 3rd term of the expansion of (3x – y)⁵.

a. -270x³y²

b. 270x³y²

c. 270x²y²

d. -270x²y²

43. Find the sum of coefficients of (3x – 4y)¹²

a. 4

b. 3

c. 2

d. 1

44. Find the constant term in the expansion of [3x³ - (1/x²)]⁵

a. -90

b. -92

c. -91

d. -89

45. Resolve the following into partial fractions: (3x² - 8x + 9)/(x-2)³

a. [3/(x-2)] + [4/(x-2)²] + [5/(x-2)³]

b. [3/(x+1)] - [2/(x+1)²] + [4/(x+1)³]

c. [2/(x+1)] + [4/(x+1)²] + [3/(x+1)³]

d. [4/(x+1)] - [2/(x+1)²] - [3/(x+1)³]

Answer Key (Handwritten)