Fundamentals of Engineering Exam Sample Math Questions

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- B, C, D, and F each equal to 0; A and E both positive.

- B, C, D, and F each equal to 0; A negative and E positive.

- A, B, E, and F each equal to 0; C and D positive.

- A, B, E, and F each equal to 0; D negative and C positive.

- A, D, E, and F each equal to 0; B negative and C positive.

- The diagram shown below shows two intersecting curves: y = x, and[pic 93].

[pic 94]

Which of the following expressions gives the distance from the y-axis to the centroid of the area bounded by the two curves shown in the diagram?

- [pic 95]

- [pic 96]

- [pic 97]

- [pic 98]

- Find the radius for the circle with the equation [pic 99].

- 1 b. 2 c. 3 d. 4

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- Find the value of the limit: [pic 100]

- 0 b. ½ c. 1 d. 2

- Find the area bounded by [pic 101]and [pic 102].

- 1/6 b. 1/3 c. ½ d. 2

- Find the solution as [pic 103], for [pic 104]

- y = 0 b. [pic 105] c. [pic 106] d. y = 5

- It takes a pigeon X, 2 hours to fly straight home averaging 20 km/h. It takes pigeon Y, 2 hours and 20 minutes to fly straight home averaging 30 km/h. If both pigeons start from the same spot but fly at an angle [pic 107] to each other, about how far apart do they live?

- 96 km b. 87 km c. 80 km d. 73 km

- A matrix B has eigenvalues (characteristic values) λ found from which of the following equations?

- [pic 108]

- [pic 109]

- [pic 110]

- [pic 111]

- The divergence of the vector function [pic 112]at the point (0, 1, 1) is

- -4 b. -1 c. 0 d. 4

- A right circular cone cut parallel with the axis of symmetry could reveal a

- circle b. hyperbola c. ellipse d. parabola

- If [pic 113]then[pic 114]

- [pic 115] c. [pic 116]

- [pic 117] d. [pic 118]

- Write the compex product [pic 119] in polar form.

- [pic 120] b. [pic 121] c. [pic 122] d. [pic 123]

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Questions 36-38: Given the set of equations represented by [pic 124], where

[pic 125]

- Determine the adjoint matrix [pic 126]

- [pic 127] b. [pic 128] c. [pic 129] d. [pic 130]

- Determine the inverse matrix [pic 131]

- [pic 132] b. [pic 133] c. [pic 134] d. [pic 135]

- Determine the eigenvalues (characteristic values) associated with the matrix [pic 136].

- 2, 6 b. 5, 0 c. 0, 4 d. 4, -1

- If [pic 137], then [pic 138]

- 4

- [pic 139]

- .25

- 2

- Find the distance between the points P ( 1, -3, 5 ) and Q ( -3, 4, -2 ).

- [pic 140] b. [pic 141] c. [pic 142] d. [pic 143]

- The rectangular coordinates of a point are (-3, -5.2 ), find the polar coordinates for the same point.

- [pic 144] b. [pic 145] c. [pic 146] d. [pic 147]

- Find the x-value of the absolute minimum for the equation [pic 148]in the interval [pic 149].

- -3 b. [pic 150] c. 0 d. 3

Problems 43 & 44 use the following information: The population of a bacteria colony doubles every 3 days and has a present population of 50000.

- What is the equation describing the population growth?

- [pic 151]

- [pic 152]

- [pic 153]

- [pic 154]

- How long will it take for the population to triple?

- 1.6 days b. 4.5 days c. 4.8 days d. 7.5 days

Problems 45-46 are based on the following equation: [pic 155]

- What conic section is described by this equation?

- Circle

- Ellipse

- Parabola

- Hyperbola

- What are the coordinates of the focus of the conic section?

- (1,-1) b. (0, -1/4) c. (1/4, 0) d. ( 0, 1/4)

- The area enclosed by the curve [pic 156] is

- π b. π/2 c. 2π d. 4π

- The derivative of [pic 157] is

- [pic 158]

- [pic 159]

- [pic 160]

- [pic 161]

- [pic 162]

- 52/9 b. 0 c. 52/3 d. 26/3

- If [pic