FE Review

MATHEMATICS I

Problem StatementsCopyright 2008 J. B. O’Neal

Straight Line

1. A straight line passes through the point (1,4) and has

a slope of 5. The equation for this line is:

(A) y = 5x +1 (B) y = x/5 +1

(C) y = x/5 +1 (D) y = 5x-1

2. These three lines enclose a triangle:

x-y = 0; x = 0; 2y+x = 6

The vertices of this triangle are at:

(A) (3,0), (0,0), (2,3) (B) (2,3), (0,0), (2,2)(C) (0,0), (0,3), (2,2) (D) (2,2), (3,0), (0,0)

Quadratic Equation

3. The solutions to the equation x2 + x = 30 are:

(A) -5,6 (B) 5,-6 (C) 5,6 (D) -5.-6

4. Parabolas, hyperbolas, circles and ellipses are all

examples of :

(A) polyhedrons (B) surfaces

(C) conic sections (D) quadratic sections

5. The equation x - y2 + 7y + 4 =0 describes:

(A) an ellipse (B) a parabola

(C) a hyperbola (D) a circle

6. Which of the following equations describes an

ellipse with a center at (4,-3):

(A) (x-4)2 + 2(y+3)2 = 4 (B) (x+4) + 2(y-3) = 1

(C) 4(x+4)2 + 3(y-3)2 = 1 (D) (x-4)2 + 2(y-3)2 = 1

Trigonometry

7. Sin 360 is equal to:

(A) -sin 360 (B) 0.5(sin 180+ cos 180)

(C) -cos 360 (D) 1/csc 360

The next two problems concern the power triangle

pictured below. In this figure P is the power in Watts, Q

is the reactive power in VARS, θ is the power factor

angle, and S is the apparent power in VA.

Q

S

P

8. If S = 1000VA, and θ = 600, what is

P in Watts?

(A) 500 (B) 550 (C) 600 (D) 650

9. In the power triangle above, cos θ is called the power

factor. If the power factor, cos θ = 0.4, and P =

20,000 Watts; Q, in VARS is most

nearly:

(A) 40000 (B) 43000 (C) 46000 (D) 48000

Matrices

10. If and

then the matrix product AB is equal to:

(A) [16] (B) [18] (C) [19] (D) [20]

135 A

3

4

2

B

Determinants

11. The determinant of

(A) 22 (B) 28 (C) 36 (D) 50

314

422

321

Vectors

12. Given the vectors:

A = 7i - 4j + 2k

B = -2i + 2j – 5k

A x B is equal to:

(A) 16i-41j+22k (B)16i+31j+6k

(C) 14i+31j+22k (D) 16i-31j+32k

13. If A = 7i - 4j + 2k, and B = -2i + 2j – 5k,

B ∙ A is equal to:

(A) -32 (B) -8 (C) +8 (D) +32

14. The vectors A = 3i - 4j + 2k and B = 2i - 3j + 4k

determine a plane. The unit vector perpendicular

to this plane is:

(A) -(22i+8j+k) (B) -10i-8j-k

(C) 22i+8j+k (D) -.078(10i+8j+k)

Differential Calculus

15. If y is a function of x, its derivative y′(x) =

is defined as:

(A) lim (B) lim

Δx→0 Δx→0

(C) lim (D) lim

Δx→0 Δx→0

dx

dyyDx )(

yx /

x

xyxxy )()(

x

xyxxy )()(( ) ( )y x x x

x

16. If is the partial derivative of y with respect to x,

then is equal to:

(A) z + 4z (B) 3x2 + x + 4 (C) zx + x3 (D) z + 3x2

x

y

zxzxx

43

17. d(cos2x)/dx =

(A) -sin2x (B) 2cos2x

(C) -2sin2x (D) -2cos2x

18. An object is moving is a straight line so that its

distance from its starting position is given by

D = 12 + t3 + t4. The rate of change of acceleration at

time t = 3 is:

(A) 24 (B) 78 (C) 86 (D)144

Integral Calculus

19.

(A) 4π (B) 2π (C) π (D) π/2

dxx2

0

2sin

20. The area under the curve e-x in the first quadrant is:

(A) e-1 (B) 1 (C) e (D) π

21. What is the area enclosed by the lines y = 2x+1,

y = 0, x = 0 and x = 1. (hint, first draw a sketch of

the area)

(A)1 (B) 1.5 (C) 2 (D) 2.5

22. The area in the first quadrant bounded by the lines

y = 2 and the curve x = y5/2 is most nearly:

(A) 3.0 (B) 3.2 (C) 3.4 (D) 3.6

Differential Equations

23. What is the general solution for y:

(A) C1e-3x + C2e

-x (B) C1e3x + C2e

x

(C) C1e-4x + C2e

-x (D) (C1x + C2)e4x

0342

2

ydx

dy

dx

yd

24. What is the general solution for y:

(A) C1e-2x + C2e

-x (B) C1 e-x + C2e-4x

(C) C1cos 2x + C2sin2x (D) (C1x + C2)e-2x

08822

2

ydx

dy

dx

yd

25. What is the general solution for y(x): y′ + 3y = 0

(A) Ce3x (B) Ce-3x (C) Cxe3x (D) Cxe-3

26. Given the following differential equation and

boundary condition

What is the complete solution for y?

(A)3e-6x (B) 6e-6x (C) 6e-3x (D) -3e-6x

.3)0(,06 yydx

dy

27. A rectangular pulse has duration 0.5 sec, a magnitude

of 4 and is centered on 0. Its Fourier Transform is:

(A) (B)

(C) (D) sin(.25 )

2.25

sin(.25 )4

.25

2 ( .5)

4 ( .5)