FE Review MATHEMATICS I Problem Statements Copyright 2008 J. B. O’Neal
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)