# Mathematics And Advanced Engineering Mathematics

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Mathematics andAdvanced Engineering MathematicsDr. Elisabeth Brownc 2019

MathematicsFundamentals of Engineering (FE)Other Disciplines Computer-Based Test (CBT)Exam Specifications2 of 37

Mathematics1. What is the value of x in the equation given by log3 2 x 4(a) 10E. Brown(b)1(c)3(d)5log3 x3 of 372 1?

Mathematics2. Consider the sets X and Y given by X { 5 , 7 , 9 } and Y { ,relation R from X to Y given by R { ( 5 ,What is the matrix of R ?(a)h0 1 0 1 1 1DISCRETE MATHE. Browni(b)230 16740 151 1(c)), (7,"0 0 11 1 14 of 37} and the), (9, ), (9,#(d)230 16741 050 1)}.

Mathematics5 of 373. What is the x-intercept of the straight line that passes through the point ( 0 , 3 )and is perpendicular to the line given by y 1.5 x 4 ?(a)E. Brown0, 3(b)2, 0(c)2, 0(d) 9,02

Mathematics4. What is the smallest x-intercept of the parabola given by y 2 x2 x(a)E. Brown1 p433,0!(b)( 1, 0)(c)1p433,0!(d)6 of 374?p1 33,04!

Mathematics5. What is the volume of the largest sphere with center5, 4, 9that is contained inthe first octant?256(a) 3MENSURATION OF AREAS AND VOLUMESE. Brown(b)4(c)64 (d)7 of 3764 3

Mathematics6. The exact value of cos (a) 0.9995TRIGONOMETRYE. Brown7 12 (b)is most nearlyp3 1p2 2(c)p13p2 2(d)p348 of 37

Mathematics7. Consider the complex numbers z1 2 2 j and z2 2 \the product z1 z2 ?p(a) 2 3E. Brown2 2 2p3 jp5 (b) 4 2 \12(c) 2p9 of 37 . What is the value of63 2 2 2p3 jp (d) 4 2 \10

Mathematics 10 of 37 7 (continued). Consider the complex numbers z1 2 2 j and z2 2 \ .6What is the value of the product z1 z2 ?p(a) 2 32 2 2p3 j5 (b) 4 2 \12ALGEBRA OF COMPLEX NUMBERSE. Brownp(c) 2p3 2 2 2p3 jp(d) 4 2 \ 10

Mathematics 11 of 378. What are the real numbers a and b such that the complex number z can be written as z a b j ?1(a) a , b 32(b)a ALGEBRA OF COMPLEX NUMBERSE. Brown1, b 04(c)a 17, b 1010(d)a 1 2j3 j1, b 10710

Mathematics 12 of 379. The value of the angle , shown below, is most nearly(a) 29.7E. Brown(b)55.9(c)50.3(d)81.6

Mathematics 13 of 379 (continued). The value of the angle , shown below, is most nearly(a) 29.7E. Brown(b)55.9(c)50.3(d)81.6

Mathematics 14 of 3710. What is the radius of the circle given by the equation x2 y 2 6 x 10 y 14 0 ?pp(a) 2 5 (b) 20 (c) 4 3 (d) 4CONIC SECTIONSE. Brown

Mathematics 15 of 3711. The roots of the cubic equation given by x3(a) x (c)E. Brown0.5, 1.2, 2.6no solutions exist(b)(d)4 x2 6 0 are most nearlyx x 3.514, 0, 3.5141.086, 1.572, 3.514

Mathematics 16 of 3712. What is the maximum value of the function f (x) x3(a)8(b)0DIFFERENTIAL CALCULUSDERIVATIVES AND INDEFINITE INTEGRALSE. Brown(c)6(d)4 x2 6 ?no maximum exists

Mathematics 17 of 37@f (x, y)13. What isof f (x, y) 4 ln(y)@y(a)(c)4y4p sec(x) sin yy1 1pp sec(x) sin y2 yDERIVATIVES AND INDEFINITE INTEGRALSE. Brownsec(x) cos(b)(d)py 15 x ?4 1 1p p sec(x) sin yy 2 y4 1 1p p sec(x) sin yy 2 y 15x ln(15)1

Mathematics 18 of 3713 (continued). f (x, y) 4 ln(y)DERIVATIVES AND INDEFINITE INTEGRALSE. Brownsec(x) cospy 15 x

Mathematics 19 of 37x214. The value of the limit limisx!0 sin(x)(a) does not existE. Brown(b)0(c)1(d)2

Mathematics 20 of 3715. The indefinite integral of f (x) x sin 2 x is(a)1111x cos 2 x sin 2 x(b)x cos 2 x sin 2 x C24241 211(c)x cos 2 x C (d)x cos 2 x sin 2 x C422DERIVATIVES AND INDEFINITE INTEGRALSE. Brown

Mathematics 21 of 3715 (continued). The indefinite integral of f (x) x sin 2 x is(a)1111x cos 2 x sin 2 x(b)x cos 2 x sin 2 x C24241 211(c)x cos 2 x C (d)x cos 2 x sin 2 x C422DERIVATIVES AND INDEFINITE INTEGRALSE. Brown

Mathematics 22 of 3716. What is the area of the region of the first quadrant of the xy-plane that is boundedby the curve y 2 x2 , the line y 9 , and the y-axis?9p(a)2(b)DERIVATIVES AND INDEFINITE INTEGRALSE. Brown486(c)27p2(d)18p2

Mathematics 23 of 3716 (continued). What is the area of the region of the first quadrant of the xy-planethat is bounded by the curve y 2 x2 , the line y 9 , and the y-axis?9(a) p2(b)DERIVATIVES AND INDEFINITE INTEGRALSE. Brown486(c)27p2(d)18p2

Mathematics 24 of 3717. What is the first moment of area with respect to the y-axis for the area in the firstquadrant bounded by the curve y x2 , the line y 9 , and the y-axis?486(a)5E. Brown(b)812(c)814(d)27

Mathematics 25 of 3717 (continued). What is the first moment of area with respect to the y-axis for the area in the firstquadrant bounded by the curve y x2 , the line y 9 , and the y-axis?(a)E. Brown4865(b)812(c)814(d)27

Mathematics 26 of 3718.If y(x) 1Xan xn for coefficients an, n 0, 1, 2, . . ., what series given below is equal to y 0(x) ?n 0(a)1Xn 0E. Brownan n 1xn 1(b)1Xn 0n an xn(c)1Xn 1n an xn 1(d)1Xn 0n an xn1

Mathematics 27 of 3719. What is the Maclaurin series expansion of e 3x ?(a)1Xn 0n en1(b)1X3 nxn!n 0DERIVATIVES AND INDEFINITE INTEGRALSE. Brown(c)1Xn 00(d)1X3n nxn!n 0

Mathematics 28 of 3720. The indefinite integral of(a) 5 ln x 2 (c)INTEGRAL CALCULUSE. Brown5 ln x 2 5is2(x 2) (x 1)5 ln x 1 5 Cx 1(b)5 ln x 1 5 ln (x 1)2 C5x 2(d)55 Cx 1 (x 1)25 ln x 2 5 Cx 1

Mathematics 29 of 3720 (continued). The indefinite integral of(a) 5 ln x 2 (c)5 ln x 2 5 ln x 1 (b)5 ln x 1 5 ln (x 1)2 CDERIVATIVES AND INDEFINITE INTEGRALSE. Brown5 Cx 15is2(x 2) (x 1)5x 2(d)55 Cx 1 (x 1)25 ln x 2 5 Cx 1

Mathematics 30 of 3721. What is the Fourier transform of F (t) ?(a) 2 f (t)E. Brown(b)2 f ( t)(c)2 f ( !)(d)2 f (!)

Mathematics 31 of 3721 (continued). What is the Fourier transform of F (t) ?(a) 2 f (t)E. Brown(b)2 f ( t)(c)2 f ( !)(d)2 f (!)

Mathematics 32 of 3722. What is the Fourier series of f (t) 3 cos 4 t on the interval(a) 3 cos 4 t(b)1 Xn2 cos(4 n t) (nh i0,?21) sin(4 n t)n 1(c)1Xn 1E. Brown3 cos(4 n t)(d)1 Xn 13 n cos(2 n t) nsin(2 n t)2

Mathematics 33 of 3723. Consider the curve given by the function f (x) x2 2 x . The area under thecurve for 0 x 1.5 , approximated by using the forward rectangular rule withx 12 , is most nearly9(a)8E. Brown(b)178(c)138(d)78

Mathematics 34 of 3724. Consider the exact area, Ac, under the curve f (x) x2 2 x for 0 x 1.5 .Ac falls most nearly between which of the following precision limits?(a)E. Brown71 88(b)71 84(c)131 88(d)13 18

Mathematics 35 of 3725. For matrices A (a)E. Brownh1"1323i#and B (b)"12051does not exist#, what is AT B ?(c)h143i(d)"143#

Mathematics 36 of 3726. What is the curl of the vector field F (c)DETERMINANTSE. Brown(a) x y3 j 33xy z, x ,z3 ?3 x2 3 x y 2 z k (b)x y3 i 3 x y2 z j 3223220 , x y , 3x 3xy z(d)0 , x y , 3x 3xy z

Mathematics 37 of 37Mathematics and Advanced Engineering MathematicsExam Specifications Topic [ Example Question(s) in this Review ]A.Analytic geometry [ 5, 10 ]trigonometry [ 6, 9 ]B.Calculus [ 12, 13, 14, 15, 16, 17, 18, 19, 20 ]C.Di erential equations -D.Numerical methods - e.g., algebraic equations [ 3, 12 ]see Di erential Equations video!roots of equations [ 3, 4, 11, 12 ]approximations [ 23, 24 ]precision limits [ 24 ]E.Linear algebra (e.g., matrix operations) [ 25, 26 ]Dr. Elisabeth Brown c 2019

Advanced Engineering Mathematics Dr. Elisabeth Brown c 2019 1. Mathematics 2of37 Fundamentals of Engineering (FE) Other Disciplines Computer-Based Test (CBT) Exam Speciﬁcations. Mathematics 3of37 1. What is the value of x in the equation given by log 3 2x 4 log 3 x2 1? (a) 10 (b) 1(c)3(d)5 E. Brown . Mathematics 4of37 2. Consider the sets X and Y given by X {5, 7,9} and Y { ,} and the .

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