Basic Engineering Mathematics, Fifth Edition

(Amelia) #1

Revision Test 6 : Quadratics, logarithms and exponentials


This assignment covers the material contained in Chapters 14–16.The marks available are shown in brackets at the
end of each question.



  1. Solve the following equations by factorization.
    (a) x^2 − 9 =0(b)x^2 + 12 x+ 36 = 0
    (c) x^2 + 3 x− 4 =0(d)3z^2 −z− 4 = 0
    (9)

  2. Solvethefollowingequations,correct to3decimal
    places.
    (a) 5x^2 + 7 x− 3 =0(b)3a^2 + 4 a− 5 = 0
    (8)

  3. Solvetheequation3x^2 −x− 4 =0bycompleting
    the square. (6)

  4. Determine the quadratic equationinxwhose roots
    are 1 and−3. (3)

  5. The bending momentM at a point in a beam
    is given byM=


3 x( 20 −x)
2

wherexmetres is
the distance from the point of support. Deter-
mine the value ofxwhen the bending moment is
50Nm. (5)


  1. The currentiflowing throughan electronic device
    is given by i=( 0. 005 v^2 + 0. 014 v) amperes
    wherevis the voltage. Calculate the values ofv
    wheni= 3 × 10 −^3 .(6)

  2. Evaluate the following, correct to 4 significant
    figures.


(a) 3.2ln4. 92 −5lg17.9(b)

5 ( 1 −e−^2.^65 )
e^1.^73

(4)


  1. Solve the following equations.
    (a) lgx=4(b)lnx= 2
    (c) log 2 x=5(d)5x= 2
    (e) 3^2 t−^1 = 7 t+^2 (f) 3e^2 x= 4. 2 (18)
    9. Evaluate log 16


(
1
8

)
(4)


  1. Write the following as the logarithm of a single
    number.


(a) 3log2+2log5−

1
2

log16

(b) 3log3+

1
4

log16−

1
3

log27 (8)


  1. Solve the equation
    log(x^2 + 8 )−log( 2 x)=log3. (5)

  2. Evaluate the following, each correct to 3 decimal
    places.
    (a) ln462. 9


(b) ln0. 0753

(c)

ln3. 68 −ln2. 91
4. 63

(3)


  1. Expandxe^3 xto six terms. (5)

  2. Evaluatevgiven thatv=E


(
1 −e−

t
CR

)
volts
when E=100V,C= 15 μF, R=50k and
t= 1 .5s. Also, determine the time when the
voltage is 60V. (8)


  1. Plot a graph of y=


1
2

e−^1.^2 x over the range
x=−2tox=+1 and hence determine, correct to
1 decimal place,
(a) the value ofywhenx=− 0 .75, and
(b) the value ofxwheny= 4 .0(8)
Free download pdf