Basic Engineering Mathematics, Fifth Edition

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)

6. 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)


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

(a) 3.2ln4. 92 −5lg17.9(b)

5 ( 1 −e−^2.^65 )

e^1.^73

(4)

8. 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)

10. 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)

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


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

(b) ln0. 0753

(c)

ln3. 68 −ln2. 91

4. 63

(3)

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


14. 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)

15. 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)