Basic Engineering Mathematics, Fifth Edition

Revision Test 7 : Graphs

This assignment covers the material contained in Chapters 17–19.The marks available are shown in brackets at the
end of each question.

1. Determine the value ofPin the followingtable of
   values.
   x 0 1 4

y= 3 x− 5 − 5 − 2 P (2)

2. Assuming graph paper measuring 20cm by 20cm
   is available, suggest suitable scales for the follow-
   ing ranges of values.
   Horizontal axis: 5N to 70N; vertical axis: 20mm
   to 190mm. (2)


3. Correspondingvaluesobtainedexperimentallyfor
   two quantities are:

x − 5 − 3 − 1 0 2 4

y − 17 − 11 − 5 − 2 4 10

Plot a graph of y(vertically) againstx (hori-

zontally) to scales of 1cm=1 for the horizontal

x-axis and 1cm=2 for the verticaly-axis. From

the graph, find

(a) the value ofywhenx=3,

(b) the value ofywhenx=−4,

(c) the value ofxwheny=1,

(d) the value ofxwheny=−20. (8)

4. If graphs ofyagainstxwere to be plotted for each
   of the following,state (i) the gradient, and (ii) the
   y-axis intercept.
   (a) y=− 5 x+3(b)y= 7 x
   (c) 2y+ 4 = 5 x (d) 5x+ 2 y= 6

(e) 2x−

y

3

=

7

6

(10)

5. TheresistanceRohmsofacopperwindingismea-
   sured at various temperaturest◦C and the results
   are as follows.

R() 38 47 55 62 72

t(◦C) 16 34 50 64 84

Plot a graph ofR(vertically) againstt(horizon-

tally) and find from it

(a) the temperature when the resistance is 50,

(b) the resistance when the temperature is 72◦C,

(c) the gradient,

(d) the equation of the graph. (10)

6. xand yare two related variables and all other
   letters denote constants. For the stated laws to
   be verified it is necessary to plot graphs of the
   variables in a modified form. State for each
   (a) what should be plotted on the vertical axis,
   (b) what should be plotted on the horizontal axis,
   (c) the gradient,
   (d) the vertical axis intercept.
   (i) y=p+rx^2 (ii) y=

a

x

+bx (4)

7. The following results give corresponding values
   of two quantitiesxandywhich are believed to be
   related by a law of the formy=ax^2 +bxwhere
   aandbare constants.

y 33.9 55.5 72.8 84.1 111.4 168.1

x 3.4 5.2 6.5 7.3 9.1 12.4

Verify the law and determine approximate values

ofaandb.

Hence determine (i) the value ofywhenxis 8.0

and (ii) the value ofxwhenyis 146.5 (18)

8. By taking logarithms of both sides ofy=kxn,
   show that lgyneeds to be plotted vertically and
   lgxneeds to be plotted horizontally to produce
   a straight line graph. Also, state the gradient and
   vertical-axis intercept. (6)


9. By taking logarithms of both sides ofy=aekx
   show that lnyneeds to be plotted vertically and
   xneeds to be plotted horizontally to produce a
   straight line graph. Also, state the gradient and
   vertical-axis intercept. (6)


10. Show from the following results of voltageVand
    admittanceYof an electrical circuit that the law
    connecting the quantities is of the formV=kYn
    and determine the values ofkandn.

Voltage

V(volts) 2.88 2.05 1.60 1.22 0.96

Admittance,

Y(siemens) 0.52 0.73 0.94 1.23 1.57

(12)