AM F5 C2 Linear Law PDF Sample

8/12/2019 AM F5 C2 Linear Law PDF Sample

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SPM Add Math Form 5 Chapter 2 Linear Law

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CHAPTER 2 : LINEAR LAW

LINES OF BEST FIT

Drawing Lines of Best Fit

1) An experiment was carried out to determine how the temperature at a liquid, TC, varied

with time, t s, when heated. Plot the graph, T against t. Draw the line of best fit.

t 50 100 150 200 250 300

T 40.0 44.0 49.5 52.0 55.1 60.0

2) The following table shows values of two variables, Pand Q, obtained in an experiment.

Plot the graph, Qagainst P. Draw the line of best fit.

P 10 20 30 40 50 60Q 0.60 0.51 0.39 0.28 0.2 0.10

Equations for Lines of Best Fit

3) The following table shows how the weight of a child, Wkg varies with age, Ymonths.

Y (months) 3 4 5 6 7 8

W (kg) 5.5 6.1 6.5 7.1 7.5 8.1

(a) Plot the graph, W against Y. Draw the line of best fit.(b) Use the graph to find W in terms of Y.

4) The diagram shows the graph of y againstx. Express y in terms of x.

5) The velocity of a ball, v, dropped from a fixed height is related to time, t. The corresponding

values are tabulated as shown below.

t (s) 2 4 6 8 10

v (m s-1) 29.6 49.4 68.9 87.8 108.0

(a) Plot the graph of v against t. Draw the line of best fit.

(b) From the graph, find

(i) v if t=5 s,

(ii) t if v=112 m s-1.

(c) Find v in terms of t.

(d) Hence, determine the time when the velocity is 200m s-1.

y

x

(0,c)*8,16)

(12,20)


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6) The diagram shows the graph of y againstx.

(a) Express y in terms of x.

(b) Find the value of

(i) y whenx=6,

(ii) x when y=30.

APPLYING LINEAR LAW TO NON-LINEAR RELATIONS

Converting non-linear equations to the linear form

7) Convert the following non-linear equations to the linear form Y=mX+c. Determine Y, X, m

and c.

(a) y = ax2+b (c) y= abx

(b) ax+y =

(d) y=

+

8) Given y= 2x2+3x, express the equation in the linear form Y=mX+c. Hence, state the value of

mand c.

The value of constants in a non-linear equation

9) Two constants are related by the equation y=ax+

. Values of the two variables are shown

in the following table.

x 1 2 3 4 5

y 3.00 4.5 6.3 8.3 10

(a) Convert the equation y=ax+

to the linear form, Y=mX+c.

(b) Plot the graph of Y againstX. Draw the line of best fit.

(c) From the graph, estimate the value of a and b.

10) The diagram shows the graph of1

againstx. Express y in terms of x.

11) The diagram shows the graph of log10y against log10x. Express y in terms of x.

y

x

2

(10,22)

x

(5,30)

(10,40)

1y

log10y

log10x

1

(1,3)


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12) Variables xand yare related by equation y=ax3+bx. Diagram (i) shows the graph of y

againstx. Diagram (ii) shows the graph of

againstx2.

(i) (ii)

(a) Find the value ofpand q.

(b) Express yin terms ofx.

Information from lines of best f it and its equations

13) Experimental values of displacement, s,cm of an object at time, t,s is as tabulated below.

t 20 50 80 110 140

s 10.1 30.1 58.1 94.6 128.6

Variables sand tare related by the equation s=

22 +, where uand aare constants.

(a) Plot the graph of

against t. Draw the line of best fit.

(b) From the graph, determine the displacement at 100 seconds.(c) Determine the linear form of the equation. Find the values of uand a.

(d) Calculate the displacement at 200 seconds.

14) The table shows the values of two variables,x and y, obtained from an experiment.

Variablesxand yare related by the equation y=pqx+1, wherepand qare constants.

x 2 4 6 8 10 12

y 4 15 64 258 512 2048

(a) Plot the graph of log10yagainst (x+1).

(b) Use the graph to find the value of

(i) ywhenx=5,

(ii) xwhen y=100

(c) Find the value ofpand q. Hence, express yin terms ofx.

15) The values of x and yobtained in an experiment is shown in the table below. Variablesx

and yare related by the equation y=pkx, wherepand k are constants.

x 1.0 1.5 2.0 2.5 3.0 3.5

y 10.0 14.1 20.0 28.3 40.0 56.6

(a) Plot the graph of log10yagainstx. Draw the line of best fit.

y

x(1,3)

2,18)

yx

x2

(q,3)

(4,p)


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(b) Use the graph to find the value of

(i)p,

(ii)k.

16) Variables Pand Qare related by the equation P=2

2(Q+m)2 where kand mare

constants. The table shows the corresponding values of Pand Q.

Q 1 2 3 4 5 6

P 27.8 33.3 38.9 44.4 50.0 55.6

(a) Plot the graph of against Q. Draw the line of best fit.(b) Use the graph to find the value of kand m.

(c) Find the value of P when Q=3.5

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AM F5 C2 Linear Law PDF Sample

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