4linear law

8/7/2019 4Linear Law

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Additional Mathematics Linea

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Linear Law Paper 1

1. Determine the equation of each of the following straight linesEx1. y

Q(2,8)

P(0,2)

x

(a y

Q(3,6)

P(0,3

x

(b) yQ(4, 8)

P(0,3)

x

Ex2 y

Q(3,8)

P(1,2)

x

(a) y

Q(6,13)

P(1,3)x

(b) y P(1,7)

Q(3,1)x

Ex3 yP(2,6)

Q(4,2)

x2

(a) yP(1,8)

Q(3,2)

x2

b) yQ(4,6)

P(0,3)x

2


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Ex4

y2

Q(3, 12)

P( -2, 2) x

(a) y2

Q(4,13)

P(-1,3)

x

(b)

y2

P(0,8)

Q(4,5)

x

Ex5 log10 y

A(-2, 12)

B(3, 2)

x

(a) log10 y

A( -4, 8)

B( 2, 2)

x

(b) log10 y

B( 4, 7)

A(0,2)

x

Ex6 log10 y

B(4,8)

A(2,3)log

10x

(a) log10 y

B( 4,7)

A(2,1 )

log10

x

(b) log 10 y

A(0, 7 )

B(3,2)log

10x


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2. Diagram shows the straight line graph of21 against x

y. Express y in terms of x

3. Two variables x and y are related by the equation 5 log10 y = k x + b where k and b are constants.

Diagram shows the straight line graph of log10 y against x. Determine the value of k and b.

4. Diagram shows the straight line graph of1y

against xx

.

(a) find the value of p,

(b) express y in terms of x.

(0,6)

(1, p )

(3, 0

1y

x

x

log 10 y

x

3 4

(6, 7)

1 10

(5, 2 )

1

y

x2


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5 . Diagram shows the straight line graph of3( )x y against x . Given that x and y are related by the

equation p( x+ y - k ) = x 3 . Determine

(a) the value of p and q.

(b) the value of y when x = 2.

6.Two variables x and y are related by equation x 2 y = p x3 q , where p and q are constants. When the

graph of y against1

xis drawn, a straight line is obtained. Given that the line passes through the points

( 3, 0 ) and ( 1, 6 ) , determine the value of p and q.

(0,2)

(3,8)x +y

x3


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1.Table 1 shows the values of two variables , x and y, obtained from an experiment.

Variables x and y are related by the equation22

py kx x

k!

, where p and k are constants.

x 2 3 4 5 6 7

y 8 13.2 20 27.5 36.6 45.5

Table 1

(a) Plot yx

against x, using a scale of 2 cm to 1 unit on both axes.

Hence draw the line of best fit.(b)Use your graph in (a) to find the value of

(i) p (ii) k (iii) value of y when x = 1.2 (2007P2No7)


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2..Table 1 shows the values of two variables , x and y, obtained from an experiment.

Variables x and y are related by the equationb

y axax

!

, where a and b are constants.

x 1.0 2.0 3.0 4.0 5.0 5.5y 6.2 4.9 5.3 6.0 7.0 7.5

Table 1

(c) Plot 2xy against x , using a scale of 2 cm to 5 unit on both axes.Hence draw the line of best fit.

(d)Use your graph in (a) to find the value of(ii)a (ii) b (iii) value of y when x = 2.5


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3. Table shows the values of two variables,x andy , obtained from an experiment. The

variablesx andy are related by the equationpx

rpxy ! , wherep and r are constants.

x 1.0 2.0 3.0 4.0 5.0 5.5

y 5.5 4.7 5.0 6.5 7.7 8.4

a. Plotxy against x2, by using a scale of 2 cm to 5 units on both axes.Hence , draw the line of best fit.

b. Use the graph from (a) to find the value of (2005 P2No7)i. pii. r


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4. Table shows the values of two variables,x andy , obtained from an experiment. Variablesx andy are related by theequationy = pkx+ 1 , wherep and k are constants.

x 1 2 3 4 5 6

y 4.0 5.7 8.7 13.2 20.0 28.8

a. Plot log y against ( x + 1 ) , using a scale 2 cm to 1 unit on the ( x + 1 ) axis and 2 cm to 0.2 unit on the log y axis.Hence, draw line of best fit

b. Use the graph from (a) to find the value of (2006P2No7)i. P ii. k


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Linear Law Assessment

1. Diagram shows the straight line graph of2

yagainst x

x. Given that y = 2 x3 + 6x2 calculate the

value of p and q.

2. Diagram shows the straight line graph of31 against x

y. Express y in terms of x

3. Two variables x and y are related by the equation 4 log10 y = k log10 x + h where k and h are

constants. Diagram shows the straight line graph of log10 y against log10 x. Determine the value of k and h.

log 10 y

log10 x

3 5

(6, 8)

5 10

(2, 1 )

1

y

x

3

x

( 2, p )

(q, 4)

2

y

x


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4. Diagram shows the straight line graph of2y

against xx

.

(a) find the value of p,

(b) express y in terms of x.

5. Diagram shows the straight line graph of2( )y x against x . Given that x and y are related by the

equation p( x+ y - k ) = x 3 . Determine

(a) the value of p and k.

(b) the value of y when x = 2.

6.Two variables x and y are related by equation x 2 y = p x 2+ q , where p and q are constants. When the

graph of y against2

1

xis drawn, a straight line is obtained. Given that the line passes through the points

( 2, 1 ) and ( 4, 9 ) , determine the value of p and q.

y+x

x2

(0,3)

(2,7)

(0,6)

(1, p )

(2, 0

2y

x

x

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