4linear law
TRANSCRIPT
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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