Cambridge Additional Mathematics

198 Straight line graphs (Chapter 7)

5 Find the point of intersection of the lines x¡ 2 y=5and 4 x+3y=9.

6 ABCD is a trapezium in which AB is parallel to DC,

and AbDC=90±. Find:

a the coordinates of D

b the area of the trapezium.

7 Find the points where the line 3 x+y=1intersects the curve x^2 +y^2 =29.

8 The line x+y=5meets the curve x^2 +y^2 +3xy+5x=1at P and Q. Find the equation of

the perpendicular bisector of PQ.

9 Consider two distinct points in the plane (a 1 ,b 1 ) and (a 2 ,b 2 ) where a 16 =a 2. Show that the

straight line passing through them has equation:

a y=

b 1 ¡b 2

a 1 ¡a 2

x+

a 1 b 2 ¡a 2 b 1

a 1 ¡a 2

in gradient-intercept form

b (b 1 ¡b 2 )x+(a 2 ¡a 1 )y=a 2 b 1 ¡a 1 b 2 in general form.

10 a Writeyin terms ofx.

b Hence findywhen x=4.

11

12 This table shows experimental values ofxandy: x^1234

y 8 7 : 5 11 : 33 17 : 75

a Copy and complete the following table: x^3

xy

b Plotxyagainstx^3 , and draw a straight line through the points.

c Findyin terms ofx.

d Hence findywhen x=7.

lgy

O lgx

(2 2),

(10 6),

D

A,(1 7)

B,(7 3)

C,(8 -2)

Consider the graph alongside.

a Write an equation for the line in the form

lgy=mlgx+c.

b Hence writeyin terms ofx.

xy

O ~`x

(2 4),

(4 10),

cyan magenta yellow black

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100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\198CamAdd_07.cdr Tuesday, 21 January 2014 12:19:09 PM BRIAN