Multi-Topic Questions (Chapter 33) 336 June 1995, Paper 4
a In the right angled triangle PQR, PR=xcm and
QR=(x+1)cm. The area of the triangle PQR
is 5 cm^2.
i Show that x^2 +x¡10 = 0.
ii Solve the equation x^2 +x¡10 = 0, giving
your answers correct to 1 decimal place.
Hence write down the length of PR.
b In triangle ABC, angle ACB= 120o,
AC=ycm and BC=(y+2)cm.
i Use the cosine rule to find an expression for
AB^2 in terms ofy.
ii When AB=7cm, show that
y^2 +2y¡15 = 0.
iii Factorise y^2 +2y¡ 15.
iv Solve the equation y^2 +2y¡15 = 0.
Hence write down the lengths of AC and CB.37
a BCA is the diameter of a circle, centre C, radiusr.
DAE is a tangent to the circle at A. DE=3r and
angle DCA=30o.
i Draw the diagram accurately when r=3cm.
ii Measure and write down the length of BE in
your diagram.
iii Calculate the length of the semi-circular arc
BA when r=3cm.
b In the case when r=10cm, calculate,to 2
decimal places,
i the length of DA ii the length of AE iii the length of BE
iv the length of the semi-circular arc BA.
c Comment on the relationship between the length of BE and the length of the semi-circular arc BA.38 June 1995, Paper 4
Ahmed earns$20 000each year.
a In 1991 , he paid no tax on the first$3000of his earnings. He paid25%of the rest as tax. Show
that he paid$4250as tax.
b In 1992 , he paid no tax on the first$4000of his earnings. He paid30%of the rest as tax. Calculate
how much he paid as tax.
c In 1993 , he paid no tax on the first$xof his earnings. He paid30%of the rest as tax.
i Find an expression in terms ofxfor the amount of tax he paid.
ii Calculate the value ofxif he paid$4950as tax.()x¡+¡1 cmPRxcmQ()y¡+¡2cmycm120°AB
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