Scottish school exams

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5. P and Q are towns of the same longitude such that the arc
of the earth’s circumference joining them is 500 miles long.
When the sun is directly overhead at Q its rays, assumed
parallel, strike P at an angle of 7|° to the vertical, PR. Use
this information to calculate the circumference of the earth. (6)
6. ABCD is a rectangle in a horizontal plane with AB = 16 units.
The diagonals of the rectangle intersect in O, and OX is a
vertical line 15 units long. Calculate the size of the angle
between the planes ABCD and XBC. (6)
7. A circle with centre O has a radius of 2 in. The radius OA
is produced its own length to B and a straight line XBY is
drawn in the same plane and perpendicular to OB. State
the locus of points which are 2 in from O and not more
than 3 in from the line XY. (5)
Page four

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