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4. L is any point on the side YZ of a triangle XYZ; LM is
parallel to ZX, MN is parallel to YZ, NU is parallel to XY,
UV is parallel to ZX, VW is parallel to YZ.
Prove that the line through W parallel to XY passes
through L.
If also YL : LZ =1:3, what fraction of the area of the
triangle XYZ is the area of the hexagon LUNWVM ?
X
5. The points P and Q are respectively 25 cm and 40 cm
distant from the centre of a circle of radius 24 cm.
Prove, without using tables, that the angle between the
tangents from P to the circle is double the angle between the
tangents from Q to the circle.
6. The rectangle ABCD with AB = 24 units and BC =18 units
hes in a horizontal plane. The point P is 20 units vertically
above A and the point Q is 8 units vertically above C.
(i) Find the length of PQ, leaving your answer in surd form.
(ii) Calculate the size of the angle which PQ subtends at
the centre of the rectangle.
parallel to ZX, MN is parallel to YZ, NU is parallel to XY,
UV is parallel to ZX, VW is parallel to YZ.
Prove that the line through W parallel to XY passes
through L.
If also YL : LZ =1:3, what fraction of the area of the
triangle XYZ is the area of the hexagon LUNWVM ?
X
5. The points P and Q are respectively 25 cm and 40 cm
distant from the centre of a circle of radius 24 cm.
Prove, without using tables, that the angle between the
tangents from P to the circle is double the angle between the
tangents from Q to the circle.
6. The rectangle ABCD with AB = 24 units and BC =18 units
hes in a horizontal plane. The point P is 20 units vertically
above A and the point Q is 8 units vertically above C.
(i) Find the length of PQ, leaving your answer in surd form.
(ii) Calculate the size of the angle which PQ subtends at
the centre of the rectangle.
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| Scottish school exams and circulars > Scottish Certificate of Education > 1963 > (91) |
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| Permanent URL | https://digital.nls.uk/130800224 |
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| Shelfmark | GEB.16 |
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| Description | Examination papers for the School Leaving Certificate 1888-1961 and the Scottish Certificate of Education 1962-1963. Produced by the Scotch (later 'Scottish') Education Department, these exam papers show how education developed in Scotland over this period, with a growing choice of subjects. Comparing them with current exam papers, there are obvious differences in the content and standards of the questions, and also in the layout and use of language |
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