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(46) Mathematics, Higher Grade - I
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996 EXAMINATION PAPERS.
MATHEMATICS.
Higher Grade.—I.
Wednesday, 21st June.—11 a.m. to 1 p.m.
Candidates should answer only six questions, namely, Nos. 1, 2, 3, 4,
and any two of the other five questions. Marks are given for
neatness and good style. All the figures should be accurately
drawn.
Before attempting to answer any question, candidates should read the
whole of it very carefully, since time is often lost through
misapprehension as to what is really required.
1. ABC is a triangle, right-angled at C. On AB, towards the same
side as C, the square A BOB is described. A straignt line is
drawn through B parallel to AC; from A and D, AH and DO
are drawn perpendicular to this line; and from D, DF is drawn
perpendicular to BG, produced if necessary. Prove that the
square ABDE is equal to the figure AGFDGH and that this
figure can be divided into two squares whose sides are equal to
AG and BG.
2. Draw a straight line AB6 centimetres in length, and divide it in H
so that the rectangle AB.HB = AHi. Give construction and
proof.
Measure AH, HB as accurately as you can, and verify arith¬
metically whether your construction has given the required
result.
3. AB is a chord of a circle which is produced^to P, and PT is the
tangent from P, prove that PT2 — AP. BP.
Find a point 0 in the base EF of a triangle DBF such that
DE‘i = EF.EG.
4. If the vertical angle ^4 of a triangle ABG be bisected internally
and externally by straight lines cutting the base in the points
D and E respectively, prove that the ratios BD : DC and BE : CE
are each equal to the ratio AB: AC.
If 0 be the mid point of BG, prove that 0D.0E = OB1.
Answer two questions out of the following five.
5. Construct an equilateral triangle with each side 4 inches long.
Construct (without proof) a square equal in area to the triangle.
Show that the area of the triangle is equal to 4 ^/3 square
inches and hence find i/3 correct to one decimal place by measure¬
ment from your figure.
6. Draw a rhombus ABC I), each side measuring one inch in length.
Divide each side into four equal parts, and name the points of
section taken round the figure A, E, F, G, B, H, J, K, C, L, M,
H, D, P, Q, R. Join AN, EM, FL, GG, RE, QJ, PK.
Prove that this figure enables you to measure distances less
than an inch expressed in sixteenths of an inch, and show how
to find in your figure lines equal to ^ and y-g- of an inch.
10.
15.
15.
15
15.
15.
15
996 EXAMINATION PAPERS.
MATHEMATICS.
Higher Grade.—I.
Wednesday, 21st June.—11 a.m. to 1 p.m.
Candidates should answer only six questions, namely, Nos. 1, 2, 3, 4,
and any two of the other five questions. Marks are given for
neatness and good style. All the figures should be accurately
drawn.
Before attempting to answer any question, candidates should read the
whole of it very carefully, since time is often lost through
misapprehension as to what is really required.
1. ABC is a triangle, right-angled at C. On AB, towards the same
side as C, the square A BOB is described. A straignt line is
drawn through B parallel to AC; from A and D, AH and DO
are drawn perpendicular to this line; and from D, DF is drawn
perpendicular to BG, produced if necessary. Prove that the
square ABDE is equal to the figure AGFDGH and that this
figure can be divided into two squares whose sides are equal to
AG and BG.
2. Draw a straight line AB6 centimetres in length, and divide it in H
so that the rectangle AB.HB = AHi. Give construction and
proof.
Measure AH, HB as accurately as you can, and verify arith¬
metically whether your construction has given the required
result.
3. AB is a chord of a circle which is produced^to P, and PT is the
tangent from P, prove that PT2 — AP. BP.
Find a point 0 in the base EF of a triangle DBF such that
DE‘i = EF.EG.
4. If the vertical angle ^4 of a triangle ABG be bisected internally
and externally by straight lines cutting the base in the points
D and E respectively, prove that the ratios BD : DC and BE : CE
are each equal to the ratio AB: AC.
If 0 be the mid point of BG, prove that 0D.0E = OB1.
Answer two questions out of the following five.
5. Construct an equilateral triangle with each side 4 inches long.
Construct (without proof) a square equal in area to the triangle.
Show that the area of the triangle is equal to 4 ^/3 square
inches and hence find i/3 correct to one decimal place by measure¬
ment from your figure.
6. Draw a rhombus ABC I), each side measuring one inch in length.
Divide each side into four equal parts, and name the points of
section taken round the figure A, E, F, G, B, H, J, K, C, L, M,
H, D, P, Q, R. Join AN, EM, FL, GG, RE, QJ, PK.
Prove that this figure enables you to measure distances less
than an inch expressed in sixteenths of an inch, and show how
to find in your figure lines equal to ^ and y-g- of an inch.
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| Scottish school exams and circulars > Leaving Certificate Examination > (46) Mathematics, Higher Grade - I |
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| Permanent URL | https://digital.nls.uk/144136564 |
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| Shelfmark | P.P. 1906 XXX |
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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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