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SYLLABUSES
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MATHEMATICS
[First Year] [Second
Year] [Third Year] [Fourth
Year]
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FIRST YEAR
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ALGEBRA: Fundamental processes, addition, subtraction,
multiplication, division, insertion and removal of brackets, evaluating
algebraic expressions.
Squaring simple expressions such as (a ± b).
Factorisation. Taking out a common factor, trinomial expressions,
difference of two squares. Lowest common multiple.
Addition, subtraction, multiplication and division of fractions.
Generalisation of arithmetical relations in symbols, leading to
construction of formulae in easy cases and their transposition in order
to change the subject of the formula. Numerical evaluation of formulae.
Simple ideas on powers of 10.
Logarithms of numbers, including decimals. Rules for inserting the
characteristic of logarithms of numbers, including decimals.
The practical use of tables of logarithms to base 10; their use in
simple calculations involving multiplication, division, simple powers
and roots.
Simple equations of the first degree. Easy simultaneous equations in two
unknowns of the first degree. Easy problems.
Simple graphs, including statistical graphs.
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GEOMETRY: Theoretical. (Formal proofs of theorems are not
required.)
The congruence of triangles. Properties of parallelograms and rhombus.
Isosceles triangles. Angle sum of a triangle. Exterior angle equal to
sum of interior opposite angles. Parallel lines and transversals.
Construction of diagonal scale. Greater angle opposite greater side.
Similar triangles and ratio of corresponding sides. Similar figures and
ratio of their areas. Pythagoras' theorem.
General properties of circles, including angles in same segment
equal, angle in semicircle a right angle, angle at centre double angle
at circumference, angle between tangent and chord equal to angle in
alternate segment.
Practical. (Formal proofs of construction are not required.)
To bisect a given angle. To bisect a given straight line. To
construct a right angle. To divide a straight line into a given number
of equal parts. To construct a triangle from given data. To draw a
tangent to a circle. To draw a circle through three given points. To
draw a segment of a circle which shall contain a given angle.
Simple applications to chartwork.
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TRIGONOMETRY: The six ratios for angles up to 90°. To find the
natural sine, cosine, etc., of a given angle without the aid of tables,
by constructing a right angled triangle. Use of tables, including sines,
log sines etc.
Trigonometrical ratios of 30°, 60° and 45°, with proofs.
The solution of simple right-angled triangles, including solution by
traverse table.
Use of the above in triangulation on a plane. Simple traverse.
The reciprocal relationship between ratios.
Meaning of the terms 'identity' and 'equation'.
The simple identities tan A = sin A/cos A, cos A = cos A/sin A
sinČA + CosČA = 1, 1 + tanČA = secČA, 1 + cotČA = cosecČA, and
other simple identities based thereon.
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| SECOND YEAR |
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ALGEBRA: Equations with fractions. Harder equations in one or
two unknowns.
Transpositions of formulae in harder cases and their evaluation.
Further work on graphs. Their interpretation and use. Ideas of gradient, maximum and minimum values.
Quadratic equations, solution by factors, by completing the square and by formula.
More difficult cases involving the practical use of logarithms. Logs of trigonometrical ratios.
Ratio, proportion, direct and inverse variation.
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TRIGONOMETRY: Definition of versine and haversine.
Knowledge (without proof) of the cosine formula, sine formula, tangent formula and haversine formula and their use in solving oblique angled plane triangles.
Radian measure and simple problems on the same. Approximations for ratios of small angles.
The six ratios of 0° and 180°. Graphs of the ratios. Trigonometrical ratios of (90° ± A) and of (180° - A). Harder identities.
Angle between two planes. Three dimensional plane figures. Solution by right angled trigonometry.
The elementary geometrical properties of the sphere, i.e., great circle, small circle, spherical angle, spherical triangle, length of side of spherical angle.
Knowledge (without proof) of the spherical haversine formula and its use in solving oblique spherical triangles.
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MENSURATION: Perimeters and areas of rectangle, triangle, circle, parallelogram, quadrilateral.
Surface areas of right cylinder, sphere, box-shaped bodies.
Practical application of the foregoing in simple ship problems.
Plans and elevations of simple geometrical figures.
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| THIRD YEAR |
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ALGEBRA: Definition of a logarithm. Elementary theory of indices as applied to logarithms, with easy examples.
More difficult examples on the first and second years' work, including transposition of formulae involving trigonometrical ratios.
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TRIGONOMETRY: Trigonometrical ratios from 0° to 360° and simple problems on the same. Graphs of sin A, cos A, tan A, hav A. Solution of simple equations.
The elementary geometrical properties of spherical triangles, i.e. angle sum, side sum, isosceles and equilateral triangles, greater side opposite greater angle and the converse, any two sides together greater than the third, dropping a perpendicular and use of the same in solving triangles.
Napier's Rules for the solution of right angled and quadrantal triangles. The solution of spherical triangles involving both haversine and right angled formulae.
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MENSURATION: Volume of right cylinder, right circular cone, sphere, box-shaped bodies.
Practical application of the foregoing in simple problems.
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| FOURTH YEAR |
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ALGEBRA: Sum and difference of two cubes.
Solution of easy simultaneous equations in three unknowns.
Deviation of formula for the solution of quadratic equations and its use.
More difficult graphs, including solution of simple problems by graphical methods. Solution of simultaneous equations graphically.
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TRIGONOMETRY: More difficult problems on the solution of oblique and right angled plane triangles.
Proofs of the sine and cosine formulae of plane trigonometry. Proofs of spherical cosine and haversine formulae.
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MENSURATION: Surface areas and volumes of right pyramid and
wedge.
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ALL SUBJECTS: General revision of all previous work. A
selection of more difficult examples to be worked on all parts of the
syllabus.
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