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Geometry
(i) Symmetry
(a) Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamond-shaped figure.
(b) Being given a figure, to draw its lines of symmetry. Being given part of one of the
figures listed above to draw the rest of the figure based on the given lines of symmetry (neat recognizable free hand sketches acceptable).
(ii) Similarity
(a) Areas of similar triangles are proportional to the squares on corresponding sides.
(b) Direct applications based on the above including applications to maps and models.
(iii) Loci
(a) The locus of a point equidistant from two given lines is the angle bisector of the lines.
(b) The locus of a point equidistant from two given points is the perpendicular bisector of the points.
(iv) Circles
(a) Chord Properties:
A straight line drawn from the center of a circle to bisect a chord which is not a diameter is at right angles to the chord.
The perpendicular to a chord from the center bisects the chord (without proof).
Equal chords are equidistant from the center.
Chords equidistant from the center are equal (without proof).
(b) Tangent Properties:
The tangent at any point of a circle and the radius through the point are perpendicular to each other.
If two circles touch, the point of contact lies on the straight line joining their centers.
From any point outside a circle two tangents can be drawn and they are equal in length.
If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
If a line touches a circle and from the point of contact, a chord is drawn, theangles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.
(c) Arc and chord properties:
The angle that an arc of a circle subtends at the center is double that
which it subtends at any point on the remaining part of the circle.
Angles in the same segment of a circle are equal (without proof).
Angle in a semi-circle is a right angle.
If two arcs subtend equal angles at the center, they are equal, and conversely.
If two chords are equal, they cut off equal arcs, and conversely (without proof).
If two chords intersect internally or externally then the product of the lengths of the segments are equal.
(d) Cyclic Properties:
Opposite angles of a cyclic quadrilateral are supplementary.
The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).
(e) Other:
There is one and only one circle that passes through three given points not in a straight line.
Note: Proofs of the theorems given above are to be taught unless specified otherwise.
(v) Constructions
(a) Construction of tangents to a circle from an external point.
(b) Circumscribing and inscribing a circle on a regular polygon, n= 3,4,5,6 being given length of the side of the polygon.
(c) Other simple constructions:
To construct a circle of given radius and passing through two given points.
To construct a circle touching a given line at a given point in it and passing through a given point.
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Commercial Mathematics
(i) Compound Interest
(ii) Sales Tax and Value Added Tax Computation of tax including problems involving mark-ups, discounts, list-price, profit, loss, basic/cost price including inverse cases.
(iii) Banking
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Algebra
(i) Linear Inequations Linear Inequations in one unknown for x ? N, Z, R. Solving -
(ii) Quadratic Equations
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Mensuration
(a) Circle: Area and Perimeter. Direct application problems including Inner and Outer area types.
(b) Three-dimensional solids including right circular cone and spher
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Trigonometry
Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.
Cases involving more than two right angled triangles excluded.
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Statistics
Graphical Representation: For grouped data (both continuous and discontinuous)
histograms, frequency polygons and ogives. Finding the mode from the histogram, the upper and lower Quartiles
Central Tendency: Mean, median, mode for raw and arrayed data.
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