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Geometry
(i) Angles formed at a point by two intersecting lines and parallel lines and a transversal Adjacent, supplementary, linear pair, vertically opposite, alternate, corresponding, allied (co-interior) and their properties.
(ii) Triangles
(a) Proof and numerical application of:
Sum property of angles.
Exterior angle equals sum of opposite interior angles.
(b) Congruency: four cases: SSS, SAS, AAS, RHS. Illustration through cutouts. Simple applications.
(c) Problems based on:
Angles opposite equal sides are equal and converse.
If two sides of a triangle are unequal, then the greater angle is opposite the greater side and converse.
Sum of any two sides of a triangle is greater than the third side.
Of all straight lines that can be drawn to a given line from a point outside it, the perpendicular is the shortest. Proofs not required.
(iii) Constructions (using ruler and compass)
(a) Constructions of angles and triangles involving 30°, 45°, 60°, 75°, 90°, 120°, 135° angles.
(b) Bisection of a line segment perpendicularly. Bisection of an angle and
a line using only ruler and compass.
(iv) Mid Point Theorem
(a) All axioms related to the theorem including proof and simple application.
(b) Equal intercept theorem: proof and simple application.
(c) Related construction: division of a line segment into 2 equal parts or into parts in a given ratio.
(v) Similarity
(a) As a size transformation.
(b) Comparison with congruency, keyword being proportionality.
(c) Three cases: SSS, SAS, AAS. Simple application (proof not included).
(d) Special case: a perpendicular drawn from the vertex of a right-angled triangle divides the triangle into two triangles similar to each other and also to the original triangle.
(e) Application of Basic Proportionality Theorem.
(vi) Pythagoras Theorem Simple direct applications.
(vii) Rectilinear Figures
(a) Internal angle of a regular polygon: (2n-4) 90° / n.
(b) External angle: 360° / n.
(c) Parallelogram:
Both pairs of opposite sides equal (without proof).
Both pairs of opposite angles equal.
One pair of opposite sides equal and parallel (without proof).
Diagonals bisect each other and bisect the parallelogram.
Rhombus as a special parallelogram whose diagonals meet at right angles.
In a rectangle, diagonals are equal, in a square they are equal and meet at right angles.
(d) Construction of a parallelogram and regular hexagon using scale and compass only.
(e) Proof and use of area theorems on parallelograms:
Parallelograms on the same base and between the same parallels are equal in area.
The area of a parallelogram is equal to that of a rectangle of the same base and on the same altitude (without proof).
The area of a triangle is half that of a parallelogram on the same base and between the same parallels.
Triangles between the same base and between the same parallels are equal
in area (without proof).
Triangles with equal areas on the same bases have equal corresponding altitudes.
Note: Proofs of the theorems given above are to be taught unless specified otherwise.
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Arithmetic
Irrational Numbers
Rational, irrational numbers as real numbers, their place in the number system. Surds and rationalization of surds.
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Commercial Mathematics
Percentage; Percentage increase/decrease applications: increase/decrease in price, addition/subtraction of tax, effect of discount/mark-up, profit/loss.
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Algebra
Expansions (a ± b)2 (a ± b)3 (x ± a)(x ± b)
Factorisation
a2– b2 a3 ± b3 ax2+ bx + c, by splitting the middle term.
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Statistics
Tabulation of raw data using tally-marks.
Understanding and recognition of raw, arrayed and grouped data.
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Mensuration
Formulae for area and perimeter of simple 2-D figures: triangle (including Hero’s formula for area), square, rhombus, rectangle, parallelogram and trapezium. Simple direct problems based on these including those involving inner and outer dimensions, cost.
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Trigonometry
Trigonometric Ratios: sine, cosine, tangent of an angle and their reciprocals.
Trigonometric ratios of standard angles- 0, 30, 45, 60, 90 degrees.
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Co-ordinate Geometry
Dependent and independent variables.
Ordered pairs, co-ordinates of points and plotting them in the Cartesian Plane.
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