The syllabus consists of four units: (i) Algebra (ii) Geometry (iii) Mensuration (iv) Statistics and Probability.
|IV||Statistics and Probability||4|
Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem.
Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.
Recall of algebraic expressions and identities. Verification of identities:
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(x ± y)3 = x3 ± y3 ± 3xy (x ± y)
x³ ± y³ = (x ± y) (x² ± xy + y²)
x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx) and their use in factorization of polynomials.
Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, secant, sector, segment subtended angle.
5. SURFACE AREAS AND VOLUMES
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.
History, Repeated experiments and observed frequency approach to probability.
Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on statistics).