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Algebra
(i) Linear Inequations Linear Inequations in one unknown for x ? N, Z, R. Solving -
Algebraically.
Representation of solution on the number line.
(ii) HCF and LCM of polynomials by factorization.
(iii) Quadratic Equations
(a) Quadratic equations in one unknown. Solving by:
Factorisation.
Formula.
Nature of roots
(b) Solving problems.
(iv) Reflection
(a) Reflection of a point in a line:
x=0, y =0, x= a, y=a, the origin.
(b) Invariant points.
(v) Ratio and Proportion
(a) Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios.
(b) Continued proportion, mean proportion (geometric mean).
(c) Componendo and dividendo, alternendo and invertendo properties.
(d) Direct applications.
(e) Direct problems.
(vi) Factorization
(a) Using Factor Theorem.
(b) Remainder Theorem.
(c) Factorising a polynomial completely after obtaining one factor.
Note: f (x) not to exceed degree 3.
(vii) Matrices
(a) Order of a matrix. Row and column matrices.
(b) Comparability for addition and multiplication.
(c) Null and Identity matrices.
(d) Addition and subtraction of 2×2 matrices.
(e) Multiplication of 2×2 matrix by a non-zero rational number, a row matrix, a column matrix, a 2×2 null, identity, regular 2× 2 matrix.
(viii) Co-ordinate Geometry
(a) Distance formula.
(b) Section and Mid-point formula (Internal section only, co-ordinates of a centroid included).
(c) Equation of a line:
Slope –intercept form y = mx + c
Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as
slope/ gradient/ tan? where ? is the angle the line makes with the positive direction of the x axis. Geometric understanding of c as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.
Conditions for two lines to be parallel or perpendicular. Simple applications of all of the above.
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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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Geometry
(i) Symmetry
(ii) Similarity
(iii) Loci
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Mensuration
Circle: Area and Perimeter. Direct application problems including Inner and Outer area types.
Three-dimensional solids including right circular cone and sphere:
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Trigonometry
Trigonometric ratios of complementary angles and direct application:
sin A = cos(90 - A), cos A = sin(90 – A)
tan A = cot (90 – A), cot A = tan (90- A)
sec A = cosec (90 – A), cosec A = sec(90 – A)
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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 from the ogive, the median from the ogive.
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