Starting from the middle of April we shall begin a new series of articles discussing Algebra for ICSE 10th students. This series will take seven weeks to finish. Some weeks wold be busier and some would be tougher. Keep solving … Always remember

रुक जाना नहीं तू कहीं हार के
काँटों पे चलके मिलेंगे साये बहार के

Week 1: Linear Inequations
– Linear Inequations in one unknown for x ∈ N, W, Z, R.
– Solving and Writing the solution in set notation form.
– Representation of solution on the number line.

Week 2: Quadratic Equations in one variable
(a) Nature of roots
– Two distinct real roots if b2 – 4ac > 0
– Two equal real roots if b2 – 4ac = 0
– No real roots if b2 – 4ac < 0

(b) Solving Quadratic equations by:
– Factorisation
– Using Formula.
(c) Solving simple quadratic equation problems.

Week 3: Ratio and Proportion
(a) Proportion, Continued proportion, mean proportion
(b) Componendo, Dividendo, Alternendo, Invertendo properties and their combinations.

Week 4: Factorisation of polynomials:
(a) Factor Theorem.
(b) Remainder Theorem.
(c) Factorising a polynomial completely after obtaining one factor by factor theorem.
Note: f (x) not to exceed degree 3.

Week 5: Matrices
(a) Order of a matrix. Row and column matrices.
(b) Compatibility for addition and multiplication.
(c) Null and Identity matrices.
(d) Addition and subtraction of 2×2 matrices.
(e) Multiplication of a 2×2 matrix by
– a non-zero rational number
– a matrix.

Week 6: Arithmetic Progression
– Finding the General term of an A.P.
– Finding Sum of first ‘n’ terms of an A.P.

Week 7: Co-ordinate Geometry
(a) Reflection
– (i) Reflection of a point in a line: x=0, y =0, x= a, y=a, the origin.
– (ii) Reflection of a point in the origin.
– (iii) Invariant points.
(b) Co-ordinates expressed as (x, y), Section formula, Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines.
(i) Section and Mid-point formula (Internal section only, co-ordinates of the centroid of a triangle included).
(ii) 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
– tanθ where θ 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.