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

เคฐเฅเค เคเคพเคจเคพ เคจเคนเฅเค เคคเฅ เคเคนเฅเค เคนเคพเคฐ เคเฅ เคเคพเคเคเฅเค เคชเฅ เคเคฒเคเฅ เคฎเคฟเคฒเฅเคเคเฅ เคธเคพเคฏเฅ เคฌเคนเคพเคฐ เคเฅ

Week 1: Linear Inequations

– Linear Inequations in one unknown for x โ 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 โ 4ac > 0

– Two equal real roots if b2 โ 4ac = 0

– No real roots if b2 โ 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 2ร2 matrices.

(e) Multiplication of a 2ร2 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 โnโ 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 โintercept form y = mx + c

– Two- point form (y-y1) = m(x-x1)

– Geometric understanding of โmโ

– as slope/ gradient

– tanฮธ where ฮธ is the angle the line makes with the positive direction of the x axis.

– Geometric understanding of โcโ

– 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.