8 chapters · Topics & Key Concepts
Cartesian plane, x-axis and y-axis, origin, quadrants, abscissa and ordinate, plotting points, locating points using coordinates, distance from axes, points on axes, applications of coordinates in real life (maps, GPS, locating positions)
The Cartesian system describes the position of a point in a plane using two perpendicular number lines called axes. The horizontal line is the x-axis and the vertical line is the y-axis; they intersect at the origin. The plane is divided into four quadrants. Every point has a unique ordered pair (x, y). The order matters: (3, 2) is different from (2, 3). Sign of coordinates decides the quadrant.
Polynomials in one variable, terms and coefficients, degree of a polynomial, types (monomial, binomial, trinomial), linear polynomial, value of a polynomial, zero of a linear polynomial, graph of a linear polynomial
A polynomial is an algebraic expression with non-negative integer powers of the variable. A linear polynomial has degree 1. Every linear polynomial in one variable has exactly one zero — the value of x that makes the polynomial equal to zero. The graph of a linear polynomial is a straight line; the zero is the x-coordinate of the point where the line cuts the x-axis.
Natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, decimal expansion (terminating, non-terminating recurring, non-terminating non-recurring), representation of real numbers on the number line, laws of exponents, rationalisation
Rational numbers have terminating or non-terminating recurring decimal expansions. Irrational numbers have non-terminating non-recurring expansions. Together they form real numbers. Between any two real numbers, infinitely many rational and irrational numbers exist. Real numbers obey closure, commutative, associative and distributive properties. Rationalisation removes radicals from the denominator.
Algebraic expressions, identities, standard algebraic identities, geometric interpretation, factorisation using identities, expansion using identities, cube identities
An identity is an equality that holds true for all values of the variables. Algebraic identities are shortcuts that simplify multiplication, expansion and factorisation. They can be verified geometrically using areas of squares and rectangles. Recognising the pattern is the key to applying the right identity.
Introduction to trigonometric ratios, right-angled triangle, sides (opposite, adjacent, hypotenuse), sine, cosine, tangent, periodic phenomena, oscillations, circular motion, angle of elevation
Periodic phenomena such as a pendulum, sound waves and the rotation of Earth repeat after fixed intervals. Trigonometric ratios relate the angles of a right triangle to the ratios of its sides. These ratios are constant for a given angle, irrespective of the size of the triangle. Trigonometry is used in navigation, astronomy, engineering and physics.
Perimeter and area of plane figures, Heron's formula, area of quadrilaterals (parallelogram, rhombus, trapezium), area of circle, sector and segment, real-life applications
Perimeter is the total length of the boundary of a closed figure. Area is the space it occupies on a plane. Heron's formula calculates the area of any triangle when all three sides are known, without needing the height. Knowledge of areas is used in agriculture, construction and designing. The same figure can be divided into known shapes to compute its area.
Random experiments, outcomes, sample space, events, equally likely outcomes, empirical probability, theoretical probability, simple events, complementary events
Probability measures the chance of an event occurring. An experiment whose outcome cannot be predicted is a random experiment. The set of all possible outcomes is the sample space. Probability lies between 0 (impossible) and 1 (certain). Empirical probability is based on actual observations; theoretical probability is based on equally likely outcomes.
Sequences, patterns in numbers, arithmetic progression (AP), common difference, general term, geometric progression (GP), common ratio, general term of GP, sum of first n terms of an AP, real-life applications
A sequence is an ordered list of numbers following a rule. In an arithmetic progression each term increases by a fixed common difference. In a geometric progression each term is obtained by multiplying the previous term by a fixed ratio. Sequences help describe patterns in finance (EMIs, savings), physics (free fall) and computer science.
