Help your teen with Class 10 Maths, one chapter at a time

Every composite number is a unique product of primes. Your teen uses prime factorisation to find HCF and LCM, and proves numbers like √2, √3 and √5 are irrational.

• prime factorisation
• HCF
• LCM
• irrational
• proof by contradiction

Your teen reads zeros from graphs of linear and quadratic polynomials, and uses the relationships between zeros and coefficients: for ax² + bx + c, sum of zeros = −b/a and product = c/a.

• polynomial
• degree
• zero
• quadratic
• coefficient
• parabola

Two unknowns, two conditions. Your teen models situations with two linear equations, solves them graphically and by substitution and elimination, and decides whether a pair has one, none or infinitely many solutions.

• linear equation
• substitution
• elimination
• consistent
• inconsistent
• graphical method

Your teen forms quadratic equations from situations, solves them by factorising and by the quadratic formula, and uses the discriminant b² − 4ac to know how many real roots exist.

• quadratic
• roots
• factorise
• quadratic formula
• discriminant

Your teen identifies APs in everyday situations, finds the nth term aₙ = a + (n − 1)d and the sum Sₙ = n/2 [2a + (n − 1)d], and solves savings, salary and seating problems.

• AP
• first term
• common difference
• nth term
• sum of n terms

Two triangles are similar if they have the same shape. Your teen learns the Basic Proportionality Theorem, the AA, SSS and SAS similarity criteria, and uses similarity to find unknown heights and lengths.

• similar
• proportional
• BPT
• AA
• SSS
• SAS

Your teen finds distances between points with the distance formula, divides a segment in a given ratio with the section formula, finds midpoints, and checks if points form particular shapes.

• distance formula
• section formula
• midpoint
• collinear
• ratio

In a right triangle, ratios of sides depend only on the angle. Your teen learns sin, cos, tan and their reciprocals, the values for 0°, 30°, 45°, 60°, 90°, and the identity sin²θ + cos²θ = 1.

• sine
• cosine
• tangent
• hypotenuse
• opposite
• adjacent
• identity

Your teen uses angles of elevation and depression with trigonometric ratios to find heights of buildings, widths of rivers and distances that can’t be measured directly.

• angle of elevation
• angle of depression
• line of sight
• horizontal
• tan

Your teen learns that a tangent touches a circle at one point, is perpendicular to the radius there, and that tangents from an external point are equal in length.

• tangent
• secant
• point of contact
• radius
• external point

Your teen finds areas and arc lengths of sectors using the fraction θ/360 of a circle, and areas of segments (sector minus triangle), with practical problems like wipers and designs.

• sector
• segment
• arc
• θ/360
• radius

Your teen finds surface areas and volumes of combined solids like a cone on a hemisphere or a cylinder with hemispherical ends, choosing which surfaces count.

• curved surface area
• total surface area
• volume
• hemisphere
• frustum

Your teen finds the mean (direct and assumed-mean methods), median and mode of grouped data, and interprets what each says about real data such as marks or incomes.

• class mark
• frequency
• mean
• median
• mode
• cumulative frequency

Your teen calculates theoretical probability of events with coins, dice, cards and bags, uses complementary events, and solves problems carefully listing outcomes.

• outcome
• event
• sample space
• complementary
• equally likely