HTET Level 3 (PGT) cheat sheet

Average = sum of observations ÷ number of observations; combined average of groups = (n1x̄1 + n2x̄2) ÷ (n1 + n2).

Simple interest = P × R × T ÷ 100; compound interest amount = P(1 + R/100)^T, and CI = A − P.

Speed–time: distance = speed × time; for equal distances at speeds a and b, average speed = 2ab/(a + b).

Percentage change: successive changes of a% and b% equal a + b + ab/100 percent; a rise of x% then fall of x% gives a net loss of x²/100 percent.

Profit and loss: profit% = (SP − CP)/CP × 100; when two articles are sold at the same price with equal gain% and loss%, the seller always suffers a net loss.

Ratio and proportion: if a:b = c:d then ad = bc; duplicate ratio of a:b is a²:b², and the mean proportional of a and b is √(ab).

Time and work: if A does work in x days and B in y days, together they take xy/(x + y) days; efficiency is inversely proportional to time.

Mensuration: area of a circle = πr², circumference = 2πr, volume of a cylinder = πr²h, volume of a sphere = (4/3)πr³.

LCM × HCF = product of the two numbers; HCF of fractions = HCF of numerators ÷ LCM of denominators.

Haryana was carved out of Punjab on 1 November 1966 on the recommendation of the Shah Commission; it has 22 districts and its capital is Chandigarh, which it shares with Punjab.

Haryana's state animal is the blackbuck, state bird the black francolin, state tree the peepal, and state flower the lotus.

Major rivers: Yamuna (eastern border), Ghaggar (seasonal, often called the 'dead river' in its lower course), Markanda, Sahibi and Tangri.

Historical sites: Kurukshetra (Mahabharata battlefield, Brahma Sarovar), Panipat (three decisive battles in 1526, 1556 and 1761), Surajkund and the Aravalli ranges in the south.

Haryana is a leading producer of wheat, rice, mustard and bajra; the Green Revolution transformed districts such as Karnal and Kurukshetra.

Gurugram and Faridabad form part of the National Capital Region and are major industrial and IT hubs; the Kundli–Manesar–Palwal Expressway serves the NCR corridor.

Sports: Haryana has produced Olympic medallists in wrestling, boxing, shooting and athletics; the state sports policy funds rural talent through gramin and urban stadia.

Administration: the state legislature is unicameral (Vidhan Sabha with 90 seats); Haryana sends 10 members to the Lok Sabha and 5 to the Rajya Sabha.

Pedagogical content knowledge (Shulman) is the blend of subject mastery and knowledge of how to teach that content to specific learners.

Bloom's revised taxonomy orders objectives: remember, understand, apply, analyse, evaluate, create; higher-order objectives require application-level tasks.

Constructivist teaching uses prior knowledge, hands-on investigation and peer discussion; the teacher acts as facilitator, not sole transmitter.

Assessment types: diagnostic (before instruction), formative (during, feedback-oriented), summative (end of unit, judgement-oriented).

Lesson plan components: learning objectives, prior knowledge, teaching aids, introduction, presentation, recapitulation, evaluation, and homework.

Inquiry-based pedagogy: pose a problem, let learners hypothesise, gather and analyse data, then justify conclusions with evidence.

Concept mapping and advance organisers help learners link new content to existing schemas, supporting meaningful rather than rote learning.

Remedial teaching follows diagnostic testing and targets specific error patterns; enrichment tasks extend learners who have already mastered objectives.