Which Mathematics & Science topics matter most for CTET / State TET?

Mathematics — Pedagogical Issues, Science — Pedagogical Issues carry the highest question counts based on previous-year analyses.

Is this Mathematics & Science material free?

Yes — every chapter, practice set and flashcard deck here is free. Premium mock tests and live courses from tutors are labelled separately.

CTET / State TETMathematics & Science

Mathematics & Science for CTET / State TET

60 marks, and Pedagogical Issues alone is worth as much as three content chapters combined.

📊 60 Q · 60 marks (40% of the paper, elective)

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How toppers play this section

The Mathematics & Science block rewards a very specific insight: Pedagogical Issues is not a footnote in either subject — it is the single heaviest topic in the entire paper, worth 9-11 of 30 marks in Mathematics and another 9-11 of 30 in Science, nearly double any other individual chapter. These questions test how you would teach a concept — using manipulatives, diagnosing a student's error pattern, activity-based and constructivist teaching, NCF 2005's positions on 'math phobia' and hands-on science — rather than solving the concept itself, a genuinely different skill from content mastery, so it deserves dedicated prep time rather than being treated as common sense. Within core Mathematics, Number System and Geometry are the largest content chapters; within Science, The World of the Living is the largest single content chapter, while the other six Science content areas (Food, Materials of Daily Use, Moving Things, How Things Work, Natural Phenomena, Natural Resources) are compact 2-4 mark blocks best revised as quick NCERT-based fact sheets rather than deep study.

Chapters

Built to the CTET / State TET blueprint — notes, shortcuts, solved PYQ-style examples and practice in every chapter.

1"Mathematics — Number System""Number System is CTET Paper 2 Mathematics' foundation chapter — whole numbers and integers, fractions and decimals, the rational number system and its four algebraic properties, divisibility rules, HCF/LCM, number puzzles built from the generalised two-digit form 10a+b, and an introductory pass at squares, square roots, cubes and cube roots. At `weightPct: 8`, it carries roughly 4-5 of the Mathematics & Science paper's 60 marks — but because CTET blends content with classroom pedagogy, a real share of that count tests not whether you can compute an answer, but whether you can explain, concretely and inductively, why a number-sense rule works the way a Class VI-VIII learner should be taught to discover it."⏱ 26 min read

2"Mathematics — Algebra""Algebra is where CTET tests a habit of mind, not just a technique: algebraic expressions and terms, operations on expressions and the three basic identities, forming and solving linear equations in one variable, ratio and proportion (including direct and inverse variation), and percentage as a ratio in disguise. At `weightPct: 7`, it's worth roughly 4 of the Mathematics content questions inside the 60-question Mathematics & Science paper — but a genuine slice of that count tests something harder to drill than any formula: whether you understand why the arithmetic-to-algebra transition is difficult for a Class VI-VIII learner, and which NCERT-aligned teaching move actually fixes it."⏱ 24 min read

3"Mathematics — Geometry""CTET's Geometry chapter tests two things at once: whether you can name an angle, classify a triangle, or apply Euler's formula correctly, and whether you understand how a Class VI-VIII learner actually comes to understand these ideas — the Van Hiele levels that explain why NCERT teaches shapes through folding and tracing well before it teaches formal proof. At weightPct 8, Geometry contributes roughly 4-5 of the Mathematics section's 30 questions, spread across elementary shapes, symmetry, construction, congruence, and solids — with one stubborn, well-tested misconception sitting near the centre of it all: many students, and more teachers than CTET would like, still insist a square is not a rectangle."⏱ 26 min read

4"Mathematics — Mensuration""Mensuration is the most calculation-dense chapter in CTET's Mathematics section, and no calculator is allowed for it either. At weightPct 6, it contributes only 3-4 of the Mathematics section's 30 questions, but a disproportionate share of those marks turn on exactly two one-symbol slips — mixing up a perimeter formula with an area formula, and forgetting to square (or cube) a unit-conversion factor when moving between linear, area, and volume units. The pedagogy layer matters just as much here: NCERT's insistence on grid-counting and cut-and-rearrange activities before formula introduction is the field's direct answer to those same confusions."⏱ 24 min read

5"Mathematics — Data Handling""Data Handling is CTET Mathematics' lightest sub-topic by weight, but it's the one most directly rooted in the NCERT classroom itself — collecting real data from students, organising it into pictographs, bar graphs, histograms and pie charts, summarising it with mean, median and mode, and taking a first, deliberately informal step into probability through coin and dice trials. At weightPct 4, only about 2 of the paper's ~30 Mathematics questions come from here — but they reward precision over volume, since a scale-misreading or a mean/median/mode mix-up costs more marks in this chapter than any unfamiliar content does."⏱ 18 min read

6"Mathematics — Pedagogical Issues""Mathematics — Pedagogical Issues is the single heaviest Mathematics sub-topic on CTET Paper 2 — pure theory about how mathematics should be taught, not mathematics content itself, drawn almost entirely from NCF 2005 and NCERT's 2006 Position Paper on the Teaching of Mathematics. At weightPct 17, roughly 10 of the paper's ~30 Mathematics questions turn on getting the Position Paper's actual stance right: that the goal of school mathematics is the 'mathematisation of the child's thought processes,' not procedural drill, and that error analysis, remedial teaching and evaluation should all follow from that same principle rather than from marking a final answer right or wrong."⏱ 32 min read

7"Science — Food""Why does a plate of dal-chawal-sabzi count as a balanced diet while a plate of only rice does not? This chapter covers where our food comes from, the six components of food and what a shortfall of each one does to the body, and the simple classroom tests — iodine for starch, the Biuret test for protein, the paper-translucency test for fat — that NCERT treats as the actual teaching method, not an optional add-on. A light 5% slice of the Mathematics & Science section that CTET tests as often through a described experiment as through a bare definition."⏱ 19 min read

8"Science — Materials of Daily Use""A cotton shirt, a nylon rope, a jar of pickled mango, and a plastic bucket all trace back to the same handful of NCERT ideas: where a fibre comes from and how it becomes fabric, how we sort raw materials by their properties, how a physical change differs from a chemical one, and which separation method actually fits a given mixture. This chapter also covers the classroom-sorting activities NCF 2005 treats as concept-building tools in their own right, not just warm-up exercises — a light 5% slice of Mathematics & Science that rewards precise, non-interchangeable vocabulary over broad description."⏱ 21 min read

9"Science — The World of the Living""Why does NCERT insist a Class VI learner uproot an actual weed to compare a tap root against a fibrous one, instead of just labelling a diagram? This chapter covers plants (herbs/shrubs/trees, root/stem/leaf/flower and their functions, introductory photosynthesis), how different animals walk, fly, swim and burrow, the basic plant-versus-animal and vertebrate-versus-invertebrate divisions NCERT actually teaches at this level, reproduction and nutrition in both kingdoms, and the cell as the basic unit of life. At weightPct 6, it is one of the heavier science sub-topics in the Mathematics & Science elective, and CTET tests the field-observation teaching philosophy behind it almost as often as the biology itself."⏱ 22 min read

10"Science — Moving Things, People and Ideas""Why does an NCERT chapter about rulers, levers, and shadows also open with the story of the bullock cart, the wheel, and the telegraph? This chapter covers the physics CTET actually tests under this title — types of motion (rectilinear, circular, periodic), the story of standard measurement units, an introduction to simple machines (levers, pulleys, inclined planes) and the mechanical-advantage idea behind them, and light's rectilinear propagation through shadows (umbra and penumbra) and plane-mirror reflection — all threaded through NCERT's own distinctive move of connecting scientific development to the history of human transport and communication. At weightPct 4, it is one of CTET's lightest Science sub-topics by question count, but its breadth across four genuinely separate physics ideas means revision has to stay wide rather than deep."⏱ 17 min read

11"Science — How Things Work""Science — How Things Work carries CTET Paper 2's electric-current-and-magnetism content — simple circuits, conductors and insulators, the heating and magnetic effects of current, and the properties, making, and care of magnets — worth roughly 3 of the Mathematics & Science paper's 60 questions. CTET tests it two ways at once: NCERT Class VII-VIII content (will this bulb light, will this object attract a magnet) and pedagogy (why NCERT insists on hands-on circuit-building over diagram-only teaching), so a strong answer here means knowing the physics and the classroom reasoning behind it equally well. With zero negative marking, a half-remembered fact is always worth committing to rather than leaving blank."⏱ 20 min read

12"Science — Natural Phenomena""Science — Natural Phenomena is CTET Paper 2's lightest-weighted Science sub-topic, worth roughly 2 of the Mathematics & Science paper's 60 questions, yet it covers real ground: temperature and thermometers, the three modes of heat transfer with land-and-sea breeze as NCERT's signature example, weather versus climate and animal adaptation, and — at Class VIII depth — the basics of lightning and earthquake safety. CTET tests both the NCERT content itself and the everyday-experience-first pedagogy behind how it's taught, so knowing the facts alone is only half the preparation. With zero negative marking, every question in this chapter deserves a committed answer, not a blank."⏱ 18 min read

13Science — Natural Resources"Natural Resources threads together six NCERT Class VII-VIII chapters — air and water pollution, forests as a living resource, soil formation and erosion, coal and petroleum as fossil fuels, and the chemistry of combustion and flame — into one CTET sub-topic worth roughly 2 of the Science section's 30 questions. The content itself is straightforward NCERT recall, but CTET's real test is whether you hold the geological timescale of fossil-fuel formation firmly enough to reject the 'renewable if we just wait' trap, and can connect every conservation theme back to NCERT's preferred hands-on, project-based teaching style."⏱ 18 min read

14Science — Pedagogical Issues"Pedagogical Issues is the single heaviest of CTET's eight Science chapters, worth roughly 10 of the Science section's 30 questions — and unlike every other Science chapter, it tests no content at all, only how science should be understood and taught. Its centre of gravity is NCERT's Focus Group Position Paper on the Teaching of Science: what makes science science (empirical, provisional, process-driven), what NCF 2005 wants an upper-primary science classroom to look like, and the four validity criteria — cognitive, content, process, and historical — CTET uses to test whether a teacher actually grasps the paper's stance rather than having memorised its title."⏱ 32 min read

Topic-wise weightage in CTET / State TET

Expected question counts from previous-year paper analyses. Topics with an arrow already have a full chapter.

Topic	CTET Paper 2 Q	Priority
Mathematics — Number System	4–6	High
Mathematics — Algebra	3–5	Medium
Mathematics — Geometry	4–6	High
Mathematics — Mensuration	3–4	Medium
Mathematics — Data Handling	2–3	Low
Mathematics — Pedagogical Issues	9–11	Very high
Science — Food	2–4	Medium
Science — Materials of Daily Use	2–4	Medium
Science — The World of the Living	3–4	Medium
Science — Moving Things, People and Ideas	2–3	Low
Science — How Things Work	2–4	Medium
Science — Natural Phenomena	2–3	Low
Science — Natural Resources	2–3	Low
Science — Pedagogical Issues	9–11	Very high