Content Elective - Mathematics and Science (60 marks)
What this domain tests
The Mathematics and Science elective carries 60 marks, conventionally split 30 Mathematics and 30 Science, drawn from the Classes VI–VIII syllabus, with pedagogy embedded in the items rather than separated.
Mathematics core
- Number: place value, divisibility rules, integers, rational numbers, laws of exponents, squares, cubes and roots, LCM and HCF.
- Algebra: variable as generalised number, identities such as (a+b)² and a²−b², factorisation, linear equations in one variable, ratio and proportion, unitary method, percentage, profit and loss, simple and compound interest.
- Geometry and mensuration: angle pairs, triangle angle sum and exterior angle, congruence criteria (SSS, SAS, ASA, RHS), Pythagoras, circle terms (chord, arc, segment, tangent), perimeter and area, surface area and volume of cube, cuboid and cylinder.
- Data: mean, median, mode, bar graph, pie chart, simple probability.
Science core
- Food components and deficiency diseases; separation of substances; acids, bases, indicators; physical versus chemical change; metals and non-metals.
- Living world: photosynthesis, respiration, transport in plants, reproduction in plants and humans, the cell as the unit of life, classification.
- Force, friction, pressure, motion and measurement; light - rectilinear propagation, reflection, mirrors and lenses; sound - vibration, pitch, loudness; electric circuits in series and parallel, conductors and insulators, magnetic effects; natural resources, pollution and conservation.
Worked example
The least number which on division by 12, 15 and 18 leaves a remainder of 5: take LCM(12, 15, 18) = 180, then add 5, giving 185. The number must exceed a common multiple by 5, and the least common multiple gives the least such number; using the HCF would give 3 + 5 = 8, which fails on 12.
Traps that cost marks
- Reversing LCM and HCF keywords in word problems.
- Mixing units: perimeter is one-dimensional, area is cm², volume is cm³.
- Confusing mass with weight, and physical with chemical change.
- Assuming bulbs in series glow brighter, when parallel branches do.