CTET (Central Teacher Eligibility Test) Mathematics and Pedagogy Syllabus

In algebra, what is the difference between a variable and a constant?

A variable is a symbol (like x or y) that can take different values; a constant has a fixed value (like 5 or pi).

Define term, coefficient, and factor in an algebraic expression.

In a term, factors are the quantities multiplied together; the coefficient is the numerical factor of a term. In 7xy, the coefficient is 7 and the factors are 7, x, and y.

How are like terms and unlike terms distinguished, and why does it matter?

Like terms have the same variables with the same powers (3x and 5x); unlike terms differ (3x and 3y). Only like terms can be added or subtracted (combined).

What is the difference between an algebraic expression and an equation?

An expression is a combination of variables, constants, and operations with no equals sign (2x+3); an equation states that two expressions are equal using = (2x+3=7).

Classify polynomials by number of terms: monomial, binomial, trinomial.

A monomial has one term (5x), a binomial has two terms (x+3), and a trinomial has three terms (x^2+2x+1).

What is a linear equation in one variable, and what does its solution mean?

It is an equation where the highest power of the variable is 1, such as 2x+5=11. The solution is the value of the variable (here x=3) that makes both sides equal.

What is the golden rule for solving a linear equation by the balancing method?

Whatever operation you perform on one side of the equation must be performed equally on the other side, so the equation stays balanced.

How is a word problem converted into a linear equation?

Represent the unknown by a variable, translate the relationships in the problem into an algebraic equation, solve for the variable, then check the answer against the conditions.

What is the difference between a ratio and a proportion?

A ratio compares two quantities of the same kind by division (3:4). A proportion is a statement that two ratios are equal (3:4 = 6:8).

State the property of proportion used to check if four numbers are in proportion.

In a proportion a:b = c:d, the product of extremes equals the product of means (a x d = b x c). If the cross products are equal, the numbers are in proportion.

How do you convert a fraction or ratio into a percentage and back?

To percentage: multiply by 100 (1/4 x 100 = 25%). From percentage: divide by 100 (40% = 40/100 = 2/5).

Distinguish between direct and inverse proportion with an example.

In direct proportion, quantities increase or decrease together (more articles cost more). In inverse proportion, one increases as the other decreases (more workers take less time).

What is the unitary method?

A method to find the value of one unit first, then use it to find the value of the required number of units. E.g. if 5 pens cost Rs 50, one pen costs Rs 10, so 8 pens cost Rs 80.

Differentiate between a point, a line, a ray, and a line segment.

A point marks an exact position with no size; a line extends endlessly in both directions; a ray has one fixed endpoint and extends endlessly one way; a line segment has two endpoints and a fixed length.

Classify angles by measure: acute, right, obtuse, straight, and reflex.

Acute < 90 degrees; right = 90 degrees; obtuse between 90 and 180 degrees; straight = 180 degrees; reflex between 180 and 360 degrees.

What are parallel lines and intersecting lines?

Parallel lines lie in the same plane and never meet, staying equal distance apart. Intersecting lines cross at exactly one common point.

Classify triangles by sides and by angles.

By sides: equilateral (all equal), isosceles (two equal), scalene (none equal). By angles: acute (all < 90), right (one = 90), obtuse (one > 90).

Name the types of quadrilaterals and one distinguishing property of each.

Square (4 equal sides, 4 right angles), rectangle (opposite sides equal, 4 right angles), rhombus (4 equal sides), parallelogram (opposite sides equal and parallel), trapezium (one pair of parallel sides).

What is the angle sum property of a triangle and of a quadrilateral?

The sum of the interior angles of a triangle is 180 degrees, and the sum of the interior angles of a quadrilateral is 360 degrees.

Define radius, diameter, chord, and circumference of a circle.

Radius: distance from centre to any point on the circle. Diameter: a chord through the centre, equal to twice the radius. Chord: a segment joining two points on the circle. Circumference: the distance around the circle.

What is the difference between 2D and 3D shapes, and name the parts of a 3D solid.

2D shapes are flat with length and breadth only; 3D shapes are solids with length, breadth, and height. A solid has faces (flat surfaces), edges (where faces meet), and vertices (corners).

State the formula for the perimeter and area of a rectangle and a square.

Rectangle: perimeter = 2(length+breadth), area = length x breadth. Square: perimeter = 4 x side, area = side x side.

State the formulas for the circumference and area of a circle.

Circumference = 2 x pi x r and area = pi x r^2, where r is the radius and pi is approximately 22/7 or 3.14.

State the formula for the area of a triangle and a parallelogram.

Area of a triangle = 1/2 x base x height. Area of a parallelogram = base x height.

What is the difference between perimeter, area, and volume?

Perimeter is the length around a 2D figure (units). Area is the surface a 2D figure covers (square units). Volume is the space a 3D solid occupies (cubic units).

In data handling, what are the mean, median, and mode?

Mean is the sum of observations divided by their number (average). Median is the middle value when data is arranged in order. Mode is the value that occurs most frequently.

What is the difference between a pictograph, a bar graph, and a pie chart?

A pictograph uses pictures/symbols to show data. A bar graph uses bars of equal width to compare quantities. A pie chart uses sectors of a circle to show parts of a whole.

According to NCF 2005, what is the main aim of teaching mathematics in schools?

The higher aim is to develop the child's ability to think and reason, to mathematise (handle abstractions), and to pursue assumptions to their logical conclusion, not merely to compute. It is about 'mathematisation of the child's thought process'.

Why is using children's community and everyday (folk) mathematics important in teaching?

Linking school mathematics to the child's home language and real-life experiences (buying, measuring, games) makes learning meaningful, reduces math anxiety, and builds on the informal knowledge the child already has.

What is diagnostic and remedial teaching in mathematics, and how do they relate to evaluation?

Diagnostic teaching identifies a learner's specific errors and misconceptions through analysis of their work; remedial teaching then provides targeted instruction to correct those gaps. Both rely on continuous, comprehensive evaluation rather than only marks, treating errors as a window into the child's thinking.