CTET (Central Teacher Eligibility Test) Mathematics and Pedagogy Syllabus

Mathematics and Pedagogy syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics and Pedagogy in CTET (Central Teacher Eligibility Test), not a summary of it.

1. 1

   Number System and Arithmetic

   4 topics

   • Numbers and Place Value
     • Whole numbers, place value and number names
     • Indian and international system of numeration
   • Operations on Numbers
     • Addition, subtraction, multiplication and division
     • Factors, multiples, HCF and LCM
   • Fractions and Decimals
     • Types of fractions and operations
     • Decimals and their operations
   • Integers, Rational Numbers and Exponents
     • Operations on integers and rational numbers
     • Powers, exponents and squares/cubes
2. 2

   Algebra (Upper Primary)

   3 topics

   • Introduction to Algebra
     • Variables, constants and algebraic expressions
   • Linear Equations
     • Simple linear equations in one variable
   • Ratio, Proportion and Percentage
     • Ratio and proportion
     • Percentage, profit, loss and simple interest
3. 3

   Geometry and Mensuration

   3 topics

   • Basic Geometrical Ideas
     • Points, lines, angles and shapes
     • Symmetry and patterns
   • Shapes and Spatial Understanding
     • 2D and 3D shapes
     • Solids around us
   • Mensuration
     • Perimeter and area of plane figures
     • Volume and surface area of solids
4. 4

   Data Handling and Measurement

   3 topics

   • Data Handling
     • Collection, organisation and representation of data
     • Pictographs, bar graphs and tables
   • Money
     • Currency and transactions
   • Measurement
     • Length, weight, time, volume and temperature
5. 5

   Pedagogical Issues in Mathematics

   4 topics

   • Nature and Place of Mathematics
     • Mathematics in the curriculum
     • Logical thinking and reasoning
   • Language and Community Mathematics
     • Language of mathematics
     • Community mathematics and contextual learning
   • Diagnostic and Remedial Teaching
     • Error analysis and conceptual difficulties
     • Diagnostic and remedial strategies
   • Evaluation in Mathematics
     • Formal and informal methods of evaluation
     • Problem-solving as a strategy

Mathematics and Pedagogy flashcards for CTET (Central Teacher Eligibility Test)

20 of 50 cards from the Mathematics and Pedagogy deck — real questions with worked answers.

1. What is the difference between a number and a numeral?

   A number is an abstract idea of quantity; a numeral is the symbol or group of symbols (like 7 or VII) used to represent that number in writing.

2. In the Indian place value system, what are the place values of digits after thousands, up to crore?

   Ones, tens, hundreds, thousands, ten-thousands, lakhs (1,00,000), ten-lakhs, and crores (1,00,00,000).

3. How does the Indian place value system differ from the International system for large numbers?

   The Indian system uses lakhs and crores with comma groupings of 2 digits after the first 3 (xx,xx,xxx), while the International system uses thousands, millions, billions with groupings of 3 digits (xxx,xxx,xxx).

4. What is the difference between the face value and place value of a digit?

   Face value is the digit itself regardless of position; place value is the digit multiplied by the value of its position. In 358, the face value of 5 is 5, but its place value is 50.

5. What is the largest 5-digit number and the smallest 6-digit number, and how are they related?

   The largest 5-digit number is 99,999 and the smallest 6-digit number is 1,00,000; they are consecutive, so adding 1 to 99,999 gives 1,00,000.

6. State the four fundamental operations on numbers and their inverse pairs.

   Addition, subtraction, multiplication, and division. Subtraction is the inverse of addition, and division is the inverse of multiplication.

7. State the commutative, associative, and distributive properties with an example each.

   Commutative: a+b=b+a (2+3=3+2). Associative: (a+b)+c=a+(b+c). Distributive: a(b+c)=ab+ac, e.g. 2(3+4)=2x3+2x4.

8. What is the role of 0 and 1 as identity elements in operations?

   0 is the additive identity (a+0=a) and 1 is the multiplicative identity (a x 1 = a). Multiplying any number by 0 gives 0.

9. In the order of operations (BODMAS/DMAS), what is the correct sequence?

   Brackets, Of (orders/powers), Division, Multiplication, Addition, Subtraction. Division and multiplication are done left to right, then addition and subtraction left to right.

10. How are quotient and remainder related to dividend and divisor (Euclid's division)?

    Dividend = (Divisor x Quotient) + Remainder, where the remainder is always less than the divisor (0 <= r < divisor).

11. What is a fraction, and what do its numerator and denominator represent?

    A fraction represents a part of a whole or a group. The denominator (bottom) tells the total number of equal parts; the numerator (top) tells how many of those parts are taken.

12. Differentiate between proper, improper, and mixed fractions.

    Proper: numerator < denominator (3/5). Improper: numerator >= denominator (7/5). Mixed: a whole number with a proper fraction (1 2/5).

13. What are equivalent fractions and how are they formed?

    Equivalent fractions name the same value, e.g. 1/2 = 2/4 = 3/6. They are formed by multiplying or dividing both numerator and denominator by the same non-zero number.

14. How do you add or subtract fractions with unlike denominators?

    Find the LCM of the denominators to get a common denominator, convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators.

15. How do you convert a decimal to a fraction and a fraction to a decimal?

    Decimal to fraction: write the decimal over a power of 10 (0.75 = 75/100 = 3/4) and simplify. Fraction to decimal: divide the numerator by the denominator.

16. What is the difference between terminating and recurring (non-terminating repeating) decimals?

    A terminating decimal ends after a finite number of digits (0.25); a recurring decimal has one or more digits repeating endlessly (0.333... = 0.3 with a bar).

17. What are integers and how are they ordered on the number line?

    Integers are the set ...-3,-2,-1,0,1,2,3... including negatives, zero, and positives. On the number line, values increase to the right, so any number is greater than the one to its left.

18. State the rules of signs for multiplying and dividing integers.

    Like signs give a positive result (+ x + = +, - x - = +); unlike signs give a negative result (+ x - = -, - x + = -). The same rules apply to division.

19. What is a rational number, and is every integer a rational number?

    A rational number can be written as p/q where p and q are integers and q is not 0. Yes, every integer is rational since it can be written with denominator 1 (5 = 5/1).

20. State the laws of exponents for a^m x a^n, a^m / a^n, and (a^m)^n.

    a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn). Also a^0 = 1 and a^(-m) = 1/a^m.

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