Practice MCQs for CTET Mathematics
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These 29 CTET Mathematics Paper 2 multiple choice questions cover mathematics content and pedagogy of mathematics. Each question has the correct answer with a step-by-step explanation and a short teacher's note, so you can practise for the Central Teacher Eligibility Test and check your understanding.
Multiple Choice Questions
a. creative thinking
b. divergent thinking
c. equity in classroom
d. convergent thinking
Which one of the following is correct?
(a) Only c
(b) a & b
(c) a, b & c
(d) b & d
Show Answer & Explanation
Answer: (c) a, b & c
Explanation:
1. Open-ended problems have many answers and methods, which promotes creative and divergent thinking.
2. They also let learners of different levels participate, supporting equity, but they do not promote convergent thinking.
Teacher's Note:
1. Convergent thinking leads to one correct answer.
2. Open-ended means divergent.
a. Provide hands-on experience for the learning of the concept.
b. Provide a richer mathematics environment which will lead to deeper understanding of the concept.
c. Provide open-ended questions for discussion.
d. Promote the use of calculator.
(a) (b) and (d)
(b) (a) and (d)
(c) (a), (b) and (c)
(d) (a) and (c)
Show Answer & Explanation
Answer: (c) (a), (b) and (c)
Explanation:
1. Hands-on experience, a rich environment and open-ended discussion all build understanding of concepts.
2. Promoting calculators does not help prevent conceptual errors.
Teacher's Note:
1. Conceptual errors come from misunderstanding, so use concrete experience and discussion.
2. Calculators help calculation, not concepts.
(a) To provide some leisure time in the class
(b) To make the lecture joyful
(c) To engage students in the class while she is busy in some work
(d) To let students explore various properties of numbers and patterns
Show Answer & Explanation
Answer: (d) To let students explore various properties of numbers and patterns
Explanation:
1. The sum of a two-digit number and its reverse is 11(a + b), so the quotient is always a + b.
2. The activity lets students discover this pattern.
Teacher's Note:
1. Number tricks are used to explore patterns and reasoning.
2. Be careful with options that only call it fun.
(a) By not interfering at all as children will learn eventually
(b) By demonstrating correct procedures followed by revision
(c) By observing their work and talking to them to know their understanding
(d) By suggesting some good books for practice
Show Answer & Explanation
Answer: (c) By observing their work and talking to them to know their understanding
Explanation:
1. A teacher must first find out what the child thinks and why, through observation and conversation.
2. Only then can she plan activities that correct the misconception.
Teacher's Note:
1. Diagnose before remediating.
2. Repeating the procedure does not remove a wrong idea.
(a) analysis of errors made by the students
(b) classwork and homework done by the students
(c) projects and portfolios
(d) term-end examinations
Show Answer & Explanation
Answer: (d) term-end examinations
Explanation:
1. Formative assessment is continuous and happens during learning.
2. A term-end examination is summative.
Teacher's Note:
1. Formative: for learning. Summative: of learning.
2. Error analysis, class work and portfolios are all formative.
(a) reflect upon her classroom practices and the participation of students in her mathematics class.
(b) be satisfied with the achievements of the two groups in her class.
(c) not bother as it is the natural talent of girls to be good at mathematics than boys.
(d) make the boys in her class practice more questions.
Show Answer & Explanation
Answer: (a) reflect upon her classroom practices and the participation of students in her mathematics class.
Explanation:
1. A gap between groups suggests something in the classroom may favour one group.
2. A reflective teacher examines her practices and the participation of all students.
Teacher's Note:
1. Gender differences are not natural ability but result of practice and environment.
2. Reflection is the first step.
(a) Mathematics should be taught to only those students who plan to pursue it in higher classes.
(b) Difficult concepts should be omitted for disinterested students.
(c) Students should be provided with context which highlights the need for mathematical concepts.
(d) The concepts which are tested in year-end examination must be taught in detail.
Show Answer & Explanation
Answer: (c) Students should be provided with context which highlights the need for mathematical concepts.
Explanation:
1. Important mathematics is mathematics whose need and use the students can see in context.
2. The other options narrow mathematics to a few learners or to examinations.
Teacher's Note:
1. NCF 2005 says all children can learn worthwhile mathematics.
2. Link concepts to contexts.
(a) It is an application of geometry in algebra
(b) It is a branch of mathematics dealing with geometry and algebra
(c) It is a specialized topic in geometry
(d) It is a software used in exploring geometry
Show Answer & Explanation
Answer: (d) It is a software used in exploring geometry
Explanation:
1. GeoGebra is dynamic mathematics software.
2. It is used to construct and explore geometry (and algebra and graphs) interactively.
Teacher's Note:
1. GeoGebra is a tool, not a branch of mathematics.
2. It helps students visualise and test conjectures.
(a) Must create a stimulating atmosphere conducive to learning
(b) Must possess the desire, passion and patience to facilitate the learning among children
(c) Willing to learn new methods and strategies for introducing concepts to students
(d) Help students in securing full marks in examinations and tests
Show Answer & Explanation
Answer: (d) Help students in securing full marks in examinations and tests
Explanation:
1. Options (a) to (c) describe a facilitating, learning-oriented teacher.
2. Aiming only at full marks narrows teaching to examinations, which is not desirable.
Teacher's Note:
1. Effective teaching targets understanding, not just marks.
2. Look for the exam-centred option.
(a) Drawing different figures on a graph paper and counting the number of squares to calculate the area
(b) Drawing different figures on graph paper and counting the number of boundaries of the figures
(c) Adding the measures of all the sides of a figure drawn on a graph paper to calculate the area
(d) The area of a square is measured in square units and the area of a circle is measured in circle units
Show Answer & Explanation
Answer: (a) Drawing different figures on a graph paper and counting the number of squares to calculate the area
Explanation:
1. Area is the number of unit squares that cover a region, which is shown by counting squares on graph paper.
2. Counting boundaries or adding sides gives perimeter, not area.
Teacher's Note:
1. Area covers a surface, so its unit is a square.
2. Do not mix area with perimeter.
(a) Criterion Referenced Assessment is to evaluate the mastery learning of the students against a criteria
(b) Criterion Referenced Assessment is useful in diagnostic testing and remedial teaching
(c) Norm-Referenced Assessment tells us where a student stands compared to other students in her performance
(d) Norm-Referenced Assessment is useful in diagnostic testing and remedial teaching
Show Answer & Explanation
Answer: (d) Norm-Referenced Assessment is useful in diagnostic testing and remedial teaching
Explanation:
1. Criterion-referenced assessment compares performance with a standard, so it suits diagnosis and remediation.
2. Norm-referenced assessment only ranks students and does not diagnose, so (d) is incorrect.
Teacher's Note:
1. Norm-referenced: compared with peers. Criterion-referenced: compared with a standard.
2. Diagnosis needs criteria.
(a) Many people still use non-standard units of measurement.
(b) Non-standard units provide a good rationale for the need of a standard unit.
(c) They have no other relevance but to add some fun in a boring mathematics class.
(d) Use of non-standard units is the only way to provide some concrete experience to children with special needs before teaching measurement.
Show Answer & Explanation
Answer: (b) Non-standard units provide a good rationale for the need of a standard unit.
Explanation:
1. Measuring with hand spans or pencils gives different results for different people.
2. This shows children why a common standard unit is needed.
Teacher's Note:
1. Non-standard units come first in measurement.
2. They lead to the idea of standardisation.
(a) Like and unlike terms
(b) Algebraic identities
(c) Operations of algebraic expressions
(d) Degree of variables
Show Answer & Explanation
Answer: (a) Like and unlike terms
Explanation:
1. Monomials, binomials and trinomials are named by the number of terms.
2. So students must first know what a term is and how like and unlike terms differ.
Teacher's Note:
1. Classification of expressions is based on the number of terms.
2. Identities and operations come later.
(a) A child promptly solves mathematical problems
(b) A child has memorized all important mathematical formulae
(c) A child understands and makes connections across concepts
(d) A child knows all the standard algorithms of solving problems
Show Answer & Explanation
Answer: (c) A child understands and makes connections across concepts
Explanation:
1. NCF 2005 describes mathematisation as the ability to think logically, abstract and see relationships.
2. Understanding and connecting concepts shows this, unlike speed or memory.
Teacher's Note:
1. Mathematisation of thought is the main aim of NCF 2005.
2. Speed and memory are not the same as understanding.
(a) Arithmetic
(b) Relations and Functions
(c) Integral Calculus
(d) Differential Calculus
Show Answer & Explanation
Answer: (a) Arithmetic
Explanation:
1. Community mathematics refers to everyday mathematics used by communities such as shopkeepers, which is mostly arithmetic.
2. It does not deal with calculus.
Teacher's Note:
1. Community mathematics is the informal mathematics of daily life.
2. It is mainly arithmetic.
(a) Verification
(b) Deduction
(c) Induction
(d) Contradiction
Show Answer & Explanation
Answer: (a) Verification
Explanation:
1. Cutting and placing the angles checks the result for one triangle.
2. This is verification, not a deductive proof.
Teacher's Note:
1. Verification checks a result for examples.
2. A deductive proof uses logic that holds for every triangle.
(a) It requires the skills of recall and reproduction to solve the question
(b) A teacher should use open ended questions to enhance creativity among learners in mathematics
(c) This question hampers the student's understanding of perimeter of a rectangle
(d) Only computational skills are required to solve the question
Show Answer & Explanation
Answer: (b) A teacher should use open ended questions to enhance creativity among learners in mathematics
Explanation:
1. Many pairs have length plus breadth equal to 12 cm, so the question has several answers.
2. Such an open-ended question promotes creativity and reasoning.
Teacher's Note:
1. Open-ended questions have many correct answers.
2. They deepen understanding rather than hamper it.
3x + 4x + 7y
= 7x² + 7y
= 14x²y
This type of error is called as:
(a) Individual error
(b) Procedural error
(c) Conceptual error
(d) Error due to carelessness
Show Answer & Explanation
Answer: (c) Conceptual error
Explanation:
1. The child adds like terms wrongly into x² and then joins unlike terms by adding.
2. This shows the child does not understand like and unlike terms, so it is a conceptual error.
Teacher's Note:
1. Conceptual errors come from misunderstanding an idea, and they are repeated.
2. Careless errors are slips that the child can correct easily.
(a) Inappropriate, as the objective is vague and not well defined
(b) Appropriate, as it reflects the aim of all the units of mathematics syllabus.
(c) Appropriate, as unit of mensuration has a lot of application in day-to-day life.
(d) Inappropriate, as there is no scope of application in this topic
Show Answer & Explanation
Answer: (a) Inappropriate, as the objective is vague and not well defined
Explanation:
1. A specific objective should be precise and measurable.
2. 'Understand the application of mathematics' is too general and not specific to mensuration.
Teacher's Note:
1. Specific objectives should be written with observable action words.
2. Vague objectives cannot be assessed.
(a) The question assesses the students on their ability to compare two decimal numbers.
(b) The response of student B is wrong as 62.39 is the correct answer.
(c) There can be multiple answers to the given question.
(d) The teacher can initiate the discussion and let students critically analyse the reasoning of others.
(a) (a) and (b)
(b) (c) and (d)
(c) Only (b)
(d) (a) and (d)
Show Answer & Explanation
Answer: (d) (a) and (d)
Explanation:
1. 63.92 is closer to 64 than 62.39, so B is right and (b) is false.
2. The closest number is unique, so (c) is false, while (a) and (d) are true.
Teacher's Note:
1. Compare decimals place by place from the left.
2. Student errors can be used for discussion.
(a) to determine a whole when a fractional part is given.
(b) to understand relationship of various quantities in a context.
(c) to read a problem in English language.
(d) to give multiple correct answers for the problem.
(a) (a) and (c)
(b) (a) and (b)
(c) (b) and (d)
(d) Only (a)
Show Answer & Explanation
Answer: (b) (a) and (b)
Explanation:
1. With 2/7 eaten, 5/7 is 20, so the whole is 20 × 7 ÷ 5 = 28 cupcakes.
2. The problem tests finding the whole from a part and relating the quantities, and it has one answer.
Teacher's Note:
1. Find what fraction is left before finding the whole.
2. Reading ability is not the aim of the problem.
(a) Mathematics education cannot be value free
(b) Mathematics education is the most valuable
(c) Value based mathematics education acknowledges and incorporates social, cultural and political values in teaching learning processes
(d) In mathematics examination, asking a value based question in the end develops moral values in students
Show Answer & Explanation
Answer: (c) Value based mathematics education acknowledges and incorporates social, cultural and political values in teaching learning processes
Explanation:
1. Value-based mathematics education recognises the social, cultural and political values in teaching and learning.
2. The other options are either too general or reduce it to one exam question.
Teacher's Note:
1. Values are part of the whole teaching process, not an add-on.
2. Reject options that reduce values to a single question.
(a) Axioms are consistent.
(b) Axioms are propositions which are assumed and accepted without any evidence to prove it.
(c) Axioms are available only in geometry.
(d) Axioms are adequate.
Show Answer & Explanation
Answer: (c) Axioms are available only in geometry.
Explanation:
1. Axioms are assumed statements that are consistent and adequate.
2. They exist in all branches of mathematics, such as arithmetic and algebra, not only geometry.
Teacher's Note:
1. Axioms are accepted without proof and are used to prove theorems.
2. Peano's axioms are an example from number theory.
(a) Decomposition
(b) Pattern recognition
(c) Abstraction
(d) Expression
Show Answer & Explanation
Answer: (d) Expression
Explanation:
1. The elements of computational thinking are decomposition, pattern recognition, abstraction and algorithms.
2. Expression is not one of them.
Teacher's Note:
1. Remember DPAA: decomposition, patterns, abstraction, algorithms.
2. Questions often add a distractor like expression.
(a) Using simple, friendly, and clear language that relates with local language
(b) Introducing mathematical ideas, symbols and signs by connecting them with child's own language
(c) Discouraging the use of local language to express mathematical terms in the classroom
(d) Facilitating learners to associate number concepts, vocabulary, quantities etc. to express their thoughts
Show Answer & Explanation
Answer: (c) Discouraging the use of local language to express mathematical terms in the classroom
Explanation:
1. Communication improves when children use their own and local language to express ideas.
2. Discouraging the local language blocks expression.
Teacher's Note:
1. NEP 2020 and NCF stress the home language.
2. Link new terms to the child's language.
(a) 4 candies cost Rs. 5, and so 10 candies cost Rs. 12.50
(b) Ravi's mother's age is two times that of Ravi's age at present, so when Ravi will be 30 years old, his mother will be 60 years old.
(c) A car covers 8 km in 3 hours at a constant speed, it will cover 12 km in 4.5 hours.
(d) The ratio of number of teachers to that of students in a school has to be 2:30, so for 300 students, there has to be 20 teachers.
Show Answer & Explanation
Answer: (b) Ravi's mother's age is two times that of Ravi's age at present, so when Ravi will be 30 years old, his mother will be 60 years old.
Explanation:
1. (a) 4:5 = 10:12.5 is proportional, (c) 8/3 = 12/4.5 is proportional, and (d) 2:30 = 20:300 is proportional.
2. (b) is not, because the age ratio changes over time: the difference stays constant, so when Ravi is 30 his mother will be older than 60.
Teacher's Note:
1. Proportion needs a constant ratio.
2. Age problems are additive, not proportional.
(a) Using mathematical laboratories
(b) Using mathematical games and puzzles
(c) Using open ended questions
(d) Using only formal algorithms
Show Answer & Explanation
Answer: (d) Using only formal algorithms
Explanation:
1. Laboratories, games and open-ended questions build understanding.
2. Using only formal algorithms leads to rote learning and is not suitable.
Teacher's Note:
1. NCF 2005 discourages mechanical drill.
2. The word 'only' makes an option suspect.
(a) It helps teachers in organizing time and resources available with him.
(b) It helps in giving a balanced emphasis to various aspects of content.
(c) It helps in designing a systematic, sequential and graded arrangement of content.
(d) It helps students to manage their teaching learning experiences.
Show Answer & Explanation
Answer: (d) It helps students to manage their teaching learning experiences.
Explanation:
1. Unit planning is done by the teacher to organise time, resources and content in sequence.
2. Students do not plan the teaching-learning experiences, so (d) is not an advantage.
Teacher's Note:
1. Planning is a teacher's task.
2. Eliminate options that give the planning role to students.
(a) density property of numbers
(b) divisible property of fractions
(c) infinite property of fractions
(d) density property of fractions
Show Answer & Explanation
Answer: (d) density property of fractions
Explanation:
1. Between any two fractions there is another fraction, for example their average.
2. This is the density property of fractions.
Teacher's Note:
1. Whole numbers are not dense, but fractions are.
2. The property is named for the set concerned.
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Multiple Choice Questions (MCQs) for CTET Mathematics
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FAQs
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By solving our CTET Mathematics Paper 2 MCQs with Answers Set 04, CTET students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the .
Yes, MCQs for CTET have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CTET exams.
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