Objective Questions and Answers: 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) In CCE, assessment process includes assessment of previous knowledge, understanding level and learning process.
(b) For CCE, teachers feel that each one of them has to give some home assignment every day to assess children's learning.
(c) CCE is all about converting marks into grades.
(d) In CCE, there is more testing and less teaching.
Show Answer & Explanation
Answer: (a) In CCE, assessment process includes assessment of previous knowledge, understanding level and learning process.
Explanation:
1. CCE is continuous (regular, during learning) and comprehensive (covers scholastic and co-scholastic areas).
2. It looks at prior knowledge, understanding and the learning process, not only final marks.
3. Options b, c and d describe misconceptions about CCE.
Teacher's Note:
1. CCE is meant to reduce stress and testing, not increase it.
2. Grading is only a reporting tool, not the purpose of CCE.
A. It represents a conceptual analysis of a concept using contributory sub-concepts.
B. They are directional, with arrows showing which concepts are prerequisite for which others.
C. They cannot be used for diagnostic purposes to identify difficulties in learning a particular concept.
D. They cannot be used frequently as they are very time consuming.
Choose the correct option:
(a) B and D
(b) Only C
(c) C and D
(d) A and B
Show Answer & Explanation
Answer: (d) A and B
Explanation:
1. A concept map breaks a concept into linked sub-concepts (A is true).
2. Arrows show prerequisite order (B is true).
3. Concept maps can be used diagnostically and are not too time consuming to use, so C and D are false.
Teacher's Note:
1. Concept maps help locate the missing prerequisite behind a learning difficulty.
2. Statements with 'cannot' are usually the false ones in such questions.
(a) Mathematics at school level requires special aptitude in learners.
(b) Primary concepts in mathematics are abstract in nature.
(c) Mathematics is based on deductive reasoning.
(d) Mathematics is much more abstract and hierarchic than most of the other subjects which children learn at the same age.
Show Answer & Explanation
Answer: (a) Mathematics at school level requires special aptitude in learners.
Explanation:
1. Mathematics is abstract, hierarchical and deductive (b, c, d are true).
2. NCF 2005 holds that all children can learn mathematics, so special aptitude is not required at school level.
Teacher's Note:
1. The belief that mathematics is only for the gifted is a myth NCF 2005 rejects.
2. Hierarchic means later topics depend on earlier ones.
A. It can be understood as a line of reasoning that intends to show or explain why a mathematical result is true.
B. It is always helpful in mathematics in the same manner as in other empirical disciplines.
C. It can also be a part of the heuristic approach in mathematics education.
D. It is less useful for elementary grade students as its assessment will be difficult.
Choose the correct option:
(a) A and C
(b) B and C
(c) A and B
(d) A and D
Show Answer & Explanation
Answer: (a) A and C
Explanation:
1. A is the standard description of argumentation.
2. C is true: argumentation supports discovery (heuristic) learning.
3. B is false because mathematics is deductive, not empirical; D is false because argumentation is useful at every level.
Teacher's Note:
1. Argumentation develops reasoning from the early grades.
2. Reject statements with 'always' or that dismiss young learners.
(a) not important at all as it does not help in developing mathematical understanding.
(b) a proposition or conclusion that has been proved.
(c) important for students of secondary level only.
(d) a proposition or conclusion that is assumed to be true on a tentative basis without proof.
Show Answer & Explanation
Answer: (d) a proposition or conclusion that is assumed to be true on a tentative basis without proof.
Explanation:
1. A conjecture is a statement believed true on evidence or patterns but not yet proved.
2. Once proved it becomes a theorem, so option b is wrong.
Teacher's Note:
1. Making and testing conjectures is a key part of mathematical reasoning at all levels.
2. Conjecture: unproved; theorem: proved.
(a) Generalisation
(b) Theorem
(c) Conjecture
(d) Axiom
Show Answer & Explanation
Answer: (c) Conjecture
Explanation:
1. The statement is based on a pattern (5, 7, 11, 13, ...) and is not proved.
2. It is actually false (for example 25 = 6×4 + 1 is not prime), so it cannot be a theorem or axiom.
3. An unproved, tentative statement from a pattern is a conjecture.
Teacher's Note:
1. Every prime above 3 is 6k ± 1, but the converse is false.
2. Patterns suggest conjectures; only proof makes them theorems.
A. Simrat pays ₹ 60,000 as rent for three months. How much will she have to pay for a whole year if the rent per month remains same?
B. Cost of three dozen bananas is ₹45. Calculate the number of bananas that can be purchased for ₹ 12.50.
C. Joey and Jenny are going to school. Joey started walking before Jenny. When Joey was at the third block, Jenny was at the first block. If both are walking with the same speed, then where would Jenny be if Joey is at the ninth block?
Which of the following is correct with respect to the above three questions?
(a) Only A is based on unitary method.
(b) B and C are daily life problems based on unitary method.
(c) A and C are daily life problems based on unitary method.
(d) A and B are daily life problems based on unitary method.
Show Answer & Explanation
Answer: (d) A and B are daily life problems based on unitary method.
Explanation:
1. A: rent for 1 month = 20,000, then ×12; B: price of 1 banana = 45/36, then find the number for ₹12.50 (10 bananas). Both use the unitary method.
2. C: the gap between them stays 2 blocks (additive), so Jenny would be at block 7. This is not proportional.
Teacher's Note:
1. Constant difference means additive reasoning, not proportion.
2. Check whether the ratio, not the difference, stays constant before using unitary method.
(A) It can be understood as a line of reasoning that intends to show or explain why a mathematical result is true
(B) A mathematical argument might be a formal or informal proof.
(C) It can also be a part of the Heuristic approach in mathematics education
(D) It cannot be used for teaching mathematics as argumentation is important only for social science
Choose the correct option.
(a) (A) and (D)
(b) (A), (B) and (C)
(c) (A), (B) and (D)
(d) (C) and (D)
Show Answer & Explanation
Answer: (b) (A), (B) and (C)
Explanation:
1. A, B and C correctly describe argumentation in mathematics.
2. D is false because reasoning and argument are central to mathematics.
Teacher's Note:
1. Arguments in class may be informal explanations or formal proofs.
2. Discard options that include the false statement D.
(a) Conservation of area
(b) Conservation of volume
(c) Estimation
(d) Proportional Thinking
Show Answer & Explanation
Answer: (d) Proportional Thinking
Explanation:
1. Half the cake needs half the butter, so the ratio butter : cake stays constant.
2. Keeping the ratio constant is proportional thinking.
Teacher's Note:
1. Proportional thinking is multiplicative, not additive.
2. Recipes and scaling are standard examples of proportion.
(a) focusing on formal algorithm in the class
(b) solving many questions herself in the class
(c) using summative assessment strategies
(d) using alternate pedagogical strategies
Show Answer & Explanation
Answer: (d) using alternate pedagogical strategies
Explanation:
1. Conceptual errors arise from misunderstanding, so repeating the same method will not help.
2. Trying alternate strategies (models, activities, examples) helps the child rebuild the concept.
Teacher's Note:
1. Diagnose the error first, then re-teach differently.
2. Summative tests only measure; they do not remedy.
(a) Wastes too much time of classroom teaching
(b) Gives opportunity to teacher to perform other activities of the class
(c) Should be a regular practice of the class
(d) Gives students a chance to relax in the class
Show Answer & Explanation
Answer: (c) Should be a regular practice of the class
Explanation:
1. Independent attempts build problem solving, confidence and ownership of learning.
2. So the practice should be regular, not occasional.
Teacher's Note:
1. Productive struggle is part of learning mathematics.
2. The teacher should monitor and support, not leave the class unattended.
Name of the place: Auli, Srinagar, Shimla, Ooty, Bangaluru
Temperature (°C): −10, −4, 3, 12, 27
Questions:
A. Which place has the lowest and highest temperature?
B. What is the difference between temperature of Ooty and Bangaluru?
C. Arrange the places in the increasing order of temperature.
D. Is the temperature of Srinagar and Shimla taken together less than the temperature of Shimla?
Which of the following is most appropriate in the context of above situation?
(a) It can be used to introduce Data handling to grade V learners.
(b) It can be used to introduce the concept of Integers to grade VI learners.
(c) The question is misleading for students.
(d) It can be used as an integrated assessment activity after teaching integers and Data handling.
Show Answer & Explanation
Answer: (d) It can be used as an integrated assessment activity after teaching integers and Data handling.
Explanation:
1. The questions need negative numbers (integers) and reading and arranging data, so students must already know both topics.
2. Hence the set suits an integrated assessment after teaching integers and data handling.
Teacher's Note:
1. Questions like D (adding −4 and 3) need prior knowledge of integer operations.
2. Such tasks are better for assessing than introducing a topic.
(a) Establishing Relationships
(b) Recognition
(c) Analysis
(d) Axiomatics
Show Answer & Explanation
Answer: (a) Establishing Relationships
Explanation:
1. Observing properties is Level 2 (analysis), but linking shapes and verifying properties informally is Level 3 (informal deduction, or establishing relationships).
2. Formal proofs and axiom systems belong to Level 4 or 5, which the students have not reached.
Teacher's Note:
1. Van Hiele levels: visualisation, analysis, informal deduction, deduction, rigour.
2. Relating classes of shapes without formal proof is the clue for Level 3.
(a) Algebraic equations are solved by using mathematical symbols hence these symbols should be memorized
(b) Algebra involves the process of creating generalizations from arithmetic
(c) Algebra involves representing patterns and regularities in our world
(d) Algebra is more abstract and symbolic hence cannot be taught through concrete experiences
Choose the correct option.
(a) (a) and (d)
(b) (b) and (d)
(c) (a) and (c)
(d) (b) and (c)
Show Answer & Explanation
Answer: (d) (b) and (c)
Explanation:
1. Generalising from arithmetic (b) and representing patterns with symbols (c) match the statement.
2. Memorising symbols (a) and denying concrete experiences (d) do not.
Teacher's Note:
1. Algebra can be introduced through patterns and concrete situations.
2. Treat symbols as tools for expressing generality, not things to memorise.
(a) Assessment in Mathematics is done only to test if the student knows or does not know the answer.
(b) Assessment in Mathematics is designed to test the student's capability of arriving at a unique answer using the correct procedures.
(c) Assessment techniques in Mathematics focus on process of learning hence gives scope of discussing multiple ways of doing a problem.
(d) Assessment is focused on testing the memorisation of facts and formulae rather than concept learning.
Choose the correct option
(a) (b) and (c)
(b) Only (c)
(c) (a), (c) and (d)
(d) (a), (b) and (d)
Show Answer & Explanation
Answer: (a) (b) and (c)
Explanation:
1. Anxiety is fuelled by right-or-wrong assessment, a single correct answer and memorisation: statements (a), (b) and (d).
2. Statement (c) describes process-focused assessment, which reduces anxiety, so it is not a reason. The correct combination is (a), (b) and (d), which is the last option.
Teacher's Note:
1. Process-focused assessment lowers fear; product-only assessment raises it.
2. Check each statement separately before choosing the combination.
(A) Looking for patterns
(B) Solving a problem using a formula
(C) Making and testing conjectures
Choose the correct option:
(a) (A) and (B)
(b) (A) and (C)
(c) (B) and (C)
(d) Only (C)
Show Answer & Explanation
Answer: (b) (A) and (C)
Explanation:
1. Reasoning involves finding patterns and making and testing conjectures.
2. Applying a formula is routine computation, not reasoning.
Teacher's Note:
1. Reasoning means justifying and generalising, not just calculating.
2. Formula application is procedural skill.
(a) Drawing a picture of a dice on the blackboard and talk about the possible outcomes
(b) Giving the definition of probability followed by solving textbook questions
(c) Asking students to throw a dice or flip a coin and note down the number of times each possibility occurs
(d) Asking students to find out information about probability from the internet
Show Answer & Explanation
Answer: (c) Asking students to throw a dice or flip a coin and note down the number of times each possibility occurs
Explanation:
1. An activity based method has students do an experiment themselves.
2. Throwing a dice or tossing a coin and recording outcomes lets children discover probability from data.
Teacher's Note:
1. Activities should come before formal definitions.
2. Drawing or telling is teacher-centred.
(a) To draw a table of axioms
(b) To explain the steps of drawing figures
(c) To give an argument or justification of statements
(d) To use observation
Show Answer & Explanation
Answer: (c) To give an argument or justification of statements
Explanation:
1. A proof is a chain of logical statements, each justified by earlier results.
2. So students should learn to give an argument or justification for each statement.
Teacher's Note:
1. Observation and measurement are not proof.
2. Encourage 'why' for every step.
(a) Clinometer
(b) Manometer
(c) Spherometer
(d) Vernier Callipers
Show Answer & Explanation
Answer: (a) Clinometer
Explanation:
1. A clinometer measures angles of elevation, and the ratios of height to distance give the trigonometric ratios.
2. A manometer measures pressure, a spherometer curvature and vernier callipers small lengths.
Teacher's Note:
1. A clinometer can be made from a protractor, string and weight.
2. Use it for height and distance activities.
(a) Design a bangle for your sister using a flexible metal wire.
(b) How will you derive the area of a circle by dividing it into smaller pieces?
(c) What will be the area of a circle with diameter 20 cm?
(d) Buy the right amount of paint for painting a circular table in school.
Show Answer & Explanation
Answer: (d) Buy the right amount of paint for painting a circular table in school.
Explanation:
1. An authentic task applies the concept to a real-life situation.
2. Buying paint for a circular table needs the area of a circle; a bangle involves circumference, not area.
Teacher's Note:
1. Authentic tasks connect the learned concept to real use.
2. Check that the task actually uses the concept taught.
(a) Punish the student so that he/she does not repeat the mistake.
(b) Ask the student to rote memorise the theorem.
(c) Use multisensory models and teaching aids to help student understand various theorems and their applications.
(d) Tell the student to copy the steps of solved problems from the black board and apply the method for similar problems.
Show Answer & Explanation
Answer: (c) Use multisensory models and teaching aids to help student understand various theorems and their applications.
Explanation:
1. The difficulty is conceptual, so the remedy should build understanding.
2. Multisensory models and aids help the learner see and use the theorems.
Teacher's Note:
1. Punishment and rote learning do not build understanding.
2. Concrete models support geometric thinking.
(a) Credit and debit statements in bank account.
(b) Various blood groups like A+, AB+, O- etc.
(c) Temperature going below and above 0 °C.
(d) Slowing down of a vehicle as negative acceleration and speeding up as positive acceleration.
Show Answer & Explanation
Answer: (b) Various blood groups like A+, AB+, O- etc.
Explanation:
1. Integers model opposite quantities: credit and debit, temperature above and below zero, acceleration and deceleration.
2. Blood group signs + and − are only labels and do not represent numbers, so this cannot explain integers.
Teacher's Note:
1. Choose contexts where a quantity has a size and an opposite direction.
2. Labels using the signs + and − are not numbers.
(a) There is lack of rigorous written practice of questions among students
(b) They do not practice from model test papers
(c) They make alternative interpretations of concepts
(d) Their socio-economic status affects their performance
Show Answer & Explanation
Answer: (c) They make alternative interpretations of concepts
Explanation:
1. Errors usually show systematic alternative conceptions that students have built.
2. So the most appropriate reason is their alternative interpretation of concepts.
Teacher's Note:
1. Errors are windows into thinking and should be analysed.
2. Do not blame practice or background first.
(a) Asking open-ended questions
(b) Asking questions based on recall of formulae, tables and figures
(c) Asking closed ended questions
(d) Giving problems based on use of only formal algorithms
Show Answer & Explanation
Answer: (a) Asking open-ended questions
Explanation:
1. Higher order skills need explanation, multiple approaches and reasoning.
2. Open-ended questions allow this; recall, closed and algorithm-only questions test lower-order skills.
Teacher's Note:
1. Higher order: analyse, evaluate, create.
2. Open-ended tasks reveal thinking.
(A) Solving real life problems using mathematical abstractions
(B) Finding alternate ways to solve problems
(C) Stating the theorem and writing its proof
Choose the correct option:
(a) (A) and (B)
(b) (B) and (C)
(c) (A) and (C)
(d) Only (B)
Show Answer & Explanation
Answer: (a) (A) and (B)
Explanation:
1. Modelling real problems and finding alternate methods need original thinking.
2. Stating a known theorem and its proof is reproduction.
Teacher's Note:
1. Creativity means new ways, not recall.
2. Look for original or flexible approaches.
(a) Emphasing on the significance of zero in various contexts
(b) Passing her time as students are not in mood of studying
(c) Developing problem solving skills among the students
(d) Using her mathematics class to develop life skills among the students
Show Answer & Explanation
Answer: (a) Emphasing on the significance of zero in various contexts
Explanation:
1. The debate topic is the importance of zero.
2. Students discuss its role in different contexts, so the teacher is emphasising the significance of zero.
Teacher's Note:
1. Match the activity to its direct aim.
2. Debate here is about a concept, not problem solving.
(a) What mathematics education can do to engage the mind of every student and how it can strengthen the student's resources
(b) What mathematics education can do to improve communication skills of every child and how it can make them employable
(c) What mathematics education can do to control the dropout rate of children and how it can improve their scores
(d) What mathematics education can do to prepare students for olympiads and how it can help to choose right subject stream in higher classes.
Show Answer & Explanation
Answer: (a) What mathematics education can do to engage the mind of every student and how it can strengthen the student's resources
Explanation:
1. NCF 2005 states two concerns: what mathematics can do to engage the mind of every student, and how it can strengthen the student's resources.
2. The other options are not stated as the twin concerns.
Teacher's Note:
1. NCF 2005 focuses on every child's mind and resources.
2. Be wary of options about scores or employability.
(a) Taylor's abacus
(b) Tangram
(c) Geoboard
(d) Geo-gebra
Show Answer & Explanation
Answer: (d) Geo-gebra
Explanation:
1. Taylor's abacus, tangram pieces and geoboard can be felt by touch.
2. GeoGebra depends on screen visuals, so it cannot be used by visually challenged students without special support.
Teacher's Note:
1. Prefer tactile aids for visually challenged learners.
2. Purely visual software is unsuitable.
(a) The mathematical model → Real life problem → The mathematical solution → The solution in real world
(b) Real life problem → The mathematical model → The mathematical solution → The solution in real world
(c) The mathematical model → Real life problem → The solution in real world → The mathematical solution
(d) The mathematical model → Real life problem → The mathematical solution → The solution in real world
Show Answer & Explanation
Answer: (b) Real life problem → The mathematical model → The mathematical solution → The solution in real world
Explanation:
1. Modelling starts from a real-life problem, which is converted into a mathematical model.
2. The model is solved mathematically and the solution is interpreted in the real world.
Teacher's Note:
1. Cycle: real problem, model, math solution, real-world interpretation.
2. Options a and d are identical and both wrongly start with the model.
Free study material for Mathematics
Multiple Choice Questions (MCQs) for CTET Mathematics
Download Multiple Choice Questions: Mathematics (CTET )
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Concept Clarification for Mathematics
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FAQs
You can get most exhaustive CTET Mathematics Paper 2 MCQs with Answers Set 01 for free on StudiesToday.com. These MCQs for CTET are updated for the 2026-27 academic session as per CTET examination standards.
Yes, our CTET Mathematics Paper 2 MCQs with Answers Set 01 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CTET paper is now competency-based.
By solving our CTET Mathematics Paper 2 MCQs with Answers Set 01, 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.
Yes, you can also access online interactive tests for CTET Mathematics Paper 2 MCQs with Answers Set 01 on StudiesToday.com as they provide instant answers and score to help you track your progress in .