CTET Mathematics Paper 2 MCQs with Answers Set 05

Objective Questions and Answers: Mathematics

Access targeted multiple-choice questions for Mathematics designed to align with the latest CTET academic syllabus for CTET . These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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Navigate directly to the 50 objective questions for Mathematics using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

These 28 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

Question 1: Identify the correct statement from among the following.
(a) Formal proofs are obtained only by inductive reasoning.
(b) Hypotheses are always formulated only through deductive logic.
(c) Conjectures have no role in construction of mathematical knowledge.
(d) Counter-examples are helpful in assessing the validity of generalisations.
Show Answer & Explanation

Answer: (d) Counter-examples are helpful in assessing the validity of generalisations.

Explanation:
1. Formal proofs use deduction, not induction, and conjectures are important in building knowledge.
2. A counter-example can show that a generalisation is false, so (d) is correct.

Teacher's Note:
1. Induction suggests a conjecture and deduction proves it.
2. One counter-example disproves a claim.

Question 2: Ravi solved an algebraic equation by adopting following steps:
2x + 14 = 26
→ 2x = 26 − 14
→ 2x = 12
→ 2x/2 = 12/2
→ x = 6
Which method did he adopt?
(a) Visualisation
(b) Transposition
(c) Estimation
(d) Trial-Error
Show Answer & Explanation

Answer: (b) Transposition

Explanation:
1. He moved 14 from the left side to the right side with a changed sign.
2. That is transposition.

Teacher's Note:
1. Transposition changes the sign of the term moved to the other side.
2. It is equivalent to doing the same operation on both sides.

Question 3: "It is more useful to know how to mathematise than to know a lot of mathematics." This statement is given by:
(a) David Wheeler
(b) George Polya
(c) Henri Poincare
(d) Srinivasa Ramanujan
Show Answer & Explanation

Answer: (a) David Wheeler

Explanation:
1. The statement is by David Wheeler, who stressed mathematisation as the main activity of learners.
2. Polya is known for problem solving.

Teacher's Note:
1. NCF 2005 also uses the term mathematisation.
2. Link each thinker with a famous idea.

Question 4: According to Dienes, while teaching mathematics, a teacher should emphasize on:
(a) Rote learning of concepts and formulae
(b) Construction of mathematical concepts followed by abstraction
(c) Abstraction followed by construction of concept
(d) Solving real world problems
Show Answer & Explanation

Answer: (b) Construction of mathematical concepts followed by abstraction

Explanation:
1. Dienes stressed that children first construct concepts through play and concrete experience.
2. Abstraction then follows the construction (constructivity principle).

Teacher's Note:
1. Dienes' stages: free play, games, search for common structure, representation, symbolisation, formalisation.
2. Construction comes before analysis.

Question 5: Integration of Technology with mathematics teaching-learning is faced with many challenges. This is because:
(a) use of technology limits the mathematical visualisation abilities of students
(b) use of calculators limits the development of computational skills in students
(c) it interferes with the role of teacher
(d) mathematics curriculum needs to be redesigned in order to integrate technology
Show Answer & Explanation

Answer: (d) mathematics curriculum needs to be redesigned in order to integrate technology

Explanation:
1. Technology does not limit visualisation and it supports rather than replaces the teacher.
2. Integrating it meaningfully needs changes in the curriculum, so (d) is the reason.

Teacher's Note:
1. Technology integration needs curriculum, training and resources.
2. Avoid options saying technology harms learning.

Question 6: Which of the following(s) is/are true about axioms in mathematics?
a. Axioms are propositions which require proofs.
b. Axioms can be used to prove other mathematical problems.
(a) Only a
(b) Only b
(c) Both a and b are correct
(d) Both a and b are incorrect
Show Answer & Explanation

Answer: (b) Only b

Explanation:
1. Axioms are accepted without proof, so (a) is false.
2. They are the starting point used to prove theorems, so (b) is true.

Teacher's Note:
1. Axioms are assumed statements.
2. Theorems are proved from them.

Question 7: A teacher poses the following problem of algebra to her class: "Does the graph x = y² ever intersect the graph of x = y² + 2? What are the different ways you would use to test your conjecture? Would your conjecture hold true for other equations of the form x = y² + b." Which of the following statement/statements is/are correct in the given context?
(a) One of the learning outcomes of posing this question is comparison and analysis of quadratic equations.
(b) Teacher should focus only on getting the solution that the two graphs will not intersect.
(c) The teacher can assess the reasoning skills of students.
(d) Such questions confuse the students and hence should be discouraged in a mathematics classroom.
(a) (a) and (c)
(b) Only (d)
(c) Only (b)
(d) (a) and (b)
Show Answer & Explanation

Answer: (a) (a) and (c)

Explanation:
1. The question asks students to compare equations, test a conjecture and generalise, which gives (a) and (c).
2. Focusing only on the answer or discouraging such questions is wrong.

Teacher's Note:
1. Such questions develop reasoning and generalisation.
2. The process matters more than the answer.

Question 8: Which among the following are the features of formative assessment at upper primary level?
(a) Identifying learning gaps
(b) Grading and ranking of students
(c) Identifying common errors
(d) Giving feedback to the students and teachers
Choose the correct option
(a) (a) and (c)
(b) (b) and (d)
(c) (a) and (b)
(d) (a), (c) and (d)
Show Answer & Explanation

Answer: (d) (a), (c) and (d)

Explanation:
1. Formative assessment finds gaps and errors and gives feedback to students and teachers.
2. Grading and ranking belong to summative assessment.

Teacher's Note:
1. Formative assessment supports learning during teaching.
2. Ranking is not its purpose.

Question 9: 6.234234234… is an example of:
(a) Non terminating recurring decimal number
(b) Non terminating decimal number
(c) Terminating decimal number
(d) Irrational number
Show Answer & Explanation

Answer: (a) Non terminating recurring decimal number

Explanation:
1. The block 234 repeats for ever, so the decimal is non-terminating and recurring.
2. Such a decimal is rational, so it is not irrational.

Teacher's Note:
1. Every recurring decimal is a rational number.
2. Choose the most specific description.

Question 10: When asked to arrange the decimal numbers 1.2, 0.13, 2.7 and 0.097 in ascending order, a class VI student arranged them in the following way: 0.13, 0.097, 1.2, 2.7. How will you address the error made by the student?
(a) Provide a similar type of example for practice
(b) Demonstrate the process of arranging decimals in ascending order once again on the black board
(c) Demonstrate the place value system of decimals using manipulatives and facilitate the student to compare his/her answer
(d) Ask the student to read the numbers once again and try to arrange them accordingly
Show Answer & Explanation

Answer: (c) Demonstrate the place value system of decimals using manipulatives and facilitate the student to compare his/her answer

Explanation:
1. The student treated 0.097 as bigger than 0.13 because 97 is greater than 13, ignoring place value; this is a place-value misconception about decimals.
2. The remedy is concrete place-value work with manipulatives, so the student can compare and correct the answer.

Teacher's Note:
1. Treat the cause of the error, not the symptom.
2. Use concrete materials for conceptual errors.

Question 11: When asked to find the sum of 5x and 3y, a child has done it in the following way: 5x + 3y = 8xy. This is an example of:
(a) Comprehension error
(b) Careless error
(c) Conceptual error
(d) Random error
Show Answer & Explanation

Answer: (c) Conceptual error

Explanation:
1. The child adds unlike terms as if they were like terms.
2. This shows a misunderstanding of the concept of like and unlike terms.

Teacher's Note:
1. 5x + 3y cannot be simplified further.
2. Do not call a repeated misunderstanding carelessness.

Question 12: Which of the following statements reflect inadequate teacher preparation at upper primary stage?
(a) Students' inability to link formal mathematics with the outside world.
(b) Students' incapacity to offer connections within mathematics or across subject areas.
(c) Mathematics curriculum has become taller and more spindly in shape.
(d) Mathematics teachers are unable to prepare students for math Olympiads.
(a) (b) and (c)
(b) (a) and (d)
(c) (a) and (b)
(d) (c) and (d)
Show Answer & Explanation

Answer: (c) (a) and (b)

Explanation:
1. Failure to link mathematics to life or to other topics and subjects reflects how it was taught, so (a) and (b) show inadequate preparation.
2. The shape of the curriculum and Olympiad preparation are not about teacher preparation.

Teacher's Note:
1. Teacher preparation shows in the connections students make.
2. Curriculum structure is a policy matter.

Question 13: Mathematics is a way of thinking, since
a. it provides opportunity to the students to engage in proofs and examining patterns.
b. students reproduce formulae and symbols during problem solving.
c. students use appropriate strategies for solving new and different problems.
(a) a and b
(b) b and c
(c) a and c
(d) Only b
Show Answer & Explanation

Answer: (c) a and c

Explanation:
1. Examining patterns, proving and choosing strategies for new problems are ways of thinking.
2. Reproducing formulae is recall, not thinking.

Teacher's Note:
1. Thinking means reasoning and problem solving.
2. Recall is a lower skill.

Question 14: A famous mathematician, George Polya, has given the four-step process for problem-solving. Which one of the following is not a step of Polya's problem solving?
(a) Understanding the problem
(b) Revise a plan
(c) Carry out a plan
(d) Look back
Show Answer & Explanation

Answer: (b) Revise a plan

Explanation:
1. Polya's steps are understand the problem, devise a plan, carry out the plan and look back.
2. 'Revise a plan' is not one of them.

Teacher's Note:
1. The second step is 'devise a plan', not revise.
2. Read each word of the options.

Question 15: Which among the following is/are features of Summative Assessment?
(a) Evaluates the student's learning at the end of an instructional unit.
(b) Students receive a grade in terms of percentage or any other form to indicate their level of performance.
(c) Can be used during the learning process in order to modify teaching and learning activities.
Choose the correct option.
(a) (a) and (b)
(b) (a) and (c)
(c) (b) and (c)
(d) (a), (b) and (c)
Show Answer & Explanation

Answer: (a) (a) and (b)

Explanation:
1. Summative assessment comes at the end of a unit and gives a grade or score.
2. Using it during learning to modify teaching is a formative feature.

Teacher's Note:
1. Summative: end, grade. Formative: during, feedback.
2. Match each statement to its type.

Question 16: Which among the following is/are features of an effective classroom discussion?
(a) It provides an opportunity for students to clarify their misconceptions.
(b) It provides an opportunity for gifted students to show their talents.
(c) It develops student's mathematical thinking and imbibe in them a fear free attitude towards mathematics.
(a) a and b
(b) b and c
(c) a and c
(d) Only c
Show Answer & Explanation

Answer: (c) a and c

Explanation:
1. Discussion clarifies misconceptions and builds thinking and a fear-free attitude, for all students.
2. It is not meant only for gifted students to show talent.

Teacher's Note:
1. Discussion is for all learners.
2. Avoid options that favour a select group.

Question 17: Which of the following strategies is NOT suitable for teaching low achievers in mathematics?
(a) Using activities centred on student's interest
(b) Giving less number of questions in a single work session
(c) Giving miscellaneous questions from textbook to solve
(d) Allocating extra time for teacher guided practice
Show Answer & Explanation

Answer: (c) Giving miscellaneous questions from textbook to solve

Explanation:
1. Low achievers need interest-based activities, small amounts of work and guided practice.
2. Miscellaneous textbook questions are too demanding and unstructured for them.

Teacher's Note:
1. Support with graded tasks.
2. Avoid overloading weak learners.

Question 18: While making a lesson plan on introducing Data handling, a middle school mathematics teacher thought of formulating a four-step process for Data handling. The four steps are given in random order.
a. Collecting the data
b. Interpreting the results
c. Formulating the questions
d. Analysing the data
Which of the following represents the correct order of process?
(a) (a), (c), (d), (b)
(b) (c), (d), (a), (b)
(c) (c), (a), (d), (b)
(d) (a), (d), (b), (c)
Show Answer & Explanation

Answer: (c) (c), (a), (d), (b)

Explanation:
1. First formulate the questions, then collect the data.
2. Then analyse the data and finally interpret the results: (c), (a), (d), (b).

Teacher's Note:
1. Data handling begins with a question.
2. Interpretation is the last step.

Question 19: 'Statistics is more than making graphs and analysing data. It includes both asking and answering questions about our world.' Which of the following options explains the meaning of given statement?
(a) In statistics, numbers have more significance than graphs for data analysis.
(b) Graphs should be used only to introduce statistics to students.
(c) Students should formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.
(d) Statistics is only about solving problems in real world.
Show Answer & Explanation

Answer: (c) Students should formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.

Explanation:
1. The statement says statistics involves asking questions and answering them with data.
2. Option (c) describes this whole process.

Teacher's Note:
1. Statistics is a cycle: question, data, analysis, conclusion.
2. Reject options that narrow it.

Question 20: Which of the following may not lead to professional development of mathematics teachers?
(a) Timely inservice training programs to help teachers upgrade their pedagogy
(b) Giving duties to teachers in implementation of policies
(c) Enhancing teachers' knowledge through seminars and conferences
(d) Getting teachers involved in various mathematics club and inter university activities
Show Answer & Explanation

Answer: (b) Giving duties to teachers in implementation of policies

Explanation:
1. Training, seminars and clubs improve knowledge and pedagogy.
2. Being given duties to implement policies is administrative and does not itself develop teaching.

Teacher's Note:
1. Professional development means learning.
2. Administrative duties are not learning.

Question 21: Which of the following may not be an appropriate model for teaching fractions in the middle school?
(a) Region or area model
(b) Length or measurement model
(c) Set model
(d) Division model
Show Answer & Explanation

Answer: (d) Division model

Explanation:
1. Region, length and set models are the standard models for showing fractions.
2. The division model is not generally treated as a model for introducing fractions, so it is the least appropriate here.

Teacher's Note:
1. Use area, length (number line) and set models for fractions.
2. The question is based on the source key; read the word 'may'.

Question 22: Which of the following transformations affect the congruency of a shape?
(a) Translation
(b) Reflection
(c) Rotation
(d) Enlargement
Show Answer & Explanation

Answer: (d) Enlargement

Explanation:
1. Translation, reflection and rotation preserve size and shape, so the image is congruent.
2. Enlargement changes size, so the image is similar, not congruent.

Teacher's Note:
1. Rigid transformations preserve congruence.
2. Enlargement preserves only similarity.

Question 23: Counter examples in mathematics classroom are useful for:
(a) Eliminating misconceptions
(b) Disproving conjectures
(c) Proving an axiom
(d) To falsify a generalization
Choose the correct option
(a) (a), (b) and (d)
(b) (b) and (d)
(c) (a), (b) and (c)
(d) (b), (c) and (d)
Show Answer & Explanation

Answer: (a) (a), (b) and (d)

Explanation:
1. A counter-example removes wrong ideas, disproves conjectures and falsifies generalisations.
2. It cannot prove an axiom, because axioms are assumed.

Teacher's Note:
1. A counter-example only disproves.
2. It never proves.

Question 24: Inductive method of teaching mathematics does not:
(a) proceed from particular to general
(b) take care of needs and interests of learners
(c) proceed from abstract to concrete
(d) encourage discovery and independent thinking
Show Answer & Explanation

Answer: (c) proceed from abstract to concrete

Explanation:
1. The inductive method goes from examples to the rule, i.e. concrete to abstract and particular to general.
2. So it does not proceed from abstract to concrete.

Teacher's Note:
1. Inductive: particular to general. Deductive: general to particular.
2. Abstract to concrete is the deductive direction.

Question 25: Which of the following describes a concept map in reference to mathematical teaching?
(a) It is a diagrammatic representation of relationship between various concepts and sub-concepts
(b) It is a map used to find directions
(c) It is a scheme of teaching to be followed strictly
(d) It is a vague description of a lesson plan
Show Answer & Explanation

Answer: (a) It is a diagrammatic representation of relationship between various concepts and sub-concepts

Explanation:
1. A concept map is a diagram that links concepts and sub-concepts with their relationships.
2. It is not a map of directions, a fixed scheme or a lesson plan.

Teacher's Note:
1. Concept maps show how ideas connect.
2. They help teachers plan and students revise.

Question 26: According to NCF (2005), which of the following may not necessarily be the goal of teaching mathematics at the upper primary level?
(a) Mathematization of the thought process of learner
(b) Introduction and building base to higher conceptualization in mathematics
(c) Building interlinkages between numbers, space and operations
(d) Helping bright students to pass competitive exams
Show Answer & Explanation

Answer: (d) Helping bright students to pass competitive exams

Explanation:
1. NCF 2005 aims at mathematisation of thinking, a base for higher concepts and links between number, space and operations.
2. Helping bright students pass competitive exams is not a goal for all learners.

Teacher's Note:
1. NCF goals are for all children.
2. Exam coaching is not a curriculum goal.

Question 27: A middle school mathematics teacher asks his students to construct a rectangle with length 7 cm and breadth 4 cm. As the students completed the task, he further instructs them:
(i) increase the length and breadth by 2 cm each and draw to see what figure you get
(ii) decrease the length and breadth by 2 cm and draw to see what figure you get
(iii) increase the length by 1 cm and decrease the breadth by 1 cm. Can you predict the type of figure without drawing?
Which principle of Zoltan Dienes theory of mathematics learning is he using in the above activity?
(a) Constructivity Principle
(b) Perceptual Variability Principle
(c) Mathematical Variability Principle
(d) Dynamic Principle
Show Answer & Explanation

Answer: (c) Mathematical Variability Principle

Explanation:
1. The teacher changes the mathematical variables (length and breadth) while keeping the concept of a rectangle.
2. Varying mathematical variables is the mathematical variability principle.

Teacher's Note:
1. Perceptual variability uses different materials for the same concept.
2. Mathematical variability changes variables of the concept.

Question 28: An orphanage has three gates. A person enters the orphanage with some fruits and gives half of the fruits and one more to the children at the first gate; similarly he gives half of the remaining fruits and one more to the children at the second gate and likewise at the third gate. At the end the person is left with only one fruit. How many fruits were in the hands of that person in starting? For solving this problem, which one of the following methods will be appropriate?
(a) Project-based
(b) Inductive - deductive
(c) Problem – posing
(d) Problem - solving
Show Answer & Explanation

Answer: (d) Problem - solving

Explanation:
1. Working backwards: 1 left means 4 before gate 3, 10 before gate 2 and 22 at the start (22 → 10 → 4 → 1).
2. Finding the answer to a given non-routine problem uses the problem-solving method.

Teacher's Note:
1. Working backwards is a useful problem-solving strategy.
2. Problem posing means making new problems.

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