Download CTET MCQs for CTET : 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.
Chapter-wise Objective Questions: Mathematics
Access the complete set of multiple-choice questions for Mathematics below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CTET textbooks.
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
(a) Mathematics anxiety can be addressed by making assessment an integral part of the daily mathematics instruction with the focus on the progress of the student.
(b) Students facing mathematics anxiety should be asked to take a greater number of tests to overcome the anxiety.
(c) Students overcome mathematics anxiety by practicing a lot of questions before the examination.
(d) Students with mathematics anxiety should be exempted from giving examinations.
Show Answer & Explanation
Answer: (a) Mathematics anxiety can be addressed by making assessment an integral part of the daily mathematics instruction with the focus on the progress of the student.
Explanation:
1. Anxiety falls when assessment is continuous, low-stress and focused on progress.
2. More tests, heavy practice or exemption do not address the cause.
Teacher's Note:
1. Continuous and comprehensive assessment reduces exam fear.
2. Exemption avoids the problem.
(a) A quadrilateral
(b) A trapezium
(c) A parallelogram
(d) A regular hexagon
Show Answer & Explanation
Answer: (a) A quadrilateral
Explanation:
1. A parallelogram, a trapezium and a regular hexagon can be cut into triangles and rectangles of known shape, giving their formulae.
2. A general quadrilateral has no single formula from such cuttings.
Teacher's Note:
1. A general quadrilateral is split into two triangles and has no standard formula.
2. Special figures have formulae.
(a) Level 2 (Relationships)
(b) Level 0 (Recognition)
(c) Level 1 (Analysis)
(d) Level 3 (Deduction)
Show Answer & Explanation
Answer: (a) Level 2 (Relationships)
Explanation:
1. Seeing a square as a special case of a rhombus and of a rectangle shows relationships among classes of figures.
2. This is Van Hiele's level 2.
Teacher's Note:
1. Level 0 recognises shapes by appearance and level 1 knows properties.
2. Level 2 relates classes of shapes.
(a) Empirical Observation
(b) Deductive Reasoning
(c) Verification
(d) Logical Reasoning
Show Answer & Explanation
Answer: (a) Empirical Observation
Explanation:
1. Proofs use deductive and logical reasoning and also verification of steps.
2. Empirical observation of examples does not prove a statement for all cases.
Teacher's Note:
1. Examples suggest but do not prove.
2. A proof must hold for all cases.
(a) Differently sized photographic images of same objects
(b) Drawings of similar looking shapes
(c) PowerPoint presentation on definition of similarity
(d) A textbook chapter on similarity
Show Answer & Explanation
Answer: (a) Differently sized photographic images of same objects
Explanation:
1. Similar figures have the same shape but different sizes.
2. Photographs of the same object enlarged or reduced show this directly and concretely.
3. The other options are drawings or definitions that do not show proportional enlargement.
Teacher's Note:
1. Introduce a concept through concrete, familiar experiences before giving its formal definition.
2. Looking similar is not the same as being mathematically similar, so use proportional enlargements.
(a) Concrete Operational Stage
(b) Pre-operational Stage
(c) Sensori-motor Stage
(d) Formal Operational Stage
Show Answer & Explanation
Answer: (d) Formal Operational Stage
Explanation:
1. The source key gives the Formal Operational stage, where abstract, hypothetical and logical reasoning develops.
2. The sensori-motor and pre-operational stages lack logical operations.
Teacher's Note:
1. Piaget links abstract mathematical reasoning to the formal operational stage (about 11 years onwards).
2. Concrete operational children reason logically only about concrete objects.
(a) Bar graph
(b) Percentages
(c) Similarity of shapes
(d) Probability
Show Answer & Explanation
Answer: (b) Percentages
Explanation:
1. A dart board with concentric circles suits similarity of circles and probability (ratio of areas).
2. The scores can be tallied and shown as a bar graph.
3. Percentages are the source key's choice as the least direct fit.
Teacher's Note:
1. Match the tool to the concept it makes visible.
2. This item is debatable, so check against the original paper.
(a) Finding the sum of three or more digit numbers by column method of addition
(b) Rounding off numbers to the nearest multiples of ten in order to add, subtract or multiply etc.
(c) Teaching the use of electronic calculator to students
(d) Making students memorize multiplication tables for multiplying large numbers
Show Answer & Explanation
Answer: (b) Rounding off numbers to the nearest multiples of ten in order to add, subtract or multiply etc.
Explanation:
1. Heuristics are rule-of-thumb strategies such as estimation and approximation.
2. Rounding off to nearest tens to make calculation easy is such a strategy.
3. Column addition and memorising tables are fixed algorithms or rote work.
Teacher's Note:
1. A heuristic is a flexible shortcut, not a fixed algorithm.
2. Estimation is a typical heuristic.
(a) Geometric thinking
(b) Algebraic thinking
(c) Statistical thinking
(d) Numerical thinking
Show Answer & Explanation
Answer: (b) Algebraic thinking
Explanation:
1. Generalising patterns from arithmetic and expressing them with symbols is the core of algebra.
2. Geometric, statistical and numerical thinking do not centre on symbolic generalisation.
Teacher's Note:
1. Algebra extends arithmetic by using letters to represent general numbers.
2. Pattern to generalisation to symbols is the usual route.
a. Every mathematical concept gives rise to more mathematical concepts.
b. Mathematical ideas grows from abstract to concrete.
c. Mathematical ideas grows from particular to general.
(a) a and b
(b) a and c
(c) b and c
(d) Only a
Show Answer & Explanation
Answer: (b) a and c
Explanation:
1. Concepts build on one another, so (a) is true.
2. Ideas grow from concrete to abstract, so (b) is false.
3. They grow from particular cases to general rules, so (c) is true.
Teacher's Note:
1. Teaching moves from concrete to abstract and from particular to general.
2. Reversed-direction statements are a common trap.
(a) Growing Aptitude in Numerical Innovations and Training
(b) Growing Ability in Numerical Innovations and Techniques
(c) Growing Aptitude in Numerical Innovations and Techniques
(d) Growing Ability in Numerical Innovations and Training
Show Answer & Explanation
Answer: (a) Growing Aptitude in Numerical Innovations and Training
Explanation:
1. The CBSE expansion of GANIT is Growing Aptitude in Numerical Innovations and Training.
2. The other options change one or two words.
Teacher's Note:
1. Ramanujan's birth anniversary is 22 December, celebrated as National Mathematics Day.
2. Learn such expansions word by word.
Statement A: If n is even, n² is even.
Statement B: If n² is not even, then n is not even.
Which of following statements is correct?
(a) B is contrapositive of A
(b) B is inverse of A
(c) B is converse of A
(d) B is reverse of A
Show Answer & Explanation
Answer: (a) B is contrapositive of A
Explanation:
1. A is p → q, with p: n is even and q: n² is even.
2. B is ~q → ~p, which is the contrapositive of A.
Teacher's Note:
1. Contrapositive swaps and negates: p → q becomes ~q → ~p.
2. A statement and its contrapositive are logically equivalent.
(i) Relationships among figures
(ii) Recognition of figures
(iii) Axiomatic Reasoning
(iv) Deductive Reasoning & formal proofs
(v) Analysis of components of figures
Choose the correct sequence.
(a) (ii), (i), (v), (iv), (iii)
(b) (i), (ii), (v), (iv), (iii)
(c) (ii), (v), (i), (iv), (iii)
(d) (iv), (iii), (ii), (v), (i)
Show Answer & Explanation
Answer: (c) (ii), (v), (i), (iv), (iii)
Explanation:
1. Van Hiele order: Recognition, Analysis, Relationships (ordering), Deduction, Axiomatic rigour.
2. That is (ii), (v), (i), (iv), (iii).
Teacher's Note:
1. Levels 0 to 4: visualisation, analysis, informal deduction, deduction, rigour.
2. Levels are sequential and cannot be skipped.
(a) how many rectangles can be made having an area of 48 cm²
(b) how many rectangles can be made having a perimeter of 24 cm
Which of the following statement is most desirable for the given activity from a reflective teachers' perspective:
(a) To develop a deeper understanding of the relationship between perimeter and area
(b) The activity is based on Inductive method of teaching
(c) It is a good activity to compare rectangles and circles
(d) The activity would be better if the teacher had posed the open ended question to be solved using the formula rather than using a paper
Show Answer & Explanation
Answer: (a) To develop a deeper understanding of the relationship between perimeter and area
Explanation:
1. Students explore rectangles of fixed area and of fixed perimeter on a grid.
2. This shows that area and perimeter vary independently, deepening understanding of both.
Teacher's Note:
1. Hands-on tasks build conceptual links between ideas.
2. Formula-only tasks would not show the relationship.
(a) Proportionality
(b) Equality
(c) Multiplication
(d) Subtraction
Show Answer & Explanation
Answer: (b) Equality
Explanation:
1. The students move numbers across the equals sign incorrectly without balancing both sides.
2. This shows they have not understood equality as a balance.
Teacher's Note:
1. Equality means both sides keep the same value.
2. Use a balance model to teach equation solving.
(a) Cube Numbers
(b) Prime Numbers
(c) Ramanujan Numbers
(d) Pythagorean Numbers
Show Answer & Explanation
Answer: (c) Ramanujan Numbers
Explanation:
1. 1729 = 1³ + 12³ = 9³ + 10³.
2. Such numbers are called Ramanujan (taxicab) numbers.
Teacher's Note:
1. 1729 is the Hardy-Ramanujan number.
2. Verify with the cubes 1, 1728, 729 and 1000.
(a) Achievement Test
(b) Norm-referenced Test
(c) Diagnostic Test
(d) Summative Test
Show Answer & Explanation
Answer: (c) Diagnostic Test
Explanation:
1. A diagnostic test probes one specific content area in depth with many questions to find weaknesses.
2. Achievement and summative tests sample widely across the syllabus.
Teacher's Note:
1. Diagnostic tests are narrow and deep.
2. They are followed by remedial teaching.
(a) Articulation level of Psychomotor domain
(b) Organization level of Affective domain
(c) Precision level of Psychomotor domain
(d) Responding level of Affective domain
Show Answer & Explanation
Answer: (c) Precision level of Psychomotor domain
Explanation:
1. Using a calculator is a physical skill, so it is psychomotor.
2. Doing it accurately and quickly corresponds to the precision level.
Teacher's Note:
1. Psychomotor levels run from imitation to precision to articulation.
2. Words like accurately and quickly point to precision.
(a) Understand the formula
(b) Apply the formula in real world situation
(c) Analyse the formula
(d) Verify the formula
Show Answer & Explanation
Answer: (b) Apply the formula in real world situation
Explanation:
1. Students use the formula on real plots around them.
2. Using learning in real contexts is application.
Teacher's Note:
1. Application of knowledge in real life is a key aim.
2. Link maths to the child's surroundings.
(a) Write the formula of area and perimeter of different 2D shapes on blackboard and ask the student to memorise them
(b) Draw some regular 2-D shapes on a graph paper and ask the students to count the number of units along the boundary and square units for perimeter and area respectively
(c) Display a chart of formulae for area and perimeter of different shapes in the class and ask students to solve questions by using formulae from the chart
(d) Start the class with a formal definition of area and perimeter of a given figure and then introducing the formula.
Show Answer & Explanation
Answer: (b) Draw some regular 2-D shapes on a graph paper and ask the students to count the number of units along the boundary and square units for perimeter and area respectively
Explanation:
1. Introduction should be concrete and activity based.
2. Counting boundary units and square units on graph paper builds the meaning of perimeter and area before formulae.
Teacher's Note:
1. Move from concrete to formal.
2. Memorising formulae first gives no understanding.
(a) It takes time to solve open-ended questions so should be given as home work.
(b) Promote conceptual understanding and multiple ways to solve a problem.
(c) Help students to memorize an algorithm.
(d) To have a variety of mathematical problems to keep students engaged.
Show Answer & Explanation
Answer: (b) Promote conceptual understanding and multiple ways to solve a problem.
Explanation:
1. Open-ended tasks have many possible approaches or answers.
2. They therefore promote thinking, conceptual understanding and multiple solution methods.
Teacher's Note:
1. Open-ended means more than one route or answer.
2. They develop creativity and reasoning.
(a) Modelled instruction
(b) Group work
(c) Individual work with teacher as guide
(d) Independent practice at home
Show Answer & Explanation
Answer: (d) Independent practice at home
Explanation:
1. Guided practice has the teacher modelling and supporting students in class.
2. Independent practice at home has no teacher guidance, so it is not guided practice.
Teacher's Note:
1. Guided practice sits between direct teaching and independent practice.
2. Gradual release: I do, we do, you do.
(a) Able to spot the patterns and make connections between mathematical concepts
(b) Shows ability to analyse, reason and make generalisations.
(c) Solve all textbook exercises using formal algorithms
(d) Enjoys solving mathematical problems and puzzles.
(a) (a), (b) and (c)
(b) (b), (c) and (d)
(c) only (d)
(d) (a), (b) and (d)
Show Answer & Explanation
Answer: (d) (a), (b) and (d)
Explanation:
1. Gifted students see patterns, reason, generalise and enjoy puzzles: (a), (b), (d).
2. Solving all exercises with formal algorithms is not a mark of giftedness.
Teacher's Note:
1. Giftedness shows in creativity and insight, not routine work.
2. Eliminate the option that describes routine behaviour.
(a) It is helpful in developing the habit of thinking, reasoning and problem solving.
(b) In mathematics laboratory concrete materials can be easily provided to the learner.
(c) Mathematics Laboratory helps learners in improving their verbal skills.
(d) It does not encourage projects based learning.
Show Answer & Explanation
Answer: (a) It is helpful in developing the habit of thinking, reasoning and problem solving.
Explanation:
1. A maths lab encourages activity, exploration and discovery.
2. This develops thinking, reasoning and problem solving.
Teacher's Note:
1. Maths labs support learning by doing and project work.
2. Option (d) is false.
(a) Have a positive attitude while communicating with students
(b) To give collaborative tasks and promote group practice problems
(c) To ask the parents of these children to provide them home tuition
(d) Such students should be singled out and made to sit on the front of bench in a math classroom
(a) (a) and (d)
(b) (a), (b) and (d)
(c) only (d)
(d) (a) and (b)
Show Answer & Explanation
Answer: (d) (a) and (b)
Explanation:
1. A positive attitude and collaborative tasks reduce fear and build confidence.
2. Singling out anxious students (d) increases anxiety, and tuition (c) is not a classroom strategy.
Teacher's Note:
1. Make the classroom supportive and non-threatening.
2. Never label or single out learners.
(a) A teacher demonstrating the use of dienes block.
(b) Students responding to a quiz by raising hands.
(c) Students working independently with Geoboards.
(d) Students working in collaboration on a project.
Show Answer & Explanation
Answer: (d) Students working in collaboration on a project.
Explanation:
1. Social constructivism (Vygotsky) says knowledge is built through social interaction.
2. Collaboration on a project reflects this.
Teacher's Note:
1. Remember the social element: peers and discussion.
2. Independent work is individual constructivism.
Which of the following statements is correct with respect to student's response?
(a) Student's generalisation is correct.
(b) Student's generalisation is correct for quadrilaterals.
(c) Such responses need to be ignored by the teacher.
(d) Student's misconception needs to be addressed by the teacher.
Show Answer & Explanation
Answer: (d) Student's misconception needs to be addressed by the teacher.
Explanation:
1. A 1 by 4 rectangle and a 2 by 2 square have equal area but are not congruent.
2. So the statement is false and the teacher should address the misconception.
Teacher's Note:
1. Congruent figures have equal area, but equal area does not imply congruence.
2. A counter-example is the best remedy.
(a) Deductive method
(b) Inductive method
(c) Proof by contradiction
(d) Proof by counter example
Show Answer & Explanation
Answer: (a) Deductive method
Explanation:
1. Geometrical proofs proceed from axioms and known results by logical steps.
2. This is the deductive method.
Teacher's Note:
1. Deductive goes from general to particular.
2. Inductive generalises from examples and does not prove.
Free study material for Mathematics
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FAQs
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By solving our CTET Mathematics Paper 2 MCQs with Answers Set 06, CTET students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the .
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