Multiple Choice Questions (MCQs) for CTET : Mathematics
Review structured MCQ sets for CTET Mathematics. Built according to official CTET guidelines, these downloadable questions support daily revision and core concept reinforcement.
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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) Protractor
(b) Clinometer
(c) Thermometer
(d) Set square
Show Answer & Explanation
Answer: (b) Clinometer
Explanation:
1. A clinometer measures angles of elevation.
2. With the distance known, tan of the angle gives the height.
Teacher's Note:
1. A simple clinometer is a protractor with a straw and a plumb line.
2. Use it for outdoor trigonometry activities.
(a) Generalization
(b) Teacher-centric approach
(c) Deductive approach
(d) Inductive approach
Show Answer & Explanation
Answer: (d) Inductive approach
Explanation:
1. Students observe several specific cases.
2. They then conclude the general rule, which is the inductive approach.
Teacher's Note:
1. Inductive goes from examples to rule.
2. Measurement gives approximate evidence, not proof.
(a) The ratio of boys to girls in a classroom is 3/5. The ratio is a fraction.
(b) The ratio of girls to total children in a classroom is 3/8. This is both a ratio and a fraction.
(c) Rimjhim walked 3/4 of a kilometre. This is a fraction and not a ratio.
Choose the correct option.
(a) Only (b)
(b) (a) and (c)
(c) (b) and (c)
(d) (a) and (b)
Show Answer & Explanation
Answer: (c) (b) and (c)
Explanation:
1. A part-to-part ratio such as boys to girls is not a fraction of the whole, so (a) is false.
2. A part-to-whole ratio (b) is both, and a measure such as 3/4 km (c) is a fraction only.
Teacher's Note:
1. Part-to-part comparisons are ratios only.
2. Part-to-whole comparisons can be fractions as well.
(a) Analytical approach
(b) Axiomatic approach
(c) Deductive approach
(d) Inductive approach
Show Answer & Explanation
Answer: (d) Inductive approach
Explanation:
1. Students measure several particular circles.
2. They then conclude that diameter = 2 × radius, which is generalising from examples (inductive).
Teacher's Note:
1. Inductive means examples first, rule later.
2. The axiomatic approach starts from axioms.
(a) Explain the meaning of variable and how it differs from a constant.
(b) Revise the rule that only "like terms" can be added.
(c) Put different values of x in both the expressions and show that they are not equal.
(d) There is no issue in the student's understanding.
Show Answer & Explanation
Answer: (c) Put different values of x in both the expressions and show that they are not equal.
Explanation:
1. 3x + 2x + 5 + 6 = 5x + 11, not 16x, so the student has a misconception.
2. Substituting values of x shows the two expressions give different values, creating conflict that leads the student to see why unlike terms cannot be added.
Teacher's Note:
1. Let the learner discover the error through a counter-example.
2. Option (b) only states a rule.
(a) I doubt that it will rain today.
(b) There is a 50-50 chance of India winning the toss in today's match.
(c) Chances are high that the prices of petrol will go down.
This type of discussion will be helpful to:
(a) Introduce the concept of estimation.
(b) Introduce the concept of probability.
(c) Introduce the concept of Data handling.
(d) Enhance creative thinking in students.
Show Answer & Explanation
Answer: (b) Introduce the concept of probability.
Explanation:
1. All three statements talk about chance and likelihood.
2. This is the idea behind probability.
Teacher's Note:
1. Start probability with everyday chance language.
2. Use words like certain, likely, unlikely.
(a) Level 0 (Visualization / Recognition)
(b) Level 1 (Analysis)
(c) Level 2 (Relationships)
(d) Level 4 (Axiomatics)
Show Answer & Explanation
Answer: (c) Level 2 (Relationships)
Explanation:
1. The student sees class inclusions among figures: square within rectangle within parallelogram.
2. Relating figures through their properties is Level 2.
Teacher's Note:
1. Level 1 lists properties; Level 2 links figures.
2. Class inclusion is the signal.
Which of the following statement(s) is/are true for the given situation?
(a) It can be used as an activity to introduce standard unit of length measurement in a class.
(b) It can be used to encourage children to estimate length of objects in daily life.
(c) It is a good activity to establish the formula for conversion of metre to centimetre or vice-versa.
(d) This type of activity should be given only as home task so that class time is utilised for solving the questions.
(a) (a) and (c)
(b) (a) and (b)
(c) (b) and (d)
(d) only (d)
Show Answer & Explanation
Answer: (b) (a) and (b)
Explanation:
1. The rope is a 1 m standard, and students compare surroundings to it, which introduces the unit and builds estimation.
2. Conversion formulae (c) are not established here, and (d) is not appropriate.
Teacher's Note:
1. Estimation develops a feel for measures.
2. Activities should be done in class.
(a) Multiplicative inverse
(b) Commutative property of fractions
(c) Multiplicative identity of fractions
(d) Closure property of fractions
Show Answer & Explanation
Answer: (a) Multiplicative inverse
Explanation:
1. \( \dfrac{a}{b} \times \dfrac{b}{a} = 1 \).
2. The number giving product 1 is the multiplicative inverse (reciprocal).
Teacher's Note:
1. The multiplicative identity is 1.
2. Zero has no reciprocal.
(a) If you want to distribute 100 candies equally among 15 students, after keeping 5 for yourself, how many candies will finally be left?
(b) There are 6 candies and 8 chocolates in a bag. If you pick one sweet randomly, what is the chance that it will be a Candy?
(c) Plot the following on a (x-y) graph : (4, 3), (0, 2), (6, 10)
(d) In a sale, the price of an electric fan decreases by 10%, if the decreased price is Rs 1200, what was the original price of the fan?
Show Answer & Explanation
Answer: (b) There are 6 candies and 8 chocolates in a bag. If you pick one sweet randomly, what is the chance that it will be a Candy?
Explanation:
1. Division with remainder, plotting points and percentage in reverse use number operations and variable relations needed for equations.
2. Simple probability is unrelated to the prerequisites for equations.
Teacher's Note:
1. Prerequisites for equations include operations, percentage and coordinates.
2. Pick the item from a different strand.
(a) Summative Assessment for Analyzing Learning
(b) Summative and Formative Assessment for Learning
(c) Structural Analysis for Advanced Learning
(d) Structured Assessment for Analyzing Learning
Show Answer & Explanation
Answer: (d) Structured Assessment for Analyzing Learning
Explanation:
1. CBSE's SAFAL is Structured Assessment For Analyzing Learning.
2. The other options change the words.
Teacher's Note:
1. SAFAL tests competencies in classes 3, 5 and 8.
2. Learn the expansion as a phrase.
(a) Criterion-referenced assessment.
(b) Formative assessment.
(c) Norm-referenced assessment.
(d) Summative assessment
Show Answer & Explanation
Answer: (b) Formative assessment.
Explanation:
1. Observation during learning with support and feedback is ongoing assessment for improvement.
2. That is formative assessment.
Teacher's Note:
1. Formative is assessment for learning.
2. Summative comes at the end.
(i) Join two square tiles side to side without overlap, which shape will be formed?
(ii) Join two identical cubes face-to-face, which shape will be formed?
(iii) Take few identical square tiles, how many of these will be needed to form a larger square?
She can use this activity to identify individual differences among her learners in their:
(a) ability to measure angles of 2-D shapes
(b) ability to estimate area and volume of given shapes
(c) ability to use spatial reasoning, prediction and visualization in problem solving situations
(d) ability to prove theorems in geometry
Show Answer & Explanation
Answer: (c) ability to use spatial reasoning, prediction and visualization in problem solving situations
Explanation:
1. The questions ask students to mentally combine shapes and predict results.
2. This involves spatial reasoning and visualisation.
Teacher's Note:
1. Spatial reasoning is a key geometry skill.
2. The tasks involve no measuring or proof.
(a) It needs practice to become a good problem solver
(b) Students are scared of solving problems
(c) We need to train teachers in adopting problem solving approach
(d) Problem solving is related to conceptual understanding
Show Answer & Explanation
Answer: (d) Problem solving is related to conceptual understanding
Explanation:
1. NCF 2005 treats problem solving as a way to build understanding and mathematical thinking.
2. Only option (d) gives this reason.
Teacher's Note:
1. NCF 2005 wants mathematisation rather than rote work.
2. The other options are not reasons for the approach.
(a) Proposition
(b) Definition
(c) Axiom
(d) Open sentence
Show Answer & Explanation
Answer: (b) Definition
Explanation:
1. The statement explains the meaning of a term.
2. A statement that gives the meaning of a term is a definition.
Teacher's Note:
1. An axiom is accepted without proof.
2. A proposition is a claim that is true or false.
(a) Using a number line showing integers and illustrating forward and backward shift
(b) Writing the rules of integer operations on the black board
(c) Telling the students to memorize the rules of integer operations
(d) Telling the students to solve the problems using guidebooks
Show Answer & Explanation
Answer: (a) Using a number line showing integers and illustrating forward and backward shift
Explanation:
1. A number line gives a concrete, visual model of adding positive and negative integers.
2. Memorising rules or using guidebooks gives no understanding.
Teacher's Note:
1. Use concrete models before rules.
2. Movement right and left shows signs and sums.
(a) It is a space for learning mathematics through play way activities and discovery methods with the help of different types of multisensory aids, objects and community resources
(b) It is a laboratory for conducting mathematical experiments
(c) A room for keeping teaching aids and charts
(d) A space where children can develop mathematical ideas on their own without any facilitation of the teacher
Show Answer & Explanation
Answer: (a) It is a space for learning mathematics through play way activities and discovery methods with the help of different types of multisensory aids, objects and community resources
Explanation:
1. A maths lab is a space for activity-based, discovery learning with multisensory aids.
2. It is not just a store room, and the teacher still facilitates.
Teacher's Note:
1. The lab is a concept for learning by doing.
2. Facilitation by the teacher is still needed.
(a) The concept of a rectangle includes both spatial and length relationships.
(b) "Chance" is relationship between the frequency of an event happening compared with all possible outcomes.
(c) The concept of a "negative integer" is based only on the "magnitude" of the number.
(d) The concept of multiplication includes the concept of area of rectangle.
Show Answer & Explanation
Answer: (c) The concept of a "negative integer" is based only on the "magnitude" of the number.
Explanation:
1. A negative integer involves direction or sign as well as magnitude, not magnitude alone.
2. The other three statements are true.
Teacher's Note:
1. Negative numbers need a sense of direction or opposite.
2. Beware of the word only.
Assertion (A): Various studies in India show that there is a high failure rate of students in mathematics.
Reason (R): As girls do not have mathematical abilities therefore maximum girls fail in mathematics.
(a) Both (A) and (R) are correct but (R) is not the correct reason for (A).
(b) Both (A) and (R) are correct but (R) is the correct reason for (A).
(c) Both (A) and (R) are incorrect.
(d) (A) is correct but (R) is incorrect.
Show Answer & Explanation
Answer: (d) (A) is correct but (R) is incorrect.
Explanation:
1. High failure in mathematics is reported, so (A) is correct.
2. The claim that girls lack mathematical ability is a myth, so (R) is incorrect.
Teacher's Note:
1. NCF 2005 says all children can learn mathematics.
2. Gender stereotypes are not valid.
(a) Exploring numerical situations, rather than just computing
(b) Encouraging students to make their own generalisations
(c) Solving linear equations in one variable and two variables
(d) Asking the students to decide whether the following conjecture, "If we multiply any whole number by 2, the answer will be an even number" is true or false?
Show Answer & Explanation
Answer: (c) Solving linear equations in one variable and two variables
Explanation:
1. Algebraic thinking comes from exploring patterns, generalising and testing conjectures.
2. Solving equations is a procedural skill and develops it least.
Teacher's Note:
1. Algebraic thinking is more than manipulating symbols.
2. Look for generalisation and reasoning.
(a) helps to plan the lesson well
(b) helps to grade the students comprehensively
(c) use to assess multiple choice questions
(d) helps to prepare a reliable question paper
Show Answer & Explanation
Answer: (c) use to assess multiple choice questions
Explanation:
1. Rubrics describe levels of performance for tasks such as projects and open responses.
2. Multiple choice questions have one right answer and need no rubric.
Teacher's Note:
1. Rubrics suit open-ended work.
2. They give clear criteria.
(a) Shapes
(b) Algebra
(c) Measurement
(d) Data Handling
Show Answer & Explanation
Answer: (a) Shapes
Explanation:
1. These materials are used to make, compare and transform shapes.
2. They mainly build geometry concepts.
Teacher's Note:
1. Geoboards show polygons, area and symmetry.
2. Match the material to the strand.
(a) Aryabhatta
(b) Mahavira
(c) Brahmagupta
(d) Srinivasa Ramanujan
Show Answer & Explanation
Answer: (b) Mahavira
Explanation:
1. Ganita Sara Sangraha was written by Mahavira (9th century CE).
2. Aryabhata wrote Aryabhatiya, and Brahmagupta wrote Brahmasphutasiddhanta.
Teacher's Note:
1. Mahavira was a Jain mathematician.
2. Match each author to his book.
(a) There are five team members in each group
(b) This box contains many sets of five pencils
(c) I am at fifth place in annual achievement in my class
(d) I have only five friends
Show Answer & Explanation
Answer: (c) I am at fifth place in annual achievement in my class
Explanation:
1. An ordinal number shows position or rank.
2. 'Fifth place' gives a rank, while the other statements count quantity.
Teacher's Note:
1. Cardinal means how many; ordinal means which position.
2. First, second and third are ordinals.
(a) Error analysis
(b) Experimentation in teaching
(c) Action research
(d) Inductive approach
Show Answer & Explanation
Answer: (c) Action research
Explanation:
1. The teacher identifies a classroom problem, tries a solution and applies the findings.
2. This cycle is action research.
Teacher's Note:
1. Action research is done by teachers in their own classrooms.
2. Its aim is to improve practice.
(a) A child can classify various shapes that look similar
(b) Child identifies and classifies shapes based on properties and not based on size or orientation
(c) Child can informally deduce general properties of a given geometrical shape and is able to see the linkages among these properties
(d) A student can follow the deductive axiomatic systems of geometry
Show Answer & Explanation
Answer: (c) Child can informally deduce general properties of a given geometrical shape and is able to see the linkages among these properties
Explanation:
1. At Level 2 (informal deduction) children see links among properties and deduce informally.
2. (a) is Level 0, (b) is Level 1, and (d) is Level 4.
Teacher's Note:
1. Level 0 visualisation, 1 analysis, 2 relationships.
2. Linking properties is the clue.
(a) Learners do not pay attention in the class
(b) The identity (a + b)³ is more difficult to arrive at
(c) They have not grasped the concept of multiplication of algebraic expressions
(d) They find the identity (a + b)³ as less useful
Show Answer & Explanation
Answer: (c) They have not grasped the concept of multiplication of algebraic expressions
Explanation:
1. (a + b)³ needs multiplying (a + b)² by (a + b), involving several terms.
2. Difficulty points to weak understanding of multiplying algebraic expressions.
Teacher's Note:
1. Look for the underlying concept, not blame.
2. Diagnose the prior skill needed.
(a) They need not learn higher mathematics as they may never need it
(b) They may not be able to learn middle school math as they don't have the skills for it
(c) The only way to teach them mathematics is drill them into learning / memorizing multiplication tables and formulae
(d) They may have rich understanding and mathematical skills of computation and conversion from their lived experiences
Show Answer & Explanation
Answer: (d) They may have rich understanding and mathematical skills of computation and conversion from their lived experiences
Explanation:
1. Children from daily-wage backgrounds handle money, measures and bargaining.
2. So they bring rich informal mathematical knowledge.
Teacher's Note:
1. NCF 2005 and RTE stress using children's prior experiences.
2. Avoid deficit assumptions.
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FAQs
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