Chapter 13: Practice Sets for Mathematics Content 📝✨
Welcome, PSTET Aspirants! 🌟
You've made it to the final chapter—the ultimate test of your preparation! This chapter contains 5 full-length practice sets covering all the mathematics topics from Part I of the PSTET Paper 1 syllabus. Each set is designed to mirror the actual exam pattern with 30 multiple-choice questions covering both content and pedagogical issues .
Practice is the key to success. These sets will help you assess your understanding, identify weak areas, and build confidence before the exam. Let's put your knowledge to the test! 🚀
PSTET Paper 1 Mathematics Exam Pattern 📋
Before diving into the practice sets, let's recall the exam structure:
Strategy Tip: Since there's no negative marking, attempt all questions! Even if you're unsure, make an educated guess.
Practice Set 1 🔢
Time: 45 minutes (suggested) | Total Questions: 30 | Marks: 30
Section A: Content Questions (1-15)
1. What is the place value of 7 in the number 5,27,648?
a) 7
b) 700
c) 7,000
d) 70,000
2. The sum of the smallest 3-digit number and the largest 2-digit number is:
a) 199
b) 200
c) 1099
d) 1100
a) 63
b) 73
c) 613
d) 415
4. Which of the following is the correct expanded form of 3,456?
a) 3000 + 400 + 50 + 6
b) 3000 + 400 + 60 + 5
c) 3000 + 500 + 40 + 6
d) 300 + 4000 + 50 + 6
a) 48
b) 56
c) 54
d) 63
a) 6
b) 7
c) 8
d) 9
7. Convert 5 metres 35 centimetres into centimetres:
a) 535 cm
b) 5035 cm
c) 5305 cm
d) 5350 cm
8. How many grams are there in 3 kilograms 250 grams?
a) 3250 g
b) 30250 g
c) 300250 g
d) 325 g
9. 2 litres 500 millilitres is equal to:
a) 2500 ml
b) 2050 ml
c) 250 ml
d) 2005 ml
10. If a dozen bananas cost ₹48, what is the cost of 1 banana?
a) ₹4
b) ₹5
c) ₹3
d) ₹6
11. What is the time shown when the hour hand is between 4 and 5, and the minute hand is at 6?
a) 4:30
b) 4:06
c) 4:60
d) 5:30
12. The number of minutes in 3 hours is:
a) 120 minutes
b) 150 minutes
c) 180 minutes
d) 300 minutes
13. Which of the following is an example of a repeating pattern?
a) 2, 4, 6, 8, 10...
b) 5, 10, 15, 20...
c) Red, Blue, Red, Blue, Red, Blue...
d) 1, 3, 6, 10, 15...
14. In a bar graph, the height of the bar for "Cricket" is 7 cm. If the scale is 1 cm = 5 students, how many students like cricket?
a) 7 students
b) 12 students
c) 35 students
d) 70 students
15. The least value assigned to * so that the number 86325 * 6 is divisible by 11 is:
a) 1
b) 2
c) 3
d) 5
Section B: Pedagogical Questions (16-30)
16. According to NCF 2005, the main aim of teaching mathematics at the primary level is to:
a) Develop speed and accuracy in calculations
b) Prepare students for higher mathematics
c) Develop the child's ability to mathematize
d) Cover the textbook syllabus completely
17. A child in Class III solves 47 + 38 = 715. This error indicates:
a) Lack of practice
b) Misunderstanding of place value
c) Carelessness
d) Poor memory
18. "Mathematics is the language in which God has written the universe" is the statement given by:
a) Galileo
b) Locke
c) B. Russell
d) Lindsay
19. Which of the following is an example of a low-cost teaching-learning material for teaching place value?
a) Plastic base-ten blocks
b) Commercial place value chart
c) Bundles of ice cream sticks
d) Laptop with math software
20. The process of identifying specific learning difficulties and designing interventions is called:
a) Evaluation
b) Diagnosis and Remediation
c) Assessment for learning
d) Continuous assessment
21. When a child counts on fingers to solve 6 + 3, this strategy is:
a) Inappropriate and should be discouraged
b) Developmentally appropriate at certain stages
c) A sign of learning disability
d) Only for slow learners
22. According to Piaget, children in the primary grades (7-11 years) are in which stage of cognitive development?
a) Sensorimotor stage
b) Pre-operational stage
c) Concrete operational stage
d) Formal operational stage
23. Asking a child "How did you get that answer?" helps the teacher to:
a) Check if the answer is correct
b) Understand the child's thinking process
c) Give marks for explanation
d) Identify careless mistakes only
24. Using the local market as a resource for teaching money is an example of:
a) Activity-based learning
b) Community mathematics
c) Textbook teaching
d) Remedial teaching
25. A teacher observes that a student consistently writes 45 as 54. This is likely a problem of:
a) Concept of zero
b) Place value understanding
c) Number reversals (dyslexia/dysgraphia tendency)
d) Poor handwriting
a) Continuous and Comprehensive Evaluation
b) Central Council of Education
c) Continuous Calculation Exercise
d) Comprehensive Child Evaluation
27. Which of the following is an example of Assessment FOR Learning (formative assessment)?
a) Term-end examination
b) Unit test for report card
c) Observing students during group work
d) Final board examination
28. A portfolio in mathematics assessment is:
a) A folder containing all test papers
b) A collection of student work showing progress over time
c) A record of attendance and homework completion
d) A file of lesson plans
29. The main purpose of error analysis in mathematics is to:
a) Assign grades to students
b) Identify what students don't know
c) Understand children's thinking and misconceptions
d) Compare students with each other
30. When teaching fractions, using paper folding activities helps children understand:
a) Fraction symbols
b) The concept of equal parts
c) Fraction addition rules
d) Memorizing numerator and denominator
Practice Set 2 🔢
Time: 45 minutes (suggested) | Total Questions: 30 | Marks: 30
Section A: Content Questions (1-15)
a) 692
b) 702
c) 6912
d) 691
a) 256
b) 264
c) 346
d) 356
3. Which number is the greatest?
a) 3,245
b) 3,254
c) 3,425
d) 3,452
a) 80
b) 90
c) 100
d) 110
a) 8
b) 9
c) 7
d) 10
6. What is the remainder when 37 is divided by 5?
a) 1
b) 2
c) 3
d) 4
a) 3500 m
b) 3050 m
c) 350 m
d) 3005 m
8. A bag of rice weighs 5 kg 250 g. What is its weight in grams?
a) 5250 g
b) 5025 g
c) 5205 g
d) 50025 g
9. A bottle contains 1 litre 250 ml of juice. How many 250 ml glasses can be filled?
a) 4 glasses
b) 5 glasses
c) 6 glasses
d) 3 glasses
10. If a pencil costs ₹5 and an eraser costs ₹3, what is the cost of 3 pencils and 2 erasers?
a) ₹21
b) ₹15
c) ₹18
d) ₹24
11. What time is it when the hour hand is at 3 and the minute hand is at 12?
a) 3:00
b) 3:12
c) 12:15
d) 12:03
12. How many days are there in a leap year?
a) 365 days
b) 366 days
c) 364 days
d) 367 days
13. Identify the pattern: 5, 10, 20, 40, ___ , ___ .
a) 50, 60
b) 80, 160
c) 60, 80
d) 45, 50
14. In a pictograph, one symbol represents 10 children. If there are 8 symbols for "Cricket", how many children like cricket?
a) 8 children
b) 10 children
c) 80 children
d) 18 children
15. The angle made between the hour hand and the minute hand of a clock when the time is 12:30 is:
a) Right angle
b) Acute angle
c) Obtuse angle
d) Straight angle
Section B: Pedagogical Questions (16-30)
16. According to NCF 2005, mathematics teaching should focus on:
a) Rigorous problem solving only
b) Explorations of patterns, estimation, and informal learning
c) Memorization of formulas
d) Speed tests and competitions
17. A student says "1/2 is smaller than 1/3 because 2 is smaller than 3." This is an example of:
a) Conceptual error
b) Procedural error
c) Careless error
d) Factual error
18. The "concrete → pictorial → abstract" progression in mathematics teaching means:
a) Start with symbols, then use pictures, then use objects
b) Start with objects, then pictures, then symbols
c) Use only one method depending on the topic
d) Avoid using objects as they distract children
19. Which of the following is NOT a principle of mathematics curriculum construction?
a) Principle of child-centeredness
b) Principle of correlation with life
c) Principle of covering maximum syllabus
d) Principle of activity-based learning
20. Diagnostic tests in mathematics are used to:
a) Assign final grades
b) Identify specific learning difficulties
c) Rank students in class
d) Prepare question papers
21. A child in Class II can count numbers but cannot add two single-digit numbers. The most appropriate remedial strategy would be:
a) Give more worksheets
b) Use concrete objects like counters or beads
c) Ask parents to teach at home
d) Move to two-digit addition
22. The language of mathematics includes all EXCEPT:
a) Symbols and notations
b) Specialized vocabulary
c) Colloquial everyday language
d) Visual representations
23. A teacher invites a shopkeeper to class to talk about how he uses mathematics. This is an example of:
a) Community mathematics
b) Textbook teaching
c) Formal assessment
d) Remedial teaching
24. Anecdotal records in mathematics assessment are:
a) Test scores recorded over time
b) Brief narrative descriptions of significant incidents
c) Attendance records
d) Homework completion records
25. The difference between Assessment OF Learning and Assessment FOR Learning is:
a) OF learning is formative, FOR learning is summative
b) OF learning is summative, FOR learning is formative
c) Both are the same
d) OF learning is for students, FOR learning is for teachers
26. A teacher notices that Riya always subtracts the smaller digit from the larger digit in each column (e.g., 43 - 28 = 25). This error indicates:
a) Lack of practice in subtraction facts
b) Misunderstanding of the borrowing concept
c) Poor attention span
d) Vision problems
27. Which of the following is an appropriate activity for teaching the concept of "dozen"?
a) Memorizing that 1 dozen = 12
b) Counting 12 eggs in an egg carton
c) Writing "1 dozen = 12" ten times
d) Reading about dozens in textbook
28. According to the NEP 2020, Foundational Literacy and Numeracy (FLN) aims to achieve universal foundational skills by:
a) 2020
b) 2025
c) 2030
d) 2040
29. A teacher should view children's errors in mathematics as:
a) Failures to be penalized
b) Windows into children's thinking
c) Signs of low intelligence
d) Reasons to lower grades
30. Using a number line to teach addition helps children understand:
a) The commutative property visually
b) The concept of "jumping forward"
c) Both a and b
d) Only subtraction
Practice Set 3 🔢
Time: 45 minutes (suggested) | Total Questions: 30 | Marks: 30
Section A: Content Questions (1-15)
1. The number 4,568 rounded to the nearest hundred is:
a) 4,500
b) 4,600
c) 4,570
d) 4,560
2. Which of the following is a prime number?
a) 21
b) 27
c) 29
d) 33
a) 1000
b) 900
c) 1100
d) 1200
a) 10
b) 11
c) 12
d) 13
5. The fraction 3/5 written in words is:
a) Three-fifth
b) Three-fifths
c) Third-fifth
d) Third-fifths
6. Which fraction is the largest?
a) 1/2
b) 1/3
c) 1/4
d) 1/5
a) 10 m 10 cm
b) 9 m 10 cm
c) 10 m 110 cm
d) 9 m 110 cm
8. A sack of potatoes weighs 25 kg 500 g. Another sack weighs 18 kg 750 g. What is their total weight?
a) 44 kg 250 g
b) 43 kg 1250 g
c) 44 kg 1250 g
d) 43 kg 250 g
9. 5 litres - 2 litres 350 ml = ?
a) 2 litres 650 ml
b) 3 litres 650 ml
c) 2 litres 350 ml
d) 3 litres 350 ml
10. Riya bought a toy for ₹175 and gave ₹200 to the shopkeeper. How much change will she get?
a) ₹35
b) ₹25
c) ₹75
d) ₹15
11. How many months have 31 days?
a) 5 months
b) 6 months
c) 7 months
d) 8 months
12. If a train leaves at 9:45 AM and reaches at 2:15 PM, what is the duration of the journey?
a) 4 hours 30 minutes
b) 5 hours 30 minutes
c) 4 hours 15 minutes
d) 5 hours 15 minutes
13. Complete the pattern: 2, 3, 5, 8, 12, ___ , ___ .
a) 15, 19
b) 17, 23
c) 16, 21
d) 18, 24
14. In a bar graph, the bars are:
a) All of different widths
b) All of the same width
c) All of different colors
d) Arranged in any order
15. The product of two numbers is 9375. The quotient obtained by dividing the larger one with the smaller one is 15. The sum of numbers is:
a) 380
b) 395
c) 400
d) 425
Section B: Pedagogical Questions (16-30)
16. Which of the following is NOT a characteristic of a constructivist mathematics classroom?
a) Children construct their own knowledge
b) Teacher is the sole authority of knowledge
c) Hands-on activities are used
d) Children's errors are seen as learning opportunities
17. A student solves 6 × 7 = 42 but writes 24 in a hurry. This is an example of:
a) Conceptual error
b) Procedural error
c) Careless error
d) Remedial need
18. "Learning by doing" in mathematics means:
a) Solving many worksheets
b) Engaging in hands-on activities and experiences
c) Memorizing and reciting tables
d) Watching the teacher solve problems
19. The main purpose of homework in mathematics should be:
a) To complete the syllabus
b) To provide additional practice
c) To keep students occupied
d) To assign grades
20. Which of the following is an example of a manipulative for teaching mathematics?
a) Textbook
b) Blackboard
c) Abacus
d) Notebook
21. A teacher should introduce the concept of "borrowing" in subtraction by:
a) Giving the rule directly
b) Using concrete materials like bundles of sticks
c) Asking students to memorize steps
d) Showing a video only
22. The term "mathematization" refers to:
a) Memorizing mathematical formulas
b) Developing the ability to think and express mathematically
c) Solving complex calculations quickly
d) Using calculators in math class
23. A child says "I'm just not good at math." This statement reflects:
a) Factual accuracy
b) Math anxiety or fixed mindset
c) Proper self-assessment
d) Teacher's evaluation
24. Which of the following is an appropriate adaptation for a gifted student in mathematics?
a) Give them more worksheets of the same level
b) Accelerate them to the next grade's content only
c) Provide enrichment activities and open-ended problems
d) Ask them to help slower students all the time
25. A teacher uses a story about a child buying vegetables to teach money concepts. This is an example of:
a) Direct instruction
b) Contextual learning
c) Drill and practice
d) Formal assessment
26. The "key" in a pictograph tells us:
a) The title of the graph
b) What each symbol represents
c) The number of categories
d) The color of the symbols
27. A teacher notices that many students are making errors in multiplication facts. The best first step is to:
a) Give them a zero in the test
b) Analyze the errors to understand the pattern
c) Move to division since they'll learn multiplication later
d) Assign extra homework
28. In a diverse classroom with varying learning levels, an effective strategy is:
a) Teaching the same content to all at the same pace
b) Differentiated instruction with varied tasks
c) Ignoring slower students and focusing on fast learners
d) Grouping all slow learners together permanently
29. Which of the following is NOT a component of CCE (Continuous and Comprehensive Evaluation)?
a) Scholastic assessment
b) Co-scholastic assessment
c) Only term-end examinations
d) Regular observation
30. The main advantage of using puzzles in mathematics teaching is:
a) They keep students quiet
b) They develop logical thinking and problem-solving skills
c) They are easy to grade
d) They cover the syllabus quickly
Practice Set 4 🔢
Time: 45 minutes (suggested) | Total Questions: 30 | Marks: 30
Section A: Content Questions (1-15)
1. The smallest 4-digit number formed using digits 2, 0, 8, 5 (using each digit only once) is:
a) 0258
b) 2058
c) 2085
d) 0258
2. Which number is 100 less than 5,234?
a) 5,134
b) 5,334
c) 5,124
d) 5,144
a) 360
b) 3,600
c) 36,000
d) 3600
a) 50
b) 60
c) 70
d) 80
5. Which fraction is equivalent to 1/2?
a) 2/3
b) 3/4
c) 2/4
d) 4/5
6. The improper fraction 7/3 can be written as:
a) 2 1/3
b) 3 1/3
c) 2 1/7
d) 1 4/3
7. Subtract 23 hg 76 dg from 79 hg 85 dg. The answer in hectograms is:
a) 5.6009
b) 56.009
c) 560.09
d) 5600.9
8. A container holds 2 litres 500 ml of milk. How much milk will 4 such containers hold?
a) 8 litres 500 ml
b) 10 litres
c) 6 litres 500 ml
d) 12 litres
9. Which is heavier: 3 kg cotton or 3 kg iron?
a) Cotton
b) Iron
c) Both are equal
d) Cannot be compared
10. Rohan had ₹500. He bought a book for ₹225.50 and a pen for ₹75.75. How much money is left?
a) ₹199.75
b) ₹198.75
c) ₹200.75
d) ₹197.75
11. How many days are there in February in a leap year?
a) 28 days
b) 29 days
c) 30 days
d) 31 days
12. A school starts at 7:45 AM and closes at 1:30 PM. How long is the school day?
a) 5 hours 45 minutes
b) 6 hours 15 minutes
c) 5 hours 15 minutes
d) 6 hours 45 minutes
13. Identify the pattern: 37 × 3 = 111, 37 × 6 = 222, 37 × 9 = 333, 37 × ____ = 444.
a) 10
b) 11
c) 12
d) 13
14. The mode of the data: 2, 3, 5, 3, 4, 3, 6 is:
a) 2
b) 3
c) 4
d) 5
15. If a : b = 1 : 2, b : c = 3 : 4, then a : c = ?
a) 1 : 4
b) 3 : 8
c) 2 : 3
d) 4 : 5
Section B: Pedagogical Questions (16-30)
16. According to Piaget, a primary school child (age 7-11) is in which stage?
a) Sensorimotor
b) Pre-operational
c) Concrete operational
d) Formal operational
17. A child says "5 + 3 = 8, so 3 + 5 should also be 8." This demonstrates understanding of:
a) Associative property
b) Commutative property
c) Distributive property
d) Identity property
18. Which of the following is the best way to teach the concept of "area" to Class 4 students?
a) Give the formula length × breadth
b) Have them count unit squares on grid paper
c) Memorize area of different shapes
d) Write the formula 10 times
19. A teacher should use the local community for teaching mathematics because it:
a) Makes mathematics relevant and contextual
b) Is easier than teaching in classroom
c) Saves preparation time
d) Is required by the principal
20. A child who has difficulty with number sense, recognizing patterns, telling time, and measuring may be suffering from:
a) Dyslexia
b) Dysgraphia
c) Dyscalculia
d) ADHD
21. The main purpose of a diagnostic test in mathematics is to:
a) Assign grades
b) Identify strengths and weaknesses
c) Rank students
d) Fulfill administrative requirements
22. Which of the following is NOT an informal method of evaluation?
a) Observational records
b) Anecdotal records
c) Term-end examination
d) Portfolio assessment
23. A teacher asks students to bring empty packets and price tags to set up a "class shop." This activity teaches:
a) Only addition
b) Money concepts, addition, subtraction, and real-life skills
c) Only multiplication
d) Only social skills
24. The statement "Child is a problem solver and a scientific investigator" relates to which theory?
a) Behaviorism
b) Constructivism
c) Cognitivism
d) Humanism
25. A teacher should respond to a student's wrong answer by:
a) Saying "That's wrong" and moving on
b) Asking the student to explain their thinking
c) Giving the correct answer immediately
d) Ignoring the answer
26. The concept of "zero" is best introduced to young children by:
a) Writing '0' on the board
b) Showing an empty set or container
c) Memorizing that 0 means nothing
d) Solving problems like 5 - 5 = 0
27. In a bar graph, the scale 1 cm = 10 students means:
a) The bar length is 10 cm
b) Each cm on the graph represents 10 students
c) There are 10 students in the class
d) The graph is 10 cm wide
28. A teacher notices that a gifted student finishes work quickly and gets bored. The best action is to:
a) Give them extra worksheets of the same type
b) Provide enrichment activities that deepen understanding
c) Ask them to sit quietly
d) Move them to a higher class
29. The main limitation of using only textbooks for teaching mathematics is that:
a) Textbooks are expensive
b) They don't provide hands-on experiences
c) They contain errors
d) They are heavy to carry
30. According to NCF 2005, mathematics teaching at primary level should NOT focus on:
a) Explorations of patterns
b) Developing estimation skills
c) Informal learning through games
d) Rigorous problem solving only
Practice Set 5 🔢
Time: 45 minutes (suggested) | Total Questions: 30 | Marks: 30
Section A: Content Questions (1-15)
1. The Roman numeral for 49 is:
a) IL
b) XLIX
c) XLVIII
d) IL
a) 36
b) 24
c) 72
d) 48
a) 800
b) 600
c) 400
d) 200
a) 12
b) 24
c) 30
d) 60
5. Which of the following is a proper fraction?
a) 5/3
b) 7/2
c) 3/4
d) 8/5
a) 3.25
b) 4.25
c) 4.00
d) 3.75
7. A rectangle has length 12 cm and breadth 8 cm. Its perimeter is:
a) 20 cm
b) 40 cm
c) 96 cm
d) 48 cm
8. The area of a square with side 9 cm is:
a) 18 cm²
b) 36 cm²
c) 81 cm²
d) 27 cm²
9. Which of the following is NOT a unit of weight?
a) Gram
b) Kilogram
c) Liter
d) Milligram
10. If 5 notebooks cost ₹125, what is the cost of 8 notebooks?
a) ₹200
b) ₹175
c) ₹250
d) ₹150
11. How many weeks are there in a year?
a) 48 weeks
b) 50 weeks
c) 52 weeks
d) 54 weeks
12. A bus leaves at 8:20 AM and reaches at 11:45 AM. How long is the journey?
a) 3 hours 25 minutes
b) 3 hours 15 minutes
c) 4 hours 25 minutes
d) 4 hours 15 minutes
13. Complete the pattern: 1, 4, 9, 16, 25, ___ , ___ .
a) 30, 35
b) 36, 49
c) 32, 39
d) 28, 32
14. The mean of 5, 8, 12, 15, 10 is:
a) 8
b) 10
c) 12
d) 15
15. If one angle of a triangle is the sum of the other two angles, then the triangle is:
a) Isosceles triangle
b) Obtuse triangle
c) Equilateral triangle
d) Right triangle
Section B: Pedagogical Questions (16-30)
16. The main aim of teaching mathematics according to NCF 2005 is to develop the child's ability to:
a) Calculate quickly
b) Mathematize
c) Memorize formulas
d) Pass examinations
17. A child says "8 + 5 = 12" consistently. This error could be due to:
a) Mislearning the fact 8 + 5 = 13
b) Poor eyesight
c) Lack of intelligence
d) Not paying attention
18. Which of the following is an example of a mathematical pattern in nature?
a) Rhythmic beats in music
b) Spiral arrangement of sunflower seeds
c) Repeating patterns in wallpaper
d) All of the above
19. The best way to introduce the concept of multiplication to Class 2 students is through:
a) Memorizing tables
b) Repeated addition using equal groups
c) Writing multiplication facts 10 times
d) Using a calculator
20. A teacher should consider errors in mathematics as:
a) Something to be punished
b) Opportunities for learning
c) Signs of failure
d) Reasons for detention
21. The language of mathematics includes specialized terms like "sum," "product," and "difference." These are best taught by:
a) Writing definitions on board
b) Using them repeatedly in context
c) Testing on vocabulary
d) Ignoring them until higher classes
22. A portfolio in mathematics helps to:
a) Show only the best work
b) Demonstrate progress over time
c) Replace all tests
d) Keep parents informed
23. A teacher uses a story about a farmer counting his cows to teach number concepts. This is an example of:
a) Direct instruction
b) Contextual learning
c) Rote learning
d) Formal assessment
24. A student who is gifted in mathematics should be provided with:
a) More worksheets of the same level
b) Enrichment activities and open-ended problems
c) Less challenging work
d) No special attention
25. The main purpose of remedial teaching in mathematics is to:
a) Complete the syllabus faster
b) Address specific learning difficulties
c) Challenge gifted students
d) Reduce teacher's workload
26. A teacher observes that a student counts on fingers to solve 6 + 3. This is:
a) A sign of learning disability
b) A developmentally appropriate strategy
c) Something to be punished
d) Not allowed in class
27. The concept of "place value" is best taught using:
a) Rote memorization
b) Bundling of sticks into tens and ones
c) Writing numbers repeatedly
d) Reading about place value in textbook
28. Which of the following is NOT a characteristic of a child-centered mathematics classroom?
a) Teacher lectures most of the time
b) Children work in groups
c) Hands-on activities are used
d) Children's ideas are valued
29. According to NEP 2020, Foundational Literacy and Numeracy (FLN) is a national priority to be achieved by:
a) 2022
b) 2025
c) 2030
d) 2047
30. The best way to help a child who has math anxiety is to:
a) Give them more difficult problems
b) Create a supportive environment where mistakes are learning opportunities
c) Tell them to work harder
d) Ignore their anxiety
Answer Keys with Explanations 🔑
Practice Set 1 Answer Key
| Q | Ans | Explanation |
|---|---|---|
| 1 | c | In 5,27,648, the digits are: 5 Lakhs, 2 Ten-thousands, 7 Thousands, 6 Hundreds, 4 Tens, 8 Ones. So 7 is in thousands place → 7,000. |
| 2 | a | Smallest 3-digit number = 100, largest 2-digit number = 99. Sum = 100 + 99 = 199. |
| 3 | b | 45 + 28 = 73 (5+8=13, carry 1; 4+2+1=7) |
| 4 | a | 3,456 = 3000 + 400 + 50 + 6 |
| 5 | b | 8 × 7 = 56 |
| 6 | b | 56 ÷ 8 = 7 |
| 7 | a | 5 m = 500 cm, + 35 cm = 535 cm |
| 8 | a | 3 kg = 3000 g, + 250 g = 3250 g |
| 9 | a | 2 litres = 2000 ml, + 500 ml = 2500 ml |
| 10 | a | 1 dozen = 12, so cost per banana = ₹48 ÷ 12 = ₹4 |
| 11 | a | Hour hand between 4 and 5 means it's after 4, minute hand at 6 means 30 minutes → 4:30 |
| 12 | c | 1 hour = 60 minutes, so 3 hours = 3 × 60 = 180 minutes |
| 13 | c | Options a, b, d are growing patterns; c is a repeating pattern |
| 14 | c | 7 cm × 5 students per cm = 35 students |
| 15 | b | Divisibility by 11: sum of digits at odd places - sum at even places = multiple of 11. (8+3+5+6) - (6+2+*) = 22 - (8+*) = 14 - * must be 0 or 11. For *, 14 - * = 11 → * = 3. Wait, check: 8+3+5+6=22, 6+2+*=8+*, difference 22-(8+*)=14-*. For 14-* to be 0 or 11, if * = 3, 14-3=11 ✓ So answer is 3. |
| 16 | c | NCF 2005 emphasizes developing the ability to mathematize |
| 17 | b | Adding 47+38 by adding 4+3=7 and 7+8=15 to get 715 shows place value misunderstanding |
| 18 | a | This famous quote is attributed to Galileo |
| 19 | c | Bundles of ice cream sticks are low-cost and effective for place value |
| 20 | b | Diagnosis identifies difficulties; remediation designs interventions |
| 21 | b | Finger counting is developmentally appropriate in early stages |
| 22 | c | Primary grades (7-11 years) are in concrete operational stage |
| 23 | b | Asking "how did you get that?" reveals thinking process |
| 24 | b | Using community resources is community mathematics |
| 25 | c | Writing 45 as 54 may indicate number reversal (dyslexia/dysgraphia) |
| 26 | a | CCE = Continuous and Comprehensive Evaluation |
| 27 | c | Observation during learning is formative assessment (assessment for learning) |
| 28 | b | Portfolio is collection of work showing progress over time |
| 29 | c | Error analysis helps understand children's thinking and misconceptions |
| 30 | b | Paper folding shows fractions as equal parts of a whole |
Practice Set 2 Answer Key
| Q | Ans | Explanation |
|---|---|---|
| 1 | b | 235 + 467 = 702 (5+7=12, carry; 3+6+1=10, carry; 2+4+1=7) |
| 2 | a | 543 - 287 = 256 (borrowing: 13-7=6, 13-8=5 with borrow, 4-2=2) |
| 3 | d | Compare: 3,452 is largest |
| 4 | b | 15 × 6 = 90 |
| 5 | b | 81 ÷ 9 = 9 |
| 6 | b | 37 ÷ 5 = 7 remainder 2 |
| 7 | a | 3 km = 3000 m, + 500 m = 3500 m |
| 8 | a | 5 kg = 5000 g, + 250 g = 5250 g |
| 9 | b | 1 litre 250 ml = 1250 ml; 1250 ÷ 250 = 5 glasses |
| 10 | a | 3 pencils = 3×5=15, 2 erasers = 2×3=6, total = 21 |
| 11 | a | Hour hand at 3, minute at 12 → 3:00 |
| 12 | b | Leap year has 366 days |
| 13 | b | Pattern doubles each time: 5×2=10, 10×2=20, 20×2=40, next 40×2=80, 80×2=160 |
| 14 | c | 8 symbols × 10 children = 80 children |
| 15 | c | At 12:30, hour hand between 12 and 1, minute at 6 → angle > 180°? Actually 12:30 makes 165°, which is obtuse (between 90 and 180) |
| 16 | b | NCF 2005 emphasizes explorations of patterns, estimation, informal learning |
| 17 | a | Misunderstanding fraction size is a conceptual error |
| 18 | b | Concrete (objects) → Pictorial (pictures) → Abstract (symbols) |
| 19 | c | Covering maximum syllabus is not a principle of curriculum construction |
| 20 | b | Diagnostic tests identify specific learning difficulties |
| 21 | b | Concrete objects help build understanding before abstract symbols |
| 22 | c | Colloquial language is everyday language, not specialized math language |
| 23 | a | Inviting community members is community mathematics |
| 24 | b | Anecdotal records are brief narrative descriptions |
| 25 | b | OF learning = summative, FOR learning = formative |
| 26 | b | Subtracting smaller from larger in each column shows borrowing misconception |
| 27 | b | Counting real eggs in a carton makes the concept concrete |
| 28 | b | NEP 2020 aims for FLN by 2025 |
| 29 | b | Errors are windows into children's thinking |
| 30 | c | Number line shows both jumping forward and commutative property visually |
Practice Set 3 Answer Key
| Q | Ans | Explanation |
|---|---|---|
| 1 | b | 4,568 rounded to nearest hundred: look at tens digit (6 ≥5), so round up → 4,600 |
| 2 | c | 29 has only two factors: 1 and 29 |
| 3 | a | 125 × 8 = 1000 |
| 4 | c | 144 ÷ 12 = 12 |
| 5 | b | 3/5 = three-fifths |
| 6 | a | When numerators are same, smaller denominator = larger fraction. 1/2 is largest. |
| 7 | a | 7 m 25 cm + 2 m 85 cm = 9 m 110 cm = 10 m 10 cm (since 110 cm = 1 m 10 cm) |
| 8 | a | 25 kg 500 g + 18 kg 750 g = 43 kg 1250 g = 44 kg 250 g |
| 9 | a | 5 litres = 4 litres 1000 ml; 4 L 1000 ml - 2 L 350 ml = 2 L 650 ml |
| 10 | b | Change = ₹200 - ₹175 = ₹25 |
| 11 | c | 7 months have 31 days: Jan, Mar, May, Jul, Aug, Oct, Dec |
| 12 | a | 9:45 to 12:00 = 2h 15m; 12:00 to 2:15 = 2h 15m; total = 4h 30m |
| 13 | b | Pattern adds increasing amounts: +1, +2, +3, +4, +5, +6 → 12+5=17, 17+6=23 |
| 14 | b | In bar graphs, bars have same width |
| 15 | c | Let numbers be x and y with x > y. xy=9375, x/y=15. Substitute x=15y: 15y²=9375 → y²=625 → y=25, x=375. Sum=400 |
| 16 | b | In constructivism, teacher is facilitator, not sole authority |
| 17 | c | Knows fact but wrote wrong due to hurry → careless error |
| 18 | b | Learning by doing means hands-on activities |
| 19 | b | Homework provides additional practice and reinforcement |
| 20 | c | Abacus is a manipulative for teaching number concepts |
| 21 | b | Concrete materials like stick bundles teach borrowing conceptually |
| 22 | b | Mathematization = ability to think and express mathematically |
| 23 | b | Negative self-talk about math ability indicates math anxiety or fixed mindset |
| 24 | c | Gifted students need enrichment and open-ended challenges |
| 25 | b | Using stories to teach is contextual learning |
| 26 | b | Key in pictograph explains what each symbol represents |
| 27 | b | First step is to analyze errors to understand patterns |
| 28 | b | Differentiated instruction addresses varying levels |
| 29 | c | CCE includes continuous assessment, not just term-end exams |
| 30 | b | Puzzles develop logical thinking and problem-solving |
Practice Set 4 Answer Key
| Q | Ans | Explanation |
|---|---|---|
| 1 | b | Smallest 4-digit number with digits 2,0,8,5: arrange in ascending order: 0,2,5,8 but 0 can't be first → 2058 |
| 2 | a | 5,234 - 100 = 5,134 |
| 3 | b | 36 × 100 = 3,600 |
| 4 | b | 540 ÷ 9 = 60 |
| 5 | c | 2/4 = 1/2 (simplify) |
| 6 | a | 7/3 = 2 1/3 (since 3×2=6, remainder 1) |
| 7 | b | Convert to same unit: 79 hg 85 dg = 79.85 hg, 23 hg 76 dg = 23.76 hg; difference = 56.09 hg = 56.009? Wait careful: 79.85 - 23.76 = 56.09 hg. But options have 56.009 - that's 56 hg 0.9 dg? Actually 56.09 hg = 56.09. Option b is 56.009 - that's different. Let's calculate properly: 79 hg 85 dg - 23 hg 76 dg = (79-23) hg + (85-76) dg = 56 hg + 9 dg = 56.09 hg. But options: a) 5.6009 b) 56.009 c) 560.9 d) 5600.9. 56.09 = 56.090, closest is b) 56.009? That's not right. Possibly the question uses different conversion: 1 hg = 1000 dg? Actually 1 hg = 100 dg? Let's check: 1 hg = 100 g, 1 dg = 0.1 g, so 1 hg = 1000 dg. So 79 hg 85 dg = 79×1000 + 85 = 79085 dg. 23 hg 76 dg = 23000+76=23076 dg. Difference = 56009 dg = 56.009 hg. Yes! So b) 56.009 is correct. |
| 8 | b | 2 L 500 ml × 4 = 8 L 2000 ml = 10 L |
| 9 | c | Both weigh 3 kg, so equal |
| 10 | b | Total spent = ₹225.50 + ₹75.75 = ₹301.25; left = ₹500 - ₹301.25 = ₹198.75 |
| 11 | b | February in leap year has 29 days |
| 12 | a | 7:45 to 12:00 = 4h 15m; 12:00 to 1:30 = 1h 30m; total = 5h 45m |
| 13 | c | Pattern: multiplier increases by 3 each time: 3,6,9,12 → 37 × 12 = 444 |
| 14 | b | Mode = most frequent number = 3 (appears 3 times) |
| 15 | b | a:b = 1:2, b:c = 3:4. Make b same: a:b = 3:6, b:c = 6:8 → a:c = 3:8 |
| 16 | c | Piaget's concrete operational stage is ages 7-11 |
| 17 | b | Commutative property: order doesn't change sum |
| 18 | b | Counting unit squares on grid paper gives concrete understanding of area |
| 19 | a | Community resources make mathematics relevant and contextual |
| 20 | c | Difficulty with numbers and related concepts indicates dyscalculia |
| 21 | b | Diagnostic tests identify strengths and weaknesses |
| 22 | c | Term-end examination is formal, not informal |
| 23 | b | Class shop teaches money concepts and real-life math skills |
| 24 | b | Constructivism views child as active problem solver |
| 25 | b | Asking for explanation helps understand thinking |
| 26 | b | Empty set shows "nothing" concretely |
| 27 | b | Scale shows relationship between graph measurement and actual value |
| 28 | b | Gifted students need enrichment, not more of the same |
| 29 | b | Textbooks alone can't provide hands-on experiences |
| 30 | d | NCF 2005 emphasizes variety, not rigorous problem solving only |
Practice Set 5 Answer Key
| Q | Ans | Explanation |
|---|---|---|
| 1 | b | 49 = 40 + 9 = XL + IX = XLIX |
| 2 | a | LCM of 12 and 18: multiples of 12: 12,24,36; multiples of 18: 18,36 → LCM = 36 |
| 3 | a | 25 × 4 = 100, 100 × 8 = 800 |
| 4 | b | 120 ÷ 5 = 24 |
| 5 | c | Proper fraction has numerator < denominator: 3/4 |
| 6 | b | 2.5 + 1.75 = 4.25 |
| 7 | b | Perimeter = 2 × (12+8) = 2 × 20 = 40 cm |
| 8 | c | Area = side² = 9² = 81 cm² |
| 9 | c | Liter is unit of capacity, not weight |
| 10 | a | Cost per notebook = ₹125 ÷ 5 = ₹25; 8 notebooks = 8 × ₹25 = ₹200 |
| 11 | c | 52 weeks in a year (52 × 7 = 364 days, plus 1 or 2 extra) |
| 12 | a | 8:20 to 11:20 = 3 hours; 11:20 to 11:45 = 25 minutes; total = 3h 25m |
| 13 | b | Square numbers: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25, next 6²=36, 7²=49 |
| 14 | b | Mean = (5+8+12+15+10)/5 = 50/5 = 10 |
| 15 | d | If one angle = sum of other two, and sum of all three = 180°, then that angle = 90° → right triangle |
| 16 | b | NCF 2005 aims to develop ability to mathematize |
| 17 | a | Consistent error in a fact indicates mislearning |
| 18 | d | Patterns exist in music, nature, and art |
| 19 | b | Multiplication as repeated addition using equal groups is developmentally appropriate |
| 20 | b | Errors are learning opportunities |
| 21 | b | Vocabulary is best taught in context through repeated use |
| 22 | b | Portfolio demonstrates progress over time |
| 23 | b | Stories provide context for learning |
| 24 | b | Gifted students need enrichment and open-ended challenges |
| 25 | b | Remedial teaching addresses specific learning difficulties |
| 26 | b | Finger counting is developmentally appropriate |
| 27 | b | Bundling sticks teaches place value concretely |
| 28 | a | Teacher lecturing most of the time is not child-centered |
| 29 | b | NEP 2020 aims for FLN by 2025 |
| 30 | b | Supportive environment reduces math anxiety |
PSTET Success Tips 🌟
Practice Regularly: Solve one practice set every few days and analyze your mistakes .
Time Management: Each set should take about 45 minutes. In the actual exam, you'll have 150 minutes for 150 questions across 5 subjects, so aim for 30-40 seconds per math question.
Analyze Errors: For every wrong answer, understand WHY you got it wrong—conceptual, procedural, or careless? This helps you improve .
Pedagogy Focus: Half the questions are on pedagogical issues. Don't neglect these—they're just as important as content .
Use Previous Papers: Practicing actual PSTET previous year papers gives you the best sense of exam pattern and difficulty .
No Negative Marking: Attempt all questions! Even if unsure, make an educated guess .
Make Notes: Create quick revision notes for formulas, properties, and key pedagogical terms .
Congratulations on completing all 12 chapters and 5 practice sets! 🎉
You've now covered the entire PSTET Paper 1 Mathematics syllabus in depth. Remember that consistent practice, reflection on errors, and connecting mathematical concepts to real-life teaching situations are the keys to success.
Best of luck for your PSTET exam! May you become the inspiring mathematics teacher your students deserve. 🌟📚🍎
Happy Studying, Future Teachers!
