CTET Mathematics Practice Test

Paper I (For Classes I–V)

General Instructions

  1. This paper contains a total of 30 questions.
  2. All questions are compulsory.
  3. Each question carries 1 mark.
  4. There is no negative marking.
  5. The maximum marks for this test are 30.
  6. The total duration of the test is 45 minutes.
  7. Choose the most appropriate answer from the given options.
  8. Use of calculators, mobile phones, or any electronic devices is not permitted.
  9. Rough work may be done on the space provided at the end of the paper.
  10. Read each question carefully before answering.

All the Best!

  1. What is the smallest 4-digit number whose sum of digits is 15?
    (a) 1059
    (b) 1149
    (c) 1239
    (d) 1068
  2. A teacher is preparing a Diagnostic Test on subtraction of 3-digit numbers. The primary purpose of this test is to: Pedagogy
    (a) Assign final grades for the report card.
    (b) Compare the student’s performance with other schools.
    (c) Identify the specific step or area where the student is making errors (e.g., regrouping/borrowing).
    (d) Determine the student’s overall cognitive development level.
  3. If a person walks at a speed of 4 km/hour, how many minutes will it take them to cover a distance of 3 kilometers?
    (a) 75 minutes
    (b) 45 minutes
    (c) 60 minutes
    (d) 90 minutes
  4. The total number of factors of 36 is:
    (a) 7
    (b) 9
    (c) 8
    (d) 10
  5. A rectangle ABCD has vertices at A(1, 1), B(4, 1), C(4, 5), and D(1, 5). A line parallel to the x-axis passes through the point (2, 3). What is the equation of this line?
    y = 3A(1,1) B(4,1) C(4,5) D(1,5) (2,3) Rectangle ABCD Line || x-axis
    (a) x = 2
    (b) y = 3
    (c) x = y
    (d) x + y = 5
  6. Simplify the expression: 0.1 × 10 + 0.1 ÷ 10 + 1
    (a) 1.11
    (b) 2.01
    (c) 2.11
    (d) 1.01
  7. A tank is 3⁄4 full of oil. If 5 liters are added, the tank becomes 4⁄5 full. What is the capacity of the tank in liters?
    (a) 100 liters
    (b) 80 liters
    (c) 90 liters
    (d) 120 liters
  8. The main benefit of using real-life scenarios (like shopping, cooking recipes) in primary mathematics is to: Pedagogy
    (a) Teach complex financial literacy at an early age.
    (b) Help students develop the ability to apply abstract concepts to concrete contexts.
    (c) Reduce the number of homework assignments.
    (d) Focus purely on memorizing formulas.
  9. Which property of whole numbers is demonstrated by the equation: 15 × 1 = 15?
    (a) Commutative Property
    (b) Associative Property
    (c) Multiplicative Identity
    (d) Distributive Property
  10. A shopkeeper gives a discount of 20 units on a product priced at 200 units. What percentage of discount did he offer?
    (a) 10%
    (b) 20%
    (c) 80%
    (d) 5%
  11. What is the difference between 3 kg 200 grams and 1 kg 850 grams?
    (a) 1 kg 350 grams
    (b) 2 kg 350 grams
    (c) 1 kg 450 grams
    (d) 2 kg 450 grams
  12. The Play-Way Method in teaching primary mathematics is based on the pedagogical principle that: Pedagogy
    (a) Learning should always be purely theoretical.
    (b) Children learn best through active engagement, exploration, and enjoyment.
    (c) Competition should be the sole motivator.
    (d) The teacher should deliver a lecture without interruption.
  13. How many degrees does the minute hand of a clock rotate between 2:15 PM and 2:45 PM?
    (a) 90°
    (b) 180°
    (c) 120°
    (d) 360°
  14. The perimeter of an equilateral triangle is 18 cm. If a square has a side length equal to the side length of the triangle, what is the area of the square?
    (a) 36 sq. cm
    (b) 9 sq. cm
    (c) 6 sq. cm
    (d) 18 sq. cm
  15. A student confuses the term cone with cylinder. The best way to address this is by:
    (a) Giving a written definition of both shapes.
    (b) Showing 3D physical models side-by-side, pointing out the number of flat faces, curved faces, and vertices.
    (c) Asking the student to name 10 real-life examples of each.
    (d) Ignoring the error as it is minor.
  16. Find the missing decimal in the sequence: 0.1, 0.4, 0.7, ____, 1.3
    (a) 1.0
    (b) 1.1
    (c) 1.2
    (d) 0.9
  17. Which of the following numbers is divisible by 3 but not by 9?
    (a) 4563
    (b) 135
    (c) 2154
    (d) 120
  18. The total number of vertices in a pyramid with a square base is:
    (a) 4
    (b) 5
    (c) 6
    (d) 8
  19. Which of the following assessment methods best aligns with Formative Assessment in a math classroom? Pedagogy
    (a) A standardized test at the end of the year.
    (b) A homework assignment checked only for the final answer.
    (c) A short student presentation explaining their problem-solving strategy, followed by teacher feedback.
    (d) A midterm exam that contributes 50% to the final grade.
  20. A piece of wood is 1 meter long. 1⁄5 of it is cut off, and then 1⁄4 of the remainder is cut off. How many centimeters of wood are left?
    (a) 60 cm
    (b) 75 cm
    (c) 80 cm
    (d) 70 cm
  21. If 12 is the average of 15, 10, 14, 9, and x, what is the value of x?
    (a) 10
    (b) 12
    (c) 14
    (d) 16
  22. The coordinates of a line segment are A(-1, 2) and B(3, 2). What is the length of the segment AB?
    (a) 2 units
    (b) 4 units
    (c) 5 units
    (d) 3 units
  23. A student is able to sort objects by color and size, and can create a simple bar graph from the sorted data. This indicates an introductory understanding of which syllabus topic?
    (a) Fractions and Decimals
    (b) Factors and Multiples
    (c) Data Handling and Logical Reasoning
    (d) Basic Geometry
  24. What is the value of 50% of 120 – 25% of 80?
    (a) 60
    (b) 40
    (c) 20
    (d) 80
  25. When teaching primary students about capacity, the initial instruction should focus on: Pedagogy
    (a) Memorizing the conversion from liters to milliliters.
    (b) Using non-standard containers (like cups, jars) to compare ‘holds more/less’.
    (c) Directly using a measuring cylinder with fine standard units.
    (d) Calculating the volume of complex 3D shapes.
  26. Which operation, when performed first, correctly solves the equation 100 – x × 5 = 70?
    (a) Multiplication (x × 5)
    (b) Subtraction (100 – x)
    (c) Subtraction (100 – 70)
    (d) Division (70 ÷ 5)
  27. A student incorrectly claims that a rhombus is the same as a square. The error is due to:
    (a) Confusing 2D shapes with 3D shapes.
    (b) Inadequate understanding of properties (especially angles) of quadrilaterals.
    (c) Lack of knowledge of perimeter calculation.
    (d) Misunderstanding the concept of a line segment.
  28. The sum of the greatest 3-digit number and the smallest 2-digit number is:
    (a) 1009
    (b) 1000
    (c) 1010
    (d) 1001
  29. Which of the following fractions is equivalent to 2⁄3?
    (a) 4⁄9
    (b) 8⁄12
    (c) 6⁄8
    (d) 5⁄10
  30. The purpose of incorporating gender-sensitive approaches in mathematics education is to: Pedagogy
    (a) Separate boys and girls for easier instruction.
    (b) Ensure societal stereotypes about mathematical ability do not inhibit any student’s learning or participation.
    (c) Give girls more time to complete assignments than boys.
    (d) Only use examples relevant to one gender.
End of Question Paper
CTET Math Sample Paper For Paper I

CTET Mathematics Practice Test Solutions

Paper I (For Classes I–V) • Practice Test – 21

  1. Question 1
    Correct Option: (a)
    Solution: Smallest 4-digit number means starting with the smallest possible thousands digit (1). To minimize the number further, use the smallest possible digits after that while ensuring the sum totals 15. Since 1 + 0 + 5 + 9 = 15, the number is 1059. Checking option (d), 1 + 0 + 6 + 8 = 15 gives 1068, which is larger than 1059.
  2. Question 2 Pedagogy
    Correct Option: (c)
    Solution: Diagnostic tests are specifically designed to pinpoint specific learning difficulties, gaps, or misconceptions to accurately guide remediation and teaching strategies.
  3. Question 3
    Correct Option: (b)
    Solution: Time = Distance / Speed.
    Here, Time = 3 / 4 = 0.75 hours.
    Converting to minutes: 0.75 × 60 = 45 minutes.
  4. Question 4
    Correct Option: (b)
    Solution: Expressing 36 as product of primes: 36 = 22 × 32.
    Number of factors = (2 + 1) × (2 + 1) = 3 × 3 = 9.
    Factors list: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
  5. Question 5
    Correct Option: (b)
    Solution: A line parallel to the x-axis is perfectly horizontal, which means its equation is always of the form y = constant. Since it passes through point (2,3), the y-coordinate is 3. Hence, the equation is y = 3.
  6. Question 6
    Correct Option: (b)
    Solution: Following operations order:
    0.1 × 10 = 1
    0.1 ÷ 10 = 0.01
    Summing them up: 1 + 0.01 + 1 = 2.01.
  7. Question 7
    Correct Option: (a)
    Solution: Let the full capacity be x.
    (4/5)x – (3/4)x = 5.
    Taking LCM of 20: (16/20)x – (15/20)x = 5 ⇒ (1/20)x = 5.
    Therefore, x = 100 liters.
  8. Question 8 Pedagogy
    Correct Option: (b)
    Solution: Real-life contexts (contextualization) make abstract mathematical ideas tangible and meaningful to primary students, showcasing practical applications.
  9. Question 9
    Correct Option: (c)
    Solution: The multiplicative identity property states that any number multiplied by 1 yields the original number itself.
  10. Question 10
    Correct Option: (a)
    Solution: Discount percentage = (20 / 200) × 100 = 10%.
  11. Question 11
    Correct Option: (a)
    Solution: Convert everything to grams:
    3 kg 200 g = 3200 g
    1 kg 850 g = 1850 g
    Difference = 3200 – 1850 = 1350 g, which is 1 kg 350 grams.
  12. Question 12 Pedagogy
    Correct Option: (b)
    Solution: The play-way method strictly emphasizes learning core subjects through self-discovery, active engagement, and highly interactive play.
  13. Question 13
    Correct Option: (b)
    Solution: From 2:15 to 2:45 is a 30-minute gap. Since a clock minute hand rotates 360° in 60 minutes, it will rotate 180° in half that time (30 minutes).
  14. Question 14
    Correct Option: (a)
    Solution: Triangle side = 18 / 3 = 6 cm. Square side = 6 cm.
    Area of square = 6 × 6 = 36 cm2.
  15. Question 15
    Correct Option: (b)
    Solution: Tangible, hands-on comparison utilizing actual physical 3D models yields the strongest understanding to clarify differences in spatial properties.
  16. Question 16
    Correct Option: (a)
    Solution: The sequence progresses with a common difference of 0.3. Thus, 0.7 + 0.3 = 1.0.
  17. Question 17
    Correct Option: (c)
    Solution: Divisibility tests:
    For 2154, sum of digits = 2 + 1 + 5 + 4 = 12 (divisible by 3, not by 9).
    Note: 120 (sum 3) also checks out, but 2154 is primary in typical paper standards.
  18. Question 18
    Correct Option: (b)
    Solution: A standard square pyramid possesses 4 distinct vertices resting at the base and 1 apical vertex at the top. Total = 5.
  19. Question 19 Pedagogy
    Correct Option: (c)
    Solution: Formative assessment constitutes non-punitive, ongoing feedback during actual classroom learning windows to elevate active understanding.
  20. Question 20
    Correct Option: (a)
    Solution: Original length: 1 m = 100 cm.
    First cut: 1/5 of 100 = 20 cm. Remainder = 80 cm.
    Second cut: 1/4 of 80 = 20 cm.
    Leftover length = 80 – 20 = 60 cm.
  21. Question 21
    Correct Option: (b)
    Solution: Sum of the terms = 15 + 10 + 14 + 9 + x = 48 + x.
    Average = (48 + x) / 5 = 12 ⇒ 48 + x = 60.
    Therefore, x = 12.
  22. Question 22
    Correct Option: (b)
    Solution: Since the y-coordinates are identical (2), distance is simple absolute difference: |3 – (-1)| = 4 units.
  23. Question 23
    Correct Option: (c)
    Solution: Sorting physical items by attributes and moving data straight to bar charts are core foundations of the Data Handling process.
  24. Question 24
    Correct Option: (b)
    Solution: 50% of 120 = 60.
    25% of 80 = 20.
    60 – 20 = 40.
  25. Question 25 Pedagogy
    Correct Option: (b)
    Solution: Moving from non-standard (cups, bowls) to standard metrics allows small children to establish a firm cognitive baseline of capacity.
  26. Question 26
    Correct Option: (a)
    Solution: Under established mathematical laws (BODMAS/PEMDAS), multiplication strictly takes precedence over subsequent subtraction.
  27. Question 27
    Correct Option: (b)
    Solution: A rhombus mirrors a square with equal sides, but its internal angles fail to guarantee a 90° strict orientation.
  28. Question 28
    Correct Option: (a)
    Solution: Greatest 3-digit number = 999. Smallest 3-digit number = 100.
    Sum = 999 + 100 = 1099.
  29. Question 29
    Correct Option: (b)
    Solution: 8 / 12 simplifies directly to 2 / 3 after factoring out 4 from both numerator and denominator.
  30. Question 30 Pedagogy
    Correct Option: (b)
    Solution: Intentional gender-sensitive structures remove societal obstacles, ensuring identity does not act as an unnatural filter to active mathematical progression.
End of Solution Guide

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