CTET Paper II - Mathematics Mock Test | 50 MCQ | 21 July 2026

CTET Paper II - Mathematics Mock Test

CTET Paper II (Classes VI - VIII) - Mathematics Full Assessment

Welcome to the targeted 50 MCQ assessment for CTET Paper II Mathematics. This practice test strictly aligns with the NCERT curriculum and CTET pattern, covering: Number System, Algebra, Geometry, Mensuration, Data Handling, and Mathematics Pedagogy.

Select your answers and click the Submit button at the bottom to check your total score and detailed solution explanations.

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SECTION I: Number System & Playing with Numbers [Questions 1 to 10]
1. What is the sum of the place value of 7 in 57,432 and the face value of 8 in 8,921?
Explanation: Place value of 7 in 57,432 = 7,000. Face value of 8 in 8,921 = 8. Sum = 7,000 + 8 = 7,008.
2. If a 9-digit number 785x367y2 is divisible by 72, then what is the value of (x + y) assuming y is the largest single digit?
Explanation: Divisibility by 72 requires divisibility by 8 and 9. Last 3 digits (7y2) divisible by 8: largest y is 9 (792 is divisible by 8). Sum of digits = 7+8+5+x+3+6+7+9+2 = 47 + x. For 47 + x to be divisible by 9, x = 4. Thus x + y = 4 + 9 = 13.
3. Which of the following statements is true regarding prime numbers?
Explanation: Multiplying any two prime numbers (e.g., 2 × 3 = 6) gives a number with factors 1, p1, p2, p1*p2, which makes it composite. (Note: 2 is an even prime, so not all primes are odd).
4. Which fraction lies strictly between 3/5 and 4/5?
Explanation: 3/5 = 0.60, 4/5 = 0.80. Converting 7/10 to decimal gives 0.70, which lies between 0.60 and 0.80.
5. What is the additive inverse of the product of (-4) and (-6)?
Explanation: Product = (-4) × (-6) = +24. The additive inverse of +24 is -24 (since 24 + (-24) = 0).
6. Three bells toll together at intervals of 9, 12, and 15 minutes respectively. If they toll together now, after how many hours will they toll together next?
Explanation: LCM(9, 12, 15) = 180 minutes. Converting minutes to hours: 180 / 60 = 3 hours.
7. Simplify: (-15) + (-8) ÷ (-2) - (-6) × 3
Explanation: Follow BODMAS: (-8) ÷ (-2) = 4. Then (-6) × 3 = -18. Expression becomes (-15) + 4 - (-18) = -11 + 18 = 7.
8. What is the total number of prime factors in the expression (2)^5 × (3)^3 × (5)^2?
Explanation: Total prime factors (counting multiplicities) = Sum of exponents = 5 + 3 + 2 = 10.
9. What is the value of 0.333... + 0.666... in fractional form?
Explanation: 0.333... = 1/3 and 0.666... = 2/3. Sum = 1/3 + 2/3 = 3/3 = 1.
10. The HCF and LCM of two numbers are 12 and 144 respectively. If one number is 36, what is the other number?
Explanation: Formula: HCF × LCM = Product of two numbers. 12 × 144 = 36 × N2 ⇒ N2 = (12 × 144) / 36 = 48.
SECTION II: Algebra, Ratio & Proportion [Questions 11 to 20]
11. If 3x + 5 = 2(x - 4), then what is the value of x^2 + 1?
Explanation: 3x + 5 = 2x - 8 ⇒ 3x - 2x = -8 - 5 ⇒ x = -13. Value of x^2 + 1 = (-13)^2 + 1 = 169 + 1 = 170.
12. Two numbers are in the ratio 4 : 5. If 6 is added to each number, the ratio becomes 5 : 6. What are the numbers?
Explanation: Let numbers be 4x and 5x. (4x + 6)/(5x + 6) = 5/6 ⇒ 24x + 36 = 25x + 30 ⇒ x = 6. Numbers are 4(6) = 24 and 5(6) = 30.
13. Subtract (2x^2 - 3xy + 5y^2) from (5x^2 + xy - 2y^2).
Explanation: (5x^2 + xy - 2y^2) - (2x^2 - 3xy + 5y^2) = (5-2)x^2 + (1 - (-3))xy + (-2 - 5)y^2 = 3x^2 + 4xy - 7y^2.
14. If x and y vary inversely and x = 12 when y = 8, what is the value of y when x = 16?
Explanation: In inverse variation, x1 * y1 = x2 * y2. (12 × 8) = (16 × y2) ⇒ 96 = 16 * y2 ⇒ y2 = 6.
15. What are the factors of x^2 - 7x + 12?
Explanation: Find numbers that multiply to +12 and add to -7: -3 and -4. So factors are (x - 3)(x - 4).
16. The mean proportional between 9 and 25 is:
Explanation: Mean proportional = √(a × b) = √(9 × 25) = √(225) = 15.
17. If 15 men can complete a work in 20 days, how many days will 25 men take to complete the same work?
Explanation: Inverse variation: M1 × D1 = M2 × D2 ⇒ 15 × 20 = 25 × D2 ⇒ 300 = 25 * D2 ⇒ D2 = 12 days.
18. Degree of the polynomial 4x^3y^2 - 7x^2y^4 + 3x^5 is:
Explanation: Degrees of terms: 4x^3y^2 (3+2=5), -7x^2y^4 (2+4=6), 3x^5 (5). Highest degree is 6.
19. If a : b = 2 : 3 and b : c = 4 : 5, then a : b : c is equal to:
Explanation: Multiply first ratio by 4 (8:12) and second ratio by 3 (12:15). Combined ratio a : b : c = 8 : 12 : 15.
20. The algebraic expression for "5 subtracted from twice a number n" is:
Explanation: "Twice a number n" is 2n. Subtracting 5 from it yields 2n - 5.
SECTION III: Geometry & 2D/3D Shapes [Questions 21 to 30]
21. Euler's formula for any 3D polyhedron connecting Vertices (V), Edges (E), and Faces (F) is:
Explanation: Euler's Formula states F + V - E = 2 (Faces + Vertices - Edges = 2).
22. How many lines of symmetry does a regular hexagon have?
Explanation: A regular polygon with n sides has n lines of symmetry. For a regular hexagon, n = 6.
23. In triangle ABC, if ∠A = 50° and ∠B = 70°, what type of triangle is ABC based on its sides?
Explanation: ∠C = 180° - (50° + 70°) = 60°. Since all three angles are different (50°, 60°, 70°), all sides are of different lengths. Hence, it is Scalene.
24. What is the measure of each interior angle of a regular octagon?
Explanation: Each interior angle = [(n - 2) × 180°] / n = [(8 - 2) × 180°] / 8 = (6 × 180°) / 8 = 135°.
25. Two supplementary angles are in the ratio 4 : 5. The smaller angle is:
Explanation: Supplementary angles add up to 180°. 4x + 5x = 180° ⇒ 9x = 180° ⇒ x = 20°. Smaller angle = 4(20°) = 80°.
26. Which of the following 3D shapes has 5 faces, 8 edges, and 5 vertices?
Explanation: A square pyramid has a square base and 4 triangular sides (Total 5 faces, 5 vertices, 8 edges).
27. If two parallel lines are intersected by a transversal, then the vertically opposite angles are always:
Explanation: Vertically opposite angles formed by intersecting lines are always equal regardless of parallel lines.
28. Can a triangle have side lengths 5 cm, 8 cm, and 14 cm?
Explanation: Triangle Inequality Theorem: 5 + 8 = 13, which is LESS than 14. Hence, a triangle cannot be formed.
29. Order of rotational symmetry of a square is:
Explanation: A square fits onto itself 4 times during a full 360° rotation (at 90°, 180°, 270°, 360°).
30. For geometric construction of a unique triangle ABC, which set of measurements is sufficient?
Explanation: SAS criterion uniquely fixes a triangle. AAA allows infinite similar triangles, Option 3 violates triangle inequality, and Option 4 has sum of two angles > 180°.
SECTION IV: Mensuration & Data Handling [Questions 31 to 40]
31. The area of a trapezium is 180 cm^2 and its height is 9 cm. If one parallel side is 16 cm, find the length of the other parallel side.
Explanation: Area = 1/2 × (a + b) × h ⇒ 180 = 1/2 × (16 + b) × 9 ⇒ 360/9 = 16 + b ⇒ 40 = 16 + b ⇒ b = 24 cm.
32. The radius of a cylindrical vessel is 7 cm and its height is 10 cm. Find its total surface area. (Take π = 22/7)
Explanation: TSA = 2πr(r + h) = 2 × (22/7) × 7 × (7 + 10) = 44 × 17 = 748 cm^2.
33. If the edge of a cube is doubled, its volume becomes how many times the original volume?
Explanation: Volume = a^3. New side = 2a. New Volume = (2a)^3 = 8a^3 (8 times original).
34. What is the median of the data set: 13, 16, 12, 14, 19, 12, 18, 15?
Explanation: Arrange in ascending order: 12, 12, 13, 14, 15, 16, 18, 19 (n = 8). Median = Average of 4th and 5th terms = (14 + 15)/2 = 14.5.
35. In a pie chart, a sector representing 25% of total budget will have a central angle of:
Explanation: Central angle = (Percentage / 100) × 360° = (25 / 100) × 360° = 90°.
36. Find the mean of first five prime numbers.
Explanation: First 5 prime numbers: 2, 3, 5, 7, 11. Sum = 28. Mean = 28 / 5 = 5.6.
37. A die is thrown once. What is the probability of getting a prime number?
Explanation: Total outcomes = {1, 2, 3, 4, 5, 6} = 6. Prime outcomes = {2, 3, 5} = 3. Probability = 3/6 = 1/2.
38. The perimeter of a rectangle is 40 cm. If its length is 12 cm, what is its area?
Explanation: 2(L + B) = 40 ⇒ 12 + B = 20 ⇒ B = 8 cm. Area = L × B = 12 × 8 = 96 cm^2.
39. The range of the data: 25, 18, 32, 45, 8, 29, 39 is:
Explanation: Range = Maximum value - Minimum value = 45 - 8 = 37.
40. The area of a circle is 154 cm^2. Find its circumference. (π = 22/7)
Explanation: Area = πr^2 = 154 ⇒ (22/7)r^2 = 154 ⇒ r^2 = 49 ⇒ r = 7 cm. Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
SECTION V: Pedagogical Issues in Mathematics [Questions 41 to 50]
41. According to NCF-2005, the main goal of Mathematics education in school is:
Explanation: NCF-2005 explicitly states that the main goal of mathematics education is the "mathematisation of child's thinking".
42. Which of the following is an example of an 'Open-Ended' question in Mathematics?
Explanation: Open-ended questions have multiple valid solutions/answers (e.g., 1×60, 2×30, 3×20, 4×15, 6×10, etc.), encouraging creative thinking.
43. According to Van Hiele's theory of geometric thought, at which level do students recognize shapes as a whole visual object without analyzing properties?
Explanation: At Level 0 (Visualisation/Recognition), children judge geometric shapes by their appearance as a whole (e.g., "It looks like a door, so it's a rectangle").
44. Diagnostic testing in Mathematics is primarily conducted to:
Explanation: Diagnostic tests pin-point specific learning gaps, errors, and misconceptions so teachers can plan effective remedial teaching.
45. Remedial teaching is most effective when provided:
Explanation: Remedial instruction must closely follow diagnostic evaluation to address misconceptions before new concepts are introduced.
46. A student repeatedly makes the error: 1/2 + 1/3 = 2/5. How should a teacher best address this misconception?
Explanation: Concrete visual representations (fraction kits/paper strips) help students conceptually realize why fractions with different denominators cannot be added directly across numerator and denominator.
47. Which mathematical process involves moving from specific concrete examples to general rule or formula?
Explanation: Inductive reasoning moves from Specific examples → Generalization/Formula. (Deductive is General formula → Specific example).
48. Formative Assessment in Mathematics aims at:
Explanation: Formative Assessment is ongoing "assessment for learning" designed to provide real-time feedback for pedagogical improvement.
49. Which learning material is most suitable for teaching 3D spatial visualization and nets of solids in Upper Primary classes?
Explanation: Geo-Nets (2D patterns that fold into 3D shapes) directly develop spatial reasoning and understanding of faces, edges, and vertices.
50. A major cause of 'Mathematics Anxiety' among upper primary students is:
Explanation: Research shows math anxiety stems from speed-oriented timed drills, rote algorithmic pressure, and fear of harsh evaluation without conceptual clarity.

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