Page 1 CBSE VIII | Mathematics Sample Paper 1 â€“ Solution CBSE Board Class VIII Mathematics Term II Sample Paper 1 â€“ Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct option: B ? ? ? ? ? ? ? ? ? ? ? 333 33 1000 5 2 5 2 5 2 5 2 5 2 10 2. Correct option: B For a hexagonal prism, V = 12, E = 18 Applying Euler's formula: F + V - E = 2 F = 2 + E â€“ V = 2 + 18 â€“ 12 = 8 3. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 4. Correct option: D Area of square = 49 cm 2 = 7 2 cm 2 Therefore, side of square is = 7 cm So the perimeter of square = 7 ? 4 = 28 cm 5. Correct answer: C 6. Correct option: C 480 15 x5 480 5 x 160 15 ? ? ? ? ? 7. Correct option: A 6k 17 29 k2 12k 34 29k 17k 34 k 2 ? ? ? ? ? ? ? ? ? Page 2 CBSE VIII | Mathematics Sample Paper 1 â€“ Solution CBSE Board Class VIII Mathematics Term II Sample Paper 1 â€“ Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct option: B ? ? ? ? ? ? ? ? ? ? ? 333 33 1000 5 2 5 2 5 2 5 2 5 2 10 2. Correct option: B For a hexagonal prism, V = 12, E = 18 Applying Euler's formula: F + V - E = 2 F = 2 + E â€“ V = 2 + 18 â€“ 12 = 8 3. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 4. Correct option: D Area of square = 49 cm 2 = 7 2 cm 2 Therefore, side of square is = 7 cm So the perimeter of square = 7 ? 4 = 28 cm 5. Correct answer: C 6. Correct option: C 480 15 x5 480 5 x 160 15 ? ? ? ? ? 7. Correct option: A 6k 17 29 k2 12k 34 29k 17k 34 k 2 ? ? ? ? ? ? ? ? ? CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 8. Correct option: D Each of the three expressions are with minimum power of x is 2; power of y is 2 and no power of z, so the greatest common factor of the three expressions is x 2 y 2 . 9. Correct answer: A Central angle = o o o Value of component 1 360 360 90 Total value 4 ? ? ? ? 10. Correct answer: C a 2 - 2ab + b 2 = a 2 - ab - ab + b 2 = a(a - b) - b(a - b) = (a - b) 2 11. Correct answer: C (2, 2) lies on the graph of y = x as x = 2 and y = 2 i.e., x = y 12. Correct answer: C If the unit place of a number is zero then it is divisible by both 5 and 10. Section B 13. (i) (ii) Page 3 CBSE VIII | Mathematics Sample Paper 1 â€“ Solution CBSE Board Class VIII Mathematics Term II Sample Paper 1 â€“ Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct option: B ? ? ? ? ? ? ? ? ? ? ? 333 33 1000 5 2 5 2 5 2 5 2 5 2 10 2. Correct option: B For a hexagonal prism, V = 12, E = 18 Applying Euler's formula: F + V - E = 2 F = 2 + E â€“ V = 2 + 18 â€“ 12 = 8 3. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 4. Correct option: D Area of square = 49 cm 2 = 7 2 cm 2 Therefore, side of square is = 7 cm So the perimeter of square = 7 ? 4 = 28 cm 5. Correct answer: C 6. Correct option: C 480 15 x5 480 5 x 160 15 ? ? ? ? ? 7. Correct option: A 6k 17 29 k2 12k 34 29k 17k 34 k 2 ? ? ? ? ? ? ? ? ? CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 8. Correct option: D Each of the three expressions are with minimum power of x is 2; power of y is 2 and no power of z, so the greatest common factor of the three expressions is x 2 y 2 . 9. Correct answer: A Central angle = o o o Value of component 1 360 360 90 Total value 4 ? ? ? ? 10. Correct answer: C a 2 - 2ab + b 2 = a 2 - ab - ab + b 2 = a(a - b) - b(a - b) = (a - b) 2 11. Correct answer: C (2, 2) lies on the graph of y = x as x = 2 and y = 2 i.e., x = y 12. Correct answer: C If the unit place of a number is zero then it is divisible by both 5 and 10. Section B 13. (i) (ii) CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 14. A number is divisible by 4 if the number formed by its last two digits is divisible by 4. (i) Consider 45748 Number formed by last two digits is 48. 48 is divisible by 4. Hence, 45748 is also divisible by 4. (ii) Consider 21404 Number formed by last two digits is 04. Now, 04 is divisible by 4. Hence, 21404 is also divisible by 4. 15. Since ABCD is an isosceles trapezoidal, we have AD = BC. Therefore, AD = BC = 4 cm. Now the perimeter of given trapezium = AB + BC + CD + DA = 12 + 4 + 8 + 4= 28 Hence, the perimeter of the given trapezium is 28 cm. 16. From the graph, it is clear that 5 students favoured orange and 1 student favoured green. Now, 5 â€“ 1 = 4 Therefore, 4 more students favoured orange colour than green. 17. Let x be the greater part. Then, 64 x ? is the smaller part. Now, according to condition given, ?? ?? 3 5(64 ) 3 320 5 xx xx 3x + 5x = 320 8x = 320 x = 40 Hence, the two parts are 40 and 24. 18. Here, Total number of outcomes = 10 + 25 = 35 Let E be the event of getting a prize. Number of outcomes favourable to event E = 10 P (E) = Number of favourable outcomes 10 2 Total number of outcomes 35 7 ?? Probability of getting a prize = Page 4 CBSE VIII | Mathematics Sample Paper 1 â€“ Solution CBSE Board Class VIII Mathematics Term II Sample Paper 1 â€“ Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct option: B ? ? ? ? ? ? ? ? ? ? ? 333 33 1000 5 2 5 2 5 2 5 2 5 2 10 2. Correct option: B For a hexagonal prism, V = 12, E = 18 Applying Euler's formula: F + V - E = 2 F = 2 + E â€“ V = 2 + 18 â€“ 12 = 8 3. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 4. Correct option: D Area of square = 49 cm 2 = 7 2 cm 2 Therefore, side of square is = 7 cm So the perimeter of square = 7 ? 4 = 28 cm 5. Correct answer: C 6. Correct option: C 480 15 x5 480 5 x 160 15 ? ? ? ? ? 7. Correct option: A 6k 17 29 k2 12k 34 29k 17k 34 k 2 ? ? ? ? ? ? ? ? ? CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 8. Correct option: D Each of the three expressions are with minimum power of x is 2; power of y is 2 and no power of z, so the greatest common factor of the three expressions is x 2 y 2 . 9. Correct answer: A Central angle = o o o Value of component 1 360 360 90 Total value 4 ? ? ? ? 10. Correct answer: C a 2 - 2ab + b 2 = a 2 - ab - ab + b 2 = a(a - b) - b(a - b) = (a - b) 2 11. Correct answer: C (2, 2) lies on the graph of y = x as x = 2 and y = 2 i.e., x = y 12. Correct answer: C If the unit place of a number is zero then it is divisible by both 5 and 10. Section B 13. (i) (ii) CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 14. A number is divisible by 4 if the number formed by its last two digits is divisible by 4. (i) Consider 45748 Number formed by last two digits is 48. 48 is divisible by 4. Hence, 45748 is also divisible by 4. (ii) Consider 21404 Number formed by last two digits is 04. Now, 04 is divisible by 4. Hence, 21404 is also divisible by 4. 15. Since ABCD is an isosceles trapezoidal, we have AD = BC. Therefore, AD = BC = 4 cm. Now the perimeter of given trapezium = AB + BC + CD + DA = 12 + 4 + 8 + 4= 28 Hence, the perimeter of the given trapezium is 28 cm. 16. From the graph, it is clear that 5 students favoured orange and 1 student favoured green. Now, 5 â€“ 1 = 4 Therefore, 4 more students favoured orange colour than green. 17. Let x be the greater part. Then, 64 x ? is the smaller part. Now, according to condition given, ?? ?? 3 5(64 ) 3 320 5 xx xx 3x + 5x = 320 8x = 320 x = 40 Hence, the two parts are 40 and 24. 18. Here, Total number of outcomes = 10 + 25 = 35 Let E be the event of getting a prize. Number of outcomes favourable to event E = 10 P (E) = Number of favourable outcomes 10 2 Total number of outcomes 35 7 ?? Probability of getting a prize = CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 19. (a + b) 2 = a 2 + 2ab + b 2 Here, a = 3 and b = -4 20. The generalized form is as below: (i) 45 = 40 + 5 = 4 × 10 + 5 × 1 (ii) 123 = 100 + 20 + 3 = 1 × 100 + 2 × 10 + 3 × 1 21. Since, volume of cuboid = l ? b ? h Here, V = 800 cm 3 , l = 20 cm and b = 10 cm 22. We know that two quantities x and y vary directly if the ratio x y remains constant, so we find the ratio in each case. x 5 7 9 11 y 15 21 36 33 Ratio x y Clearly, the ratio x y is not same for all the cases. Thus, x and y are not varying directly. 23. 1. Hence, the cost of one pen is Rs. (2x - 6). Page 5 CBSE VIII | Mathematics Sample Paper 1 â€“ Solution CBSE Board Class VIII Mathematics Term II Sample Paper 1 â€“ Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct option: B ? ? ? ? ? ? ? ? ? ? ? 333 33 1000 5 2 5 2 5 2 5 2 5 2 10 2. Correct option: B For a hexagonal prism, V = 12, E = 18 Applying Euler's formula: F + V - E = 2 F = 2 + E â€“ V = 2 + 18 â€“ 12 = 8 3. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 4. Correct option: D Area of square = 49 cm 2 = 7 2 cm 2 Therefore, side of square is = 7 cm So the perimeter of square = 7 ? 4 = 28 cm 5. Correct answer: C 6. Correct option: C 480 15 x5 480 5 x 160 15 ? ? ? ? ? 7. Correct option: A 6k 17 29 k2 12k 34 29k 17k 34 k 2 ? ? ? ? ? ? ? ? ? CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 8. Correct option: D Each of the three expressions are with minimum power of x is 2; power of y is 2 and no power of z, so the greatest common factor of the three expressions is x 2 y 2 . 9. Correct answer: A Central angle = o o o Value of component 1 360 360 90 Total value 4 ? ? ? ? 10. Correct answer: C a 2 - 2ab + b 2 = a 2 - ab - ab + b 2 = a(a - b) - b(a - b) = (a - b) 2 11. Correct answer: C (2, 2) lies on the graph of y = x as x = 2 and y = 2 i.e., x = y 12. Correct answer: C If the unit place of a number is zero then it is divisible by both 5 and 10. Section B 13. (i) (ii) CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 14. A number is divisible by 4 if the number formed by its last two digits is divisible by 4. (i) Consider 45748 Number formed by last two digits is 48. 48 is divisible by 4. Hence, 45748 is also divisible by 4. (ii) Consider 21404 Number formed by last two digits is 04. Now, 04 is divisible by 4. Hence, 21404 is also divisible by 4. 15. Since ABCD is an isosceles trapezoidal, we have AD = BC. Therefore, AD = BC = 4 cm. Now the perimeter of given trapezium = AB + BC + CD + DA = 12 + 4 + 8 + 4= 28 Hence, the perimeter of the given trapezium is 28 cm. 16. From the graph, it is clear that 5 students favoured orange and 1 student favoured green. Now, 5 â€“ 1 = 4 Therefore, 4 more students favoured orange colour than green. 17. Let x be the greater part. Then, 64 x ? is the smaller part. Now, according to condition given, ?? ?? 3 5(64 ) 3 320 5 xx xx 3x + 5x = 320 8x = 320 x = 40 Hence, the two parts are 40 and 24. 18. Here, Total number of outcomes = 10 + 25 = 35 Let E be the event of getting a prize. Number of outcomes favourable to event E = 10 P (E) = Number of favourable outcomes 10 2 Total number of outcomes 35 7 ?? Probability of getting a prize = CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 19. (a + b) 2 = a 2 + 2ab + b 2 Here, a = 3 and b = -4 20. The generalized form is as below: (i) 45 = 40 + 5 = 4 × 10 + 5 × 1 (ii) 123 = 100 + 20 + 3 = 1 × 100 + 2 × 10 + 3 × 1 21. Since, volume of cuboid = l ? b ? h Here, V = 800 cm 3 , l = 20 cm and b = 10 cm 22. We know that two quantities x and y vary directly if the ratio x y remains constant, so we find the ratio in each case. x 5 7 9 11 y 15 21 36 33 Ratio x y Clearly, the ratio x y is not same for all the cases. Thus, x and y are not varying directly. 23. 1. Hence, the cost of one pen is Rs. (2x - 6). CBSE VIII | Mathematics Sample Paper 1 â€“ Solution 24. Number of vertices (V) = 8 Number of edges (E) = 12 Let, number of faces = F Since every polyhedron satisfy Euler's formula, therefore F + V = E + 2 Or, F + 8 = 12 + 2 Or, F = 14 - 8 = 6 Hence, the number of faces is 6. Section C 25. Let B â€™s income be Rs. 100. Then, A â€™s income = Rs. 160 If A â€™s income is Rs. 160, then B â€™s income = Rs. 100. If A â€™s income is Rs 100, then B â€™s income = Rs. 100 100 Rs. 62.50 160 ?? ?? ?? ?? Therefore, B â€™s income is less than A â€™s income by (100 â€“ 62.50)%, i.e. by 37.5%. 26. Converting 5.832 into fraction, we get 5832 1000 Now, 3 3 3 3 3 5832 1000 5832 1000 2 2 2 3 3 3 3 3 2 2 2 5 5 5 233 25 18 10 1.8 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ?Read More

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