Page 1 CBSE VIII | Mathematics Sample Paper 2 - Solution CBSE Board Class VIII Mathematics Term I Sample Paper 2 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B 2. Correct answer: A Indefinitely on both sides of 0 3. Correct answer: A An octagon is made up of 8 sides. 4. Correct answer: B Original Price = Rs. 50 Increased Price = 55 - 50 = 5 Thus, Increased price Percentage increase = 100 % Original price ?? ? ?? ?? 5. Correct answer: C We know that the sum of first n odd natural numbers is n 2 . Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9 2 6. Correct answer: A 2 3 (4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. Page 2 CBSE VIII | Mathematics Sample Paper 2 - Solution CBSE Board Class VIII Mathematics Term I Sample Paper 2 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B 2. Correct answer: A Indefinitely on both sides of 0 3. Correct answer: A An octagon is made up of 8 sides. 4. Correct answer: B Original Price = Rs. 50 Increased Price = 55 - 50 = 5 Thus, Increased price Percentage increase = 100 % Original price ?? ? ?? ?? 5. Correct answer: C We know that the sum of first n odd natural numbers is n 2 . Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9 2 6. Correct answer: A 2 3 (4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. CBSE VIII | Mathematics Sample Paper 2 - Solution 7. Correct answer: B Trapezium is not a parallelogram as it has only one pair of parallel sides. 8. Correct answer: A Number of Red Rome apple = 4 × 10 = 40 9. Correct answer: A It is known that the adjacent angles of a parallelogram are supplementary. Therefore, measure of required angle = 180 o - 50 o = 130 o 10. Correct answer: B The probability of an event always lies between 0 and 1. 11. Correct answer: B Using the given pattern, 2000 2 = 4000000 12. Correct answer: C The discount 50% + 50% is equal to a single discount of 75%. The S.P. is 25% of C.P. So, S.P. = 25 1200 300 100 ?? Section B 13. (i) Let x be the multiplicative inverse of (ii) Let x be the multiplicative inverse of Or, x = 5 2 Page 3 CBSE VIII | Mathematics Sample Paper 2 - Solution CBSE Board Class VIII Mathematics Term I Sample Paper 2 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B 2. Correct answer: A Indefinitely on both sides of 0 3. Correct answer: A An octagon is made up of 8 sides. 4. Correct answer: B Original Price = Rs. 50 Increased Price = 55 - 50 = 5 Thus, Increased price Percentage increase = 100 % Original price ?? ? ?? ?? 5. Correct answer: C We know that the sum of first n odd natural numbers is n 2 . Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9 2 6. Correct answer: A 2 3 (4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. CBSE VIII | Mathematics Sample Paper 2 - Solution 7. Correct answer: B Trapezium is not a parallelogram as it has only one pair of parallel sides. 8. Correct answer: A Number of Red Rome apple = 4 × 10 = 40 9. Correct answer: A It is known that the adjacent angles of a parallelogram are supplementary. Therefore, measure of required angle = 180 o - 50 o = 130 o 10. Correct answer: B The probability of an event always lies between 0 and 1. 11. Correct answer: B Using the given pattern, 2000 2 = 4000000 12. Correct answer: C The discount 50% + 50% is equal to a single discount of 75%. The S.P. is 25% of C.P. So, S.P. = 25 1200 300 100 ?? Section B 13. (i) Let x be the multiplicative inverse of (ii) Let x be the multiplicative inverse of Or, x = 5 2 CBSE VIII | Mathematics Sample Paper 2 - Solution 14. Let x be the ten's digit of the two-digit number. Then its unit's digit = x + 7. Number = unit's digit + 10(ten's digit) = (x + 7) + 10(x) = 11x + 7. Sum of the digits = (x + 7) + (x) = 2x + 7. Given, sum of the digits is half of the whole number. Therefore, 4x + 14 = 11x + 7 4x - 11x = 7 - 14 -7x = -7 x = 1 Ten's digit of the two-digit number is x = 1. Unit's digit of the two-digit number = x + 7 = 1 + 7 = 8 Thus, the required number is 18. 15. y = ? EHP (Alternate interior angles as OP||HE) y = 40° 70° = ? EHO = z + 40 ? (Corresponding angles as OP||HE) 70° - 40° = z z = 30° ? HEP = ? EHO (Adjacent pair of angles as HO||EP) x + (z + 40 ?) = 180° x + 70 ? = 180° x = 110° 16. Total number of students = 35 i) Number of boys = 20 20 4 Required probability 35 7 ? ? ? ii) Number of girls = 15 15 3 Required probability 35 7 ? ? ? 17. 82 2 = (80 + 2) 2 In the property (a + b) 2 = a 2 + b 2 + 2ab Substituting a = 80 and b = 2, we get (80 + 2) 2 = 80 2 + 2 2 + 2 × 80 × 2 = 6400 + 4 + 320 = 6724 Page 4 CBSE VIII | Mathematics Sample Paper 2 - Solution CBSE Board Class VIII Mathematics Term I Sample Paper 2 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B 2. Correct answer: A Indefinitely on both sides of 0 3. Correct answer: A An octagon is made up of 8 sides. 4. Correct answer: B Original Price = Rs. 50 Increased Price = 55 - 50 = 5 Thus, Increased price Percentage increase = 100 % Original price ?? ? ?? ?? 5. Correct answer: C We know that the sum of first n odd natural numbers is n 2 . Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9 2 6. Correct answer: A 2 3 (4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. CBSE VIII | Mathematics Sample Paper 2 - Solution 7. Correct answer: B Trapezium is not a parallelogram as it has only one pair of parallel sides. 8. Correct answer: A Number of Red Rome apple = 4 × 10 = 40 9. Correct answer: A It is known that the adjacent angles of a parallelogram are supplementary. Therefore, measure of required angle = 180 o - 50 o = 130 o 10. Correct answer: B The probability of an event always lies between 0 and 1. 11. Correct answer: B Using the given pattern, 2000 2 = 4000000 12. Correct answer: C The discount 50% + 50% is equal to a single discount of 75%. The S.P. is 25% of C.P. So, S.P. = 25 1200 300 100 ?? Section B 13. (i) Let x be the multiplicative inverse of (ii) Let x be the multiplicative inverse of Or, x = 5 2 CBSE VIII | Mathematics Sample Paper 2 - Solution 14. Let x be the ten's digit of the two-digit number. Then its unit's digit = x + 7. Number = unit's digit + 10(ten's digit) = (x + 7) + 10(x) = 11x + 7. Sum of the digits = (x + 7) + (x) = 2x + 7. Given, sum of the digits is half of the whole number. Therefore, 4x + 14 = 11x + 7 4x - 11x = 7 - 14 -7x = -7 x = 1 Ten's digit of the two-digit number is x = 1. Unit's digit of the two-digit number = x + 7 = 1 + 7 = 8 Thus, the required number is 18. 15. y = ? EHP (Alternate interior angles as OP||HE) y = 40° 70° = ? EHO = z + 40 ? (Corresponding angles as OP||HE) 70° - 40° = z z = 30° ? HEP = ? EHO (Adjacent pair of angles as HO||EP) x + (z + 40 ?) = 180° x + 70 ? = 180° x = 110° 16. Total number of students = 35 i) Number of boys = 20 20 4 Required probability 35 7 ? ? ? ii) Number of girls = 15 15 3 Required probability 35 7 ? ? ? 17. 82 2 = (80 + 2) 2 In the property (a + b) 2 = a 2 + b 2 + 2ab Substituting a = 80 and b = 2, we get (80 + 2) 2 = 80 2 + 2 2 + 2 × 80 × 2 = 6400 + 4 + 320 = 6724 CBSE VIII | Mathematics Sample Paper 2 - Solution 18. From the graph, it is clear that: 5 students favoured orange and 1 student favoured green colour. Now, 5 - 1 = 4 Therefore, 4 more students favoured orange colour than green. 19. Cost of TV set = Rs. 36500. Sales tax = 8% of Rs. 36500 Therefore, Bill amount = Rs. (36500 + 2920) = Rs. 39420 20. First four triangular numbers are: 1, 3, 6 and 10. Now, 1 + 3 = 4 = 2 2 3 + 6 = 9 = 3 2 6 + 10 = 16 = 4 2 Here, 4, 9 and 16 all are square numbers. 21. 3(2x - 1) = 2(x + 4) + 1 6x - 3 = 2x + 8 + 1 6x – 3 - 2x = 8 + 1 (Transposing 2x to LHS ) 6x - 2x = 8 + 1 + 3 (Transposing -3 to RHS) 4x = 12 Dividing both sides by 4, x = 12 4 = 3 x = 3 22. Page 5 CBSE VIII | Mathematics Sample Paper 2 - Solution CBSE Board Class VIII Mathematics Term I Sample Paper 2 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B 2. Correct answer: A Indefinitely on both sides of 0 3. Correct answer: A An octagon is made up of 8 sides. 4. Correct answer: B Original Price = Rs. 50 Increased Price = 55 - 50 = 5 Thus, Increased price Percentage increase = 100 % Original price ?? ? ?? ?? 5. Correct answer: C We know that the sum of first n odd natural numbers is n 2 . Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9 2 6. Correct answer: A 2 3 (4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. CBSE VIII | Mathematics Sample Paper 2 - Solution 7. Correct answer: B Trapezium is not a parallelogram as it has only one pair of parallel sides. 8. Correct answer: A Number of Red Rome apple = 4 × 10 = 40 9. Correct answer: A It is known that the adjacent angles of a parallelogram are supplementary. Therefore, measure of required angle = 180 o - 50 o = 130 o 10. Correct answer: B The probability of an event always lies between 0 and 1. 11. Correct answer: B Using the given pattern, 2000 2 = 4000000 12. Correct answer: C The discount 50% + 50% is equal to a single discount of 75%. The S.P. is 25% of C.P. So, S.P. = 25 1200 300 100 ?? Section B 13. (i) Let x be the multiplicative inverse of (ii) Let x be the multiplicative inverse of Or, x = 5 2 CBSE VIII | Mathematics Sample Paper 2 - Solution 14. Let x be the ten's digit of the two-digit number. Then its unit's digit = x + 7. Number = unit's digit + 10(ten's digit) = (x + 7) + 10(x) = 11x + 7. Sum of the digits = (x + 7) + (x) = 2x + 7. Given, sum of the digits is half of the whole number. Therefore, 4x + 14 = 11x + 7 4x - 11x = 7 - 14 -7x = -7 x = 1 Ten's digit of the two-digit number is x = 1. Unit's digit of the two-digit number = x + 7 = 1 + 7 = 8 Thus, the required number is 18. 15. y = ? EHP (Alternate interior angles as OP||HE) y = 40° 70° = ? EHO = z + 40 ? (Corresponding angles as OP||HE) 70° - 40° = z z = 30° ? HEP = ? EHO (Adjacent pair of angles as HO||EP) x + (z + 40 ?) = 180° x + 70 ? = 180° x = 110° 16. Total number of students = 35 i) Number of boys = 20 20 4 Required probability 35 7 ? ? ? ii) Number of girls = 15 15 3 Required probability 35 7 ? ? ? 17. 82 2 = (80 + 2) 2 In the property (a + b) 2 = a 2 + b 2 + 2ab Substituting a = 80 and b = 2, we get (80 + 2) 2 = 80 2 + 2 2 + 2 × 80 × 2 = 6400 + 4 + 320 = 6724 CBSE VIII | Mathematics Sample Paper 2 - Solution 18. From the graph, it is clear that: 5 students favoured orange and 1 student favoured green colour. Now, 5 - 1 = 4 Therefore, 4 more students favoured orange colour than green. 19. Cost of TV set = Rs. 36500. Sales tax = 8% of Rs. 36500 Therefore, Bill amount = Rs. (36500 + 2920) = Rs. 39420 20. First four triangular numbers are: 1, 3, 6 and 10. Now, 1 + 3 = 4 = 2 2 3 + 6 = 9 = 3 2 6 + 10 = 16 = 4 2 Here, 4, 9 and 16 all are square numbers. 21. 3(2x - 1) = 2(x + 4) + 1 6x - 3 = 2x + 8 + 1 6x – 3 - 2x = 8 + 1 (Transposing 2x to LHS ) 6x - 2x = 8 + 1 + 3 (Transposing -3 to RHS) 4x = 12 Dividing both sides by 4, x = 12 4 = 3 x = 3 22. CBSE VIII | Mathematics Sample Paper 2 - Solution 23. Original number = 4000 Increased % = 35% Thus, Number of students now = Original number + 35% of 4000 24. Here, n(S) = 10 + 25 = 35 Let E be the event of getting a prize. n(E) = 10 ? ? ? ? n(E) 10 2 P(E) n(S) 35 7 Probability of getting a prize = 2 7 Section C 25. a) If we choose a scale of 1:50 for the frequency then the vertical bar chart will be as shown. b) Percentage increase in the visitors in March as compared to January is c) Percentage of visitors who came in February as compared to the total number of visitors isRead More

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