Page 1 CBSE VIII | Mathematics Sample Paper – 3 Solutions CBSE Class VIII Mathematics Sample Paper – 3 Solution Time: 3 hours Total Marks: 80 Section A 1. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 2. Correct answer: B 20 20% of x= 100 5 x x ? 3. Correct answer: A Five vertices. 4. Correct option : A ? 196 2 484 ? 1 7 2 ? ? 1 7 11 11 5. Correct answer: B 0 and 1 6. Correct answer: A 1 3 = 1 Thus, the natural number 1 is equal to its cube. 7. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 8. Correct option: A 6 17 29 2 12 34 29 17 34 2 k k kk k k ? ? ? ? ? ?? ?? Page 2 CBSE VIII | Mathematics Sample Paper – 3 Solutions CBSE Class VIII Mathematics Sample Paper – 3 Solution Time: 3 hours Total Marks: 80 Section A 1. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 2. Correct answer: B 20 20% of x= 100 5 x x ? 3. Correct answer: A Five vertices. 4. Correct option : A ? 196 2 484 ? 1 7 2 ? ? 1 7 11 11 5. Correct answer: B 0 and 1 6. Correct answer: A 1 3 = 1 Thus, the natural number 1 is equal to its cube. 7. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 8. Correct option: A 6 17 29 2 12 34 29 17 34 2 k k kk k k ? ? ? ? ? ?? ?? CBSE VIII | Mathematics Sample Paper – 3 Solutions 9. Correct answer: C The given shape has 12 edges. 10. Correct answer: D Sales tax = 4 380 15.20 100 ?? 11. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 12. Correct option: B ? ? ? ? ? 14 441 22 22 441 .693 14 x x Rs Section B (Questions 8 to 11 carry 2 marks each) 13. The number 2 5 lies between 0 and 1. Draw a number line. Mark points O and A to represent 0 and 1, respectively. Divide OA into 5 equal parts (equal to the denominator of 2 5 ).The second point, Q, represents the rational number 2 5 . 14. Steps of construction: a) Draw AC = 8 cm. b) Draw perpendicular bisector XY of AC meeting AC at O. c) From O cut off OD = 1 2 × 6 cm = 3 cm along OX and OB = 1 2 × 6 cm =3 cm along OY. d) Join AB, BC, CD and DA. Page 3 CBSE VIII | Mathematics Sample Paper – 3 Solutions CBSE Class VIII Mathematics Sample Paper – 3 Solution Time: 3 hours Total Marks: 80 Section A 1. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 2. Correct answer: B 20 20% of x= 100 5 x x ? 3. Correct answer: A Five vertices. 4. Correct option : A ? 196 2 484 ? 1 7 2 ? ? 1 7 11 11 5. Correct answer: B 0 and 1 6. Correct answer: A 1 3 = 1 Thus, the natural number 1 is equal to its cube. 7. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 8. Correct option: A 6 17 29 2 12 34 29 17 34 2 k k kk k k ? ? ? ? ? ?? ?? CBSE VIII | Mathematics Sample Paper – 3 Solutions 9. Correct answer: C The given shape has 12 edges. 10. Correct answer: D Sales tax = 4 380 15.20 100 ?? 11. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 12. Correct option: B ? ? ? ? ? 14 441 22 22 441 .693 14 x x Rs Section B (Questions 8 to 11 carry 2 marks each) 13. The number 2 5 lies between 0 and 1. Draw a number line. Mark points O and A to represent 0 and 1, respectively. Divide OA into 5 equal parts (equal to the denominator of 2 5 ).The second point, Q, represents the rational number 2 5 . 14. Steps of construction: a) Draw AC = 8 cm. b) Draw perpendicular bisector XY of AC meeting AC at O. c) From O cut off OD = 1 2 × 6 cm = 3 cm along OX and OB = 1 2 × 6 cm =3 cm along OY. d) Join AB, BC, CD and DA. CBSE VIII | Mathematics Sample Paper – 3 Solutions ABCD is the required rhombus. 15. We have, 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 are 6. 16. We have: (a + b) 2 = a 2 + b 2 + 2abTaking, a = -20 and b = -5, we get (-25) 2 = {-20 + (-5)} 2 = (-20) 2 + (-5) 2 + 2(-20)(-5) = 400 + 25 + 200 = 625 17. From the graph, it is clear that 5 students favoured orange and 1 student favoured green. Now, 5 – 1 = 4 Therefore, 4 more students favoured orange colour than green. 18. 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 Page 4 CBSE VIII | Mathematics Sample Paper – 3 Solutions CBSE Class VIII Mathematics Sample Paper – 3 Solution Time: 3 hours Total Marks: 80 Section A 1. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 2. Correct answer: B 20 20% of x= 100 5 x x ? 3. Correct answer: A Five vertices. 4. Correct option : A ? 196 2 484 ? 1 7 2 ? ? 1 7 11 11 5. Correct answer: B 0 and 1 6. Correct answer: A 1 3 = 1 Thus, the natural number 1 is equal to its cube. 7. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 8. Correct option: A 6 17 29 2 12 34 29 17 34 2 k k kk k k ? ? ? ? ? ?? ?? CBSE VIII | Mathematics Sample Paper – 3 Solutions 9. Correct answer: C The given shape has 12 edges. 10. Correct answer: D Sales tax = 4 380 15.20 100 ?? 11. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 12. Correct option: B ? ? ? ? ? 14 441 22 22 441 .693 14 x x Rs Section B (Questions 8 to 11 carry 2 marks each) 13. The number 2 5 lies between 0 and 1. Draw a number line. Mark points O and A to represent 0 and 1, respectively. Divide OA into 5 equal parts (equal to the denominator of 2 5 ).The second point, Q, represents the rational number 2 5 . 14. Steps of construction: a) Draw AC = 8 cm. b) Draw perpendicular bisector XY of AC meeting AC at O. c) From O cut off OD = 1 2 × 6 cm = 3 cm along OX and OB = 1 2 × 6 cm =3 cm along OY. d) Join AB, BC, CD and DA. CBSE VIII | Mathematics Sample Paper – 3 Solutions ABCD is the required rhombus. 15. We have, 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 are 6. 16. We have: (a + b) 2 = a 2 + b 2 + 2abTaking, a = -20 and b = -5, we get (-25) 2 = {-20 + (-5)} 2 = (-20) 2 + (-5) 2 + 2(-20)(-5) = 400 + 25 + 200 = 625 17. From the graph, it is clear that 5 students favoured orange and 1 student favoured green. Now, 5 – 1 = 4 Therefore, 4 more students favoured orange colour than green. 18. 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 CBSE VIII | Mathematics Sample Paper – 3 Solutions Hence, the perimeter of the given trapezium is 28 cm. 19. Original price of the book = Rs. 50 Increased % = 6% Thus, New Price = Original Price + 6% of Original price New price = Rs. 6 50 50 .(50 3) .53 100 Rs Rs ? ? ? ? ? 20. Area of square = (5a – 2b) 2 We use the identity (x – y ) 2 = x 2 – 2xy + y 2 Taking, x = 5a and y = 2b We get, (5a – 2b) 2 = (5a) 2 – 2(5a)(2b ) + (2b)=25a 2 – 20ab + 4b 2 21. 82 2 = (80 + 2) 2 In the property (a + b) 2 = a 2 + b 2 + 2ab, putting a = 80 and b = 2, we get: (80 + 2) 2 = 80 2 + 2 2 + 2 × 80 × 2 = 6400 + 4 + 320 = 6724 22. 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, 1 (2 7) (11 7) 2 xx ? ? ? 4x + 14 = 11x + 7 ? ? ? ? ? ? 4 11 7 14 77 xx x i.e. 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. 23. Let the required number be x. Then, 26% of x = 65 Page 5 CBSE VIII | Mathematics Sample Paper – 3 Solutions CBSE Class VIII Mathematics Sample Paper – 3 Solution Time: 3 hours Total Marks: 80 Section A 1. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 2. Correct answer: B 20 20% of x= 100 5 x x ? 3. Correct answer: A Five vertices. 4. Correct option : A ? 196 2 484 ? 1 7 2 ? ? 1 7 11 11 5. Correct answer: B 0 and 1 6. Correct answer: A 1 3 = 1 Thus, the natural number 1 is equal to its cube. 7. Correct answer: D A rational number is a number of the form p q where q? 0. So, in case of reciprocal of 0, denominator will be 0. 8. Correct option: A 6 17 29 2 12 34 29 17 34 2 k k kk k k ? ? ? ? ? ?? ?? CBSE VIII | Mathematics Sample Paper – 3 Solutions 9. Correct answer: C The given shape has 12 edges. 10. Correct answer: D Sales tax = 4 380 15.20 100 ?? 11. Correct option: C ? ? ? ? ? ? ? ? ? 22 484 2 2 11 11 2 11 2 11 22 12. Correct option: B ? ? ? ? ? 14 441 22 22 441 .693 14 x x Rs Section B (Questions 8 to 11 carry 2 marks each) 13. The number 2 5 lies between 0 and 1. Draw a number line. Mark points O and A to represent 0 and 1, respectively. Divide OA into 5 equal parts (equal to the denominator of 2 5 ).The second point, Q, represents the rational number 2 5 . 14. Steps of construction: a) Draw AC = 8 cm. b) Draw perpendicular bisector XY of AC meeting AC at O. c) From O cut off OD = 1 2 × 6 cm = 3 cm along OX and OB = 1 2 × 6 cm =3 cm along OY. d) Join AB, BC, CD and DA. CBSE VIII | Mathematics Sample Paper – 3 Solutions ABCD is the required rhombus. 15. We have, 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 are 6. 16. We have: (a + b) 2 = a 2 + b 2 + 2abTaking, a = -20 and b = -5, we get (-25) 2 = {-20 + (-5)} 2 = (-20) 2 + (-5) 2 + 2(-20)(-5) = 400 + 25 + 200 = 625 17. From the graph, it is clear that 5 students favoured orange and 1 student favoured green. Now, 5 – 1 = 4 Therefore, 4 more students favoured orange colour than green. 18. 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 CBSE VIII | Mathematics Sample Paper – 3 Solutions Hence, the perimeter of the given trapezium is 28 cm. 19. Original price of the book = Rs. 50 Increased % = 6% Thus, New Price = Original Price + 6% of Original price New price = Rs. 6 50 50 .(50 3) .53 100 Rs Rs ? ? ? ? ? 20. Area of square = (5a – 2b) 2 We use the identity (x – y ) 2 = x 2 – 2xy + y 2 Taking, x = 5a and y = 2b We get, (5a – 2b) 2 = (5a) 2 – 2(5a)(2b ) + (2b)=25a 2 – 20ab + 4b 2 21. 82 2 = (80 + 2) 2 In the property (a + b) 2 = a 2 + b 2 + 2ab, putting a = 80 and b = 2, we get: (80 + 2) 2 = 80 2 + 2 2 + 2 × 80 × 2 = 6400 + 4 + 320 = 6724 22. 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, 1 (2 7) (11 7) 2 xx ? ? ? 4x + 14 = 11x + 7 ? ? ? ? ? ? 4 11 7 14 77 xx x i.e. 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. 23. Let the required number be x. Then, 26% of x = 65 CBSE VIII | Mathematics Sample Paper – 3 Solutions 26 65 100 100 65 26 250 x x x ?? ?? ? ? ? ?? ?? ?? Hence, the required number is 250. 24. (by commutativity) (by distributivity) Section C 25. Here, at unit's place A × 5 = A That is we need to search for a number, which when multiplied to 5 gives the same unit place. Such a number is 5 or 0, as 5 × 5 = 25 or 0 × 5 = 0 Case (1) Taking 5 in place of A, we get 2 B A 5 C B 5 ? Here, B can take the value 2, which satisfy the condition, taking, B = 2, we get 2 2 5 5 1 2 5 ? Thus, A = 5, B = 2 and C = 1Read More

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