Page 1 CBSE VII | Mathematics Sample Paper 3 - Solution CBSE Board Class VII Mathematics Term I Sample Paper 3 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: A (128 ÷32)÷ (-4) = 4 ÷ (-4) = -1 2. Correct answer: A Total cost = 2.40 × 10 = Rs. 24 3. Correct answer: B The given observations can be arranged in ascending order as 4, 6, 9, 10, 11, 12 and 18 Here, number of observations = 7 (odd) Median = Middle observation = 10 4. Correct answer: A 2x + 3 = 7 If we will transpose 3 to RHS, then the term with variable will remain on one side and the constants will be on other side. So, the first step is to transpose 3 to RHS. i.e. 2x = 7 â€“ 3 5. Correct answer: C ?BCA = 180° - 150° = 30° (linear pair angles) Also, ?B = ?BCA = 30° (Angles opp. to equal sides are equal) ? ?A = 180° - 30° - 30° = 120° (Using angle sum property of triangle) 6. Correct answer: B Increased amount = 12 Rs. ×54=Rs. 6.48 100 Page 2 CBSE VII | Mathematics Sample Paper 3 - Solution CBSE Board Class VII Mathematics Term I Sample Paper 3 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: A (128 ÷32)÷ (-4) = 4 ÷ (-4) = -1 2. Correct answer: A Total cost = 2.40 × 10 = Rs. 24 3. Correct answer: B The given observations can be arranged in ascending order as 4, 6, 9, 10, 11, 12 and 18 Here, number of observations = 7 (odd) Median = Middle observation = 10 4. Correct answer: A 2x + 3 = 7 If we will transpose 3 to RHS, then the term with variable will remain on one side and the constants will be on other side. So, the first step is to transpose 3 to RHS. i.e. 2x = 7 â€“ 3 5. Correct answer: C ?BCA = 180° - 150° = 30° (linear pair angles) Also, ?B = ?BCA = 30° (Angles opp. to equal sides are equal) ? ?A = 180° - 30° - 30° = 120° (Using angle sum property of triangle) 6. Correct answer: B Increased amount = 12 Rs. ×54=Rs. 6.48 100 CBSE VII | Mathematics Sample Paper 3 - Solution 7. Correct answer: C ? 28 2 33 So the multiplicative inverse is 3 8 . 8. Correct answer: D The triangle ABC is a right angled triangle, By Pythagoras theorem, we have: c 2 = a 2 + b 2 9. Correct answer: B 21b - 32 + 7b - 20b = 21b + 7b - 20b â€“ 32 = 8b â€“ 32 10. Correct answer: D 11. Correct answer: A The two triangles can be proved to be congruent by using SAS congruency criterion. The corresponding equal parts in triangles ABC and ADE are 12. Correct answer: C Let the whole number be x. Twice of the whole number = 2x 9 added to twice of the whole number = 9 + 2x From the given information, we have: 9 + 2x = 31 2x = 31 - 9 2x = 22 x = 11 Thus, the required whole number is 11. Page 3 CBSE VII | Mathematics Sample Paper 3 - Solution CBSE Board Class VII Mathematics Term I Sample Paper 3 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: A (128 ÷32)÷ (-4) = 4 ÷ (-4) = -1 2. Correct answer: A Total cost = 2.40 × 10 = Rs. 24 3. Correct answer: B The given observations can be arranged in ascending order as 4, 6, 9, 10, 11, 12 and 18 Here, number of observations = 7 (odd) Median = Middle observation = 10 4. Correct answer: A 2x + 3 = 7 If we will transpose 3 to RHS, then the term with variable will remain on one side and the constants will be on other side. So, the first step is to transpose 3 to RHS. i.e. 2x = 7 â€“ 3 5. Correct answer: C ?BCA = 180° - 150° = 30° (linear pair angles) Also, ?B = ?BCA = 30° (Angles opp. to equal sides are equal) ? ?A = 180° - 30° - 30° = 120° (Using angle sum property of triangle) 6. Correct answer: B Increased amount = 12 Rs. ×54=Rs. 6.48 100 CBSE VII | Mathematics Sample Paper 3 - Solution 7. Correct answer: C ? 28 2 33 So the multiplicative inverse is 3 8 . 8. Correct answer: D The triangle ABC is a right angled triangle, By Pythagoras theorem, we have: c 2 = a 2 + b 2 9. Correct answer: B 21b - 32 + 7b - 20b = 21b + 7b - 20b â€“ 32 = 8b â€“ 32 10. Correct answer: D 11. Correct answer: A The two triangles can be proved to be congruent by using SAS congruency criterion. The corresponding equal parts in triangles ABC and ADE are 12. Correct answer: C Let the whole number be x. Twice of the whole number = 2x 9 added to twice of the whole number = 9 + 2x From the given information, we have: 9 + 2x = 31 2x = 31 - 9 2x = 22 x = 11 Thus, the required whole number is 11. CBSE VII | Mathematics Sample Paper 3 - Solution Section B 13. Given that, m||p and t is the transversal We know that, if two parallel lines are cut by a transversal, each pair of alternate interior angles are equal. So, ? a = ? z (pair of alternate interior angles) Thus, ? z = 57 o . 14. The numbers in ascending order are: 11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 As the number of observations (21) are odd, Median = middle observation = 11 th observation = 46 Mode is the observation that appears most often. Here, 12 appears maximum number of times (thrice). So, 12 is the mode. 15. 725 × (-35) + (-725) × 65 = 725 × (-35) - 725 × 65 = 725 x (-35 - 65) [Using distributive property] = 725 × (-100) = -72500 16. Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 Subtracting (-134) from -49, we get -49 - (-134) = -49 + 134 = 85 17. Average score = mean score ? ? ? ? ? ? ? ? ? ? ? ? ? Sum of all observations Mean= Total number of observations 12 23 10 77 15 78 90 54 23 10 1 11 393 11 35.7 18. Pie filling made in 1 minute = 9.2 kg Pie filling made in 6 minutes = 6 × 9.2 kg = 55.2 kg Page 4 CBSE VII | Mathematics Sample Paper 3 - Solution CBSE Board Class VII Mathematics Term I Sample Paper 3 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: A (128 ÷32)÷ (-4) = 4 ÷ (-4) = -1 2. Correct answer: A Total cost = 2.40 × 10 = Rs. 24 3. Correct answer: B The given observations can be arranged in ascending order as 4, 6, 9, 10, 11, 12 and 18 Here, number of observations = 7 (odd) Median = Middle observation = 10 4. Correct answer: A 2x + 3 = 7 If we will transpose 3 to RHS, then the term with variable will remain on one side and the constants will be on other side. So, the first step is to transpose 3 to RHS. i.e. 2x = 7 â€“ 3 5. Correct answer: C ?BCA = 180° - 150° = 30° (linear pair angles) Also, ?B = ?BCA = 30° (Angles opp. to equal sides are equal) ? ?A = 180° - 30° - 30° = 120° (Using angle sum property of triangle) 6. Correct answer: B Increased amount = 12 Rs. ×54=Rs. 6.48 100 CBSE VII | Mathematics Sample Paper 3 - Solution 7. Correct answer: C ? 28 2 33 So the multiplicative inverse is 3 8 . 8. Correct answer: D The triangle ABC is a right angled triangle, By Pythagoras theorem, we have: c 2 = a 2 + b 2 9. Correct answer: B 21b - 32 + 7b - 20b = 21b + 7b - 20b â€“ 32 = 8b â€“ 32 10. Correct answer: D 11. Correct answer: A The two triangles can be proved to be congruent by using SAS congruency criterion. The corresponding equal parts in triangles ABC and ADE are 12. Correct answer: C Let the whole number be x. Twice of the whole number = 2x 9 added to twice of the whole number = 9 + 2x From the given information, we have: 9 + 2x = 31 2x = 31 - 9 2x = 22 x = 11 Thus, the required whole number is 11. CBSE VII | Mathematics Sample Paper 3 - Solution Section B 13. Given that, m||p and t is the transversal We know that, if two parallel lines are cut by a transversal, each pair of alternate interior angles are equal. So, ? a = ? z (pair of alternate interior angles) Thus, ? z = 57 o . 14. The numbers in ascending order are: 11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 As the number of observations (21) are odd, Median = middle observation = 11 th observation = 46 Mode is the observation that appears most often. Here, 12 appears maximum number of times (thrice). So, 12 is the mode. 15. 725 × (-35) + (-725) × 65 = 725 × (-35) - 725 × 65 = 725 x (-35 - 65) [Using distributive property] = 725 × (-100) = -72500 16. Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 Subtracting (-134) from -49, we get -49 - (-134) = -49 + 134 = 85 17. Average score = mean score ? ? ? ? ? ? ? ? ? ? ? ? ? Sum of all observations Mean= Total number of observations 12 23 10 77 15 78 90 54 23 10 1 11 393 11 35.7 18. Pie filling made in 1 minute = 9.2 kg Pie filling made in 6 minutes = 6 × 9.2 kg = 55.2 kg CBSE VII | Mathematics Sample Paper 3 - Solution 19. Distance travelled with 1 gallon = 2 32 10 = 33 miles Distance travelled with 1 11 5= 22 gallons. 11 32 = × miles 23 16 =11× miles 3 176 = miles 3 mile Thus, Sam can go 176 3 miles with 11 2 gallons. 20. ASA congruence criterion: The Angle Side Angle (ASA) postulate states that if under correspondence, two angles and the included side of a triangle is equal to two corresponding angles and included side of another triangle, then the two triangles are congruent. Consider the triangles ABC and XYZ as shown below. Two angles and the included side are congruent. ? ABC = ? XYZ (equal angle) BC = YZ (equal side) ? ACB = ? XZY (equal angle) So, ABC XYZ Therefore, by the ASA congruence criterion, the triangles are congruent. Page 5 CBSE VII | Mathematics Sample Paper 3 - Solution CBSE Board Class VII Mathematics Term I Sample Paper 3 - Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: A (128 ÷32)÷ (-4) = 4 ÷ (-4) = -1 2. Correct answer: A Total cost = 2.40 × 10 = Rs. 24 3. Correct answer: B The given observations can be arranged in ascending order as 4, 6, 9, 10, 11, 12 and 18 Here, number of observations = 7 (odd) Median = Middle observation = 10 4. Correct answer: A 2x + 3 = 7 If we will transpose 3 to RHS, then the term with variable will remain on one side and the constants will be on other side. So, the first step is to transpose 3 to RHS. i.e. 2x = 7 â€“ 3 5. Correct answer: C ?BCA = 180° - 150° = 30° (linear pair angles) Also, ?B = ?BCA = 30° (Angles opp. to equal sides are equal) ? ?A = 180° - 30° - 30° = 120° (Using angle sum property of triangle) 6. Correct answer: B Increased amount = 12 Rs. ×54=Rs. 6.48 100 CBSE VII | Mathematics Sample Paper 3 - Solution 7. Correct answer: C ? 28 2 33 So the multiplicative inverse is 3 8 . 8. Correct answer: D The triangle ABC is a right angled triangle, By Pythagoras theorem, we have: c 2 = a 2 + b 2 9. Correct answer: B 21b - 32 + 7b - 20b = 21b + 7b - 20b â€“ 32 = 8b â€“ 32 10. Correct answer: D 11. Correct answer: A The two triangles can be proved to be congruent by using SAS congruency criterion. The corresponding equal parts in triangles ABC and ADE are 12. Correct answer: C Let the whole number be x. Twice of the whole number = 2x 9 added to twice of the whole number = 9 + 2x From the given information, we have: 9 + 2x = 31 2x = 31 - 9 2x = 22 x = 11 Thus, the required whole number is 11. CBSE VII | Mathematics Sample Paper 3 - Solution Section B 13. Given that, m||p and t is the transversal We know that, if two parallel lines are cut by a transversal, each pair of alternate interior angles are equal. So, ? a = ? z (pair of alternate interior angles) Thus, ? z = 57 o . 14. The numbers in ascending order are: 11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 As the number of observations (21) are odd, Median = middle observation = 11 th observation = 46 Mode is the observation that appears most often. Here, 12 appears maximum number of times (thrice). So, 12 is the mode. 15. 725 × (-35) + (-725) × 65 = 725 × (-35) - 725 × 65 = 725 x (-35 - 65) [Using distributive property] = 725 × (-100) = -72500 16. Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 Subtracting (-134) from -49, we get -49 - (-134) = -49 + 134 = 85 17. Average score = mean score ? ? ? ? ? ? ? ? ? ? ? ? ? Sum of all observations Mean= Total number of observations 12 23 10 77 15 78 90 54 23 10 1 11 393 11 35.7 18. Pie filling made in 1 minute = 9.2 kg Pie filling made in 6 minutes = 6 × 9.2 kg = 55.2 kg CBSE VII | Mathematics Sample Paper 3 - Solution 19. Distance travelled with 1 gallon = 2 32 10 = 33 miles Distance travelled with 1 11 5= 22 gallons. 11 32 = × miles 23 16 =11× miles 3 176 = miles 3 mile Thus, Sam can go 176 3 miles with 11 2 gallons. 20. ASA congruence criterion: The Angle Side Angle (ASA) postulate states that if under correspondence, two angles and the included side of a triangle is equal to two corresponding angles and included side of another triangle, then the two triangles are congruent. Consider the triangles ABC and XYZ as shown below. Two angles and the included side are congruent. ? ABC = ? XYZ (equal angle) BC = YZ (equal side) ? ACB = ? XZY (equal angle) So, ABC XYZ Therefore, by the ASA congruence criterion, the triangles are congruent. CBSE VII | Mathematics Sample Paper 3 - Solution 21. Let A and B be the two numbers such that, 40% of A = 2 B 3 Then, ? ?? ?? ? ? ? ? ?? ?? ?? 40 2 100 3 22 53 2 5 10 3 2 3 : 5:3 AB AB A B AB 22. Here, AB = PR (= 3.5 cm), BC = PQ (= 7.1 cm) And AC = QR (= 5 cm) This shows that the three sides of one triangle are equal to the three sides Of the other triangle. So, by SSS congruence rule, the two triangles are congruent. From the above three equality relations, it can be easily seen that A ? R, B ? P and C ? Q. So, we have ?ABC ? ?RPQRead More

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