Page 1 CBSE VI | Mathematics Sample Paper 4 – Solution CBSE Board Class VI Mathematics Term I Sample Paper 4 – Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B The number just before 1000000 is one less than 1000000. The required number = 1000000 - 1 = 999999. 2. Correct answer: B On a number line, –110 lies next to –111 on the right. Therefore, the successor of –111 is –110. 3. Correct answer: A The given fraction is 15 18 Dividing the numerator and denominator by 3, we get, 15 3 5 18 3 6 ? ? ? Thus, 15 18 is equivalent to 5 6 . 4. Correct answer: D The numbers 138 and 432 are divisible by both 2 and 3 and hence are divisible by 6. The number 653 is neither divisible by 3 nor by 2 and hence is not divisible by 6. Now, consider the number 531. The sum of the digits of the number 531 is divisible by 3, so 531 is divisible by 3. However, it is not an even number, so it is not divisible by 2. Thus, 531 is divisible by 3 but not by 6. 5. Correct answer: B 1 1 4 ( 1) 3 1 3 12 12 12 4 ? ? ? ?? ? ? ? ? ?? ?? Page 2 CBSE VI | Mathematics Sample Paper 4 – Solution CBSE Board Class VI Mathematics Term I Sample Paper 4 – Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B The number just before 1000000 is one less than 1000000. The required number = 1000000 - 1 = 999999. 2. Correct answer: B On a number line, –110 lies next to –111 on the right. Therefore, the successor of –111 is –110. 3. Correct answer: A The given fraction is 15 18 Dividing the numerator and denominator by 3, we get, 15 3 5 18 3 6 ? ? ? Thus, 15 18 is equivalent to 5 6 . 4. Correct answer: D The numbers 138 and 432 are divisible by both 2 and 3 and hence are divisible by 6. The number 653 is neither divisible by 3 nor by 2 and hence is not divisible by 6. Now, consider the number 531. The sum of the digits of the number 531 is divisible by 3, so 531 is divisible by 3. However, it is not an even number, so it is not divisible by 2. Thus, 531 is divisible by 3 but not by 6. 5. Correct answer: B 1 1 4 ( 1) 3 1 3 12 12 12 4 ? ? ? ?? ? ? ? ? ?? ?? CBSE VI | Mathematics Sample Paper 4 – Solution 6. Correct answer: C Every quadrilateral has four pairs of adjacent angles. Example: For the quadrilateral ABCD, the pairs of adjacent angles are (i) ? A, ? B (ii) ? B, ? C (iii) ? C, ? D (iv) ? D, ? A. 7. Correct answer: A Starting from zero, a jump of 4 units is made to the right to reach 4. Then, 3 jumps (each of 1 unit) are taken to the right to reach 7. So, this number line represents 4 + 3. 8. Correct Answer: A If the number can be divided by the numbers 2 and 3, then that number is divisible by 6. 9. Correct answer: B CCC stands for 300 And XL stands for 40 So, CCCXL stands for 300 + 40 = 340 10. Correct answer: A When hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 180º. Fraction = 180º 1 360º 2 ? 11. Correct answer: A 1 + 0 = 1 ? It does not represent zero 12. Correct answer: B The given shape is cuboid. Page 3 CBSE VI | Mathematics Sample Paper 4 – Solution CBSE Board Class VI Mathematics Term I Sample Paper 4 – Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B The number just before 1000000 is one less than 1000000. The required number = 1000000 - 1 = 999999. 2. Correct answer: B On a number line, –110 lies next to –111 on the right. Therefore, the successor of –111 is –110. 3. Correct answer: A The given fraction is 15 18 Dividing the numerator and denominator by 3, we get, 15 3 5 18 3 6 ? ? ? Thus, 15 18 is equivalent to 5 6 . 4. Correct answer: D The numbers 138 and 432 are divisible by both 2 and 3 and hence are divisible by 6. The number 653 is neither divisible by 3 nor by 2 and hence is not divisible by 6. Now, consider the number 531. The sum of the digits of the number 531 is divisible by 3, so 531 is divisible by 3. However, it is not an even number, so it is not divisible by 2. Thus, 531 is divisible by 3 but not by 6. 5. Correct answer: B 1 1 4 ( 1) 3 1 3 12 12 12 4 ? ? ? ?? ? ? ? ? ?? ?? CBSE VI | Mathematics Sample Paper 4 – Solution 6. Correct answer: C Every quadrilateral has four pairs of adjacent angles. Example: For the quadrilateral ABCD, the pairs of adjacent angles are (i) ? A, ? B (ii) ? B, ? C (iii) ? C, ? D (iv) ? D, ? A. 7. Correct answer: A Starting from zero, a jump of 4 units is made to the right to reach 4. Then, 3 jumps (each of 1 unit) are taken to the right to reach 7. So, this number line represents 4 + 3. 8. Correct Answer: A If the number can be divided by the numbers 2 and 3, then that number is divisible by 6. 9. Correct answer: B CCC stands for 300 And XL stands for 40 So, CCCXL stands for 300 + 40 = 340 10. Correct answer: A When hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 180º. Fraction = 180º 1 360º 2 ? 11. Correct answer: A 1 + 0 = 1 ? It does not represent zero 12. Correct answer: B The given shape is cuboid. CBSE VI | Mathematics Sample Paper 4 – Solution Section B 13. Using distributive property of multiplication over addition, we have: 101 × 33 = (100 + 1) × 33 = 3300 +33 = 3333 101 × 333 = (100 + 1) × 333 = 33300 + 333 = 33633 101 × 3333 = (100 + 1) × 3333 = 333300 + 3333 = 336633 101 × 33333 = (100 + 1) × 33333 = 3333300 + 33333 = 3366633 14. (74 × 126) – (74 × 32) + (74 × 16) = 74 × (126 – 32 + 16) = 74 × 110 = 8140 15. 21397 can be estimated as 21000 27807 can be estimated as 28000. 42305 can be estimated as 42000. On adding, we get 21000 + 28000 + 42000 = 91000. 16. 4 × [10 + (-12)] = 4 × (-2) = -8 17. The arcs which can be formed in the given circle are as follows: arc LMN, arc MNP, arc LNP and arc LMP. 18. There are unlimited number of integers both to the left and the right of zero, hence we cannot determine the biggest or the smallest integer. 19. Angles which are neither angles of the triangle nor its exterior angles are ?AXB, ?EYF and ?CZD. 20. A triangle with all three sides of different lengths is called a scalene triangle. ? ?DEF is a scalene triangle. 21. Line segments QR and ST are the chords of the circle. Page 4 CBSE VI | Mathematics Sample Paper 4 – Solution CBSE Board Class VI Mathematics Term I Sample Paper 4 – Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B The number just before 1000000 is one less than 1000000. The required number = 1000000 - 1 = 999999. 2. Correct answer: B On a number line, –110 lies next to –111 on the right. Therefore, the successor of –111 is –110. 3. Correct answer: A The given fraction is 15 18 Dividing the numerator and denominator by 3, we get, 15 3 5 18 3 6 ? ? ? Thus, 15 18 is equivalent to 5 6 . 4. Correct answer: D The numbers 138 and 432 are divisible by both 2 and 3 and hence are divisible by 6. The number 653 is neither divisible by 3 nor by 2 and hence is not divisible by 6. Now, consider the number 531. The sum of the digits of the number 531 is divisible by 3, so 531 is divisible by 3. However, it is not an even number, so it is not divisible by 2. Thus, 531 is divisible by 3 but not by 6. 5. Correct answer: B 1 1 4 ( 1) 3 1 3 12 12 12 4 ? ? ? ?? ? ? ? ? ?? ?? CBSE VI | Mathematics Sample Paper 4 – Solution 6. Correct answer: C Every quadrilateral has four pairs of adjacent angles. Example: For the quadrilateral ABCD, the pairs of adjacent angles are (i) ? A, ? B (ii) ? B, ? C (iii) ? C, ? D (iv) ? D, ? A. 7. Correct answer: A Starting from zero, a jump of 4 units is made to the right to reach 4. Then, 3 jumps (each of 1 unit) are taken to the right to reach 7. So, this number line represents 4 + 3. 8. Correct Answer: A If the number can be divided by the numbers 2 and 3, then that number is divisible by 6. 9. Correct answer: B CCC stands for 300 And XL stands for 40 So, CCCXL stands for 300 + 40 = 340 10. Correct answer: A When hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 180º. Fraction = 180º 1 360º 2 ? 11. Correct answer: A 1 + 0 = 1 ? It does not represent zero 12. Correct answer: B The given shape is cuboid. CBSE VI | Mathematics Sample Paper 4 – Solution Section B 13. Using distributive property of multiplication over addition, we have: 101 × 33 = (100 + 1) × 33 = 3300 +33 = 3333 101 × 333 = (100 + 1) × 333 = 33300 + 333 = 33633 101 × 3333 = (100 + 1) × 3333 = 333300 + 3333 = 336633 101 × 33333 = (100 + 1) × 33333 = 3333300 + 33333 = 3366633 14. (74 × 126) – (74 × 32) + (74 × 16) = 74 × (126 – 32 + 16) = 74 × 110 = 8140 15. 21397 can be estimated as 21000 27807 can be estimated as 28000. 42305 can be estimated as 42000. On adding, we get 21000 + 28000 + 42000 = 91000. 16. 4 × [10 + (-12)] = 4 × (-2) = -8 17. The arcs which can be formed in the given circle are as follows: arc LMN, arc MNP, arc LNP and arc LMP. 18. There are unlimited number of integers both to the left and the right of zero, hence we cannot determine the biggest or the smallest integer. 19. Angles which are neither angles of the triangle nor its exterior angles are ?AXB, ?EYF and ?CZD. 20. A triangle with all three sides of different lengths is called a scalene triangle. ? ?DEF is a scalene triangle. 21. Line segments QR and ST are the chords of the circle. CBSE VI | Mathematics Sample Paper 4 – Solution 22. ? ? ? ? 3 4 2 3 4 1 21 43 3 4 3 4 ? ? ? ? ? ? ? ? ? ? ? 14 13 34 14 4 13 3 12 56 39 12 95 12 ?? ? ? ? ? ? ? ? 23. (a) It is not a polygon as it is not a closed figure (b) Yes it is a polygon made of 6 sides. (c) No it is not made of line segments. (d) No it is not made of only line segments. 24. Since the number is divisible by 12, it will also be divisible by its factors i.e. 1, 2, 3, 4, 6, 12. Clearly, 1, 2, 3, 4, and 6 are the numbers other than 12 by which this number is also divisible. Section C 25. Number of circles in step 1 = 3 = 1 × 2 + 1 Number of circles in step 2 = 5 = 2 × 2 + 1 Thus, we can observe that the number of circles is obtained by multiplying the step number by 2 and then adding 1. Therefore, the number of circles in the 100 th step = (100 × 2) + 1 = 201 26. (a) (-52) + (-36) + 42 + 8 + (-22) + 46 = -(52 + 36+22) + (42 + 8+46) = -110 + 96 = -14 (b) The largest 4-digit positive integer is 9999 and the smallest 3-digit negative integer is -999. ? 9999 + (-999) = 9999 – 999 = 9000 (c) Two integers between 2 and -5 that are inverses of each other are -1 and 1. The sum of 1 and -1 is 0. Page 5 CBSE VI | Mathematics Sample Paper 4 – Solution CBSE Board Class VI Mathematics Term I Sample Paper 4 – Solution Time: 2 ½ hours Total Marks: 80 Section A 1. Correct answer: B The number just before 1000000 is one less than 1000000. The required number = 1000000 - 1 = 999999. 2. Correct answer: B On a number line, –110 lies next to –111 on the right. Therefore, the successor of –111 is –110. 3. Correct answer: A The given fraction is 15 18 Dividing the numerator and denominator by 3, we get, 15 3 5 18 3 6 ? ? ? Thus, 15 18 is equivalent to 5 6 . 4. Correct answer: D The numbers 138 and 432 are divisible by both 2 and 3 and hence are divisible by 6. The number 653 is neither divisible by 3 nor by 2 and hence is not divisible by 6. Now, consider the number 531. The sum of the digits of the number 531 is divisible by 3, so 531 is divisible by 3. However, it is not an even number, so it is not divisible by 2. Thus, 531 is divisible by 3 but not by 6. 5. Correct answer: B 1 1 4 ( 1) 3 1 3 12 12 12 4 ? ? ? ?? ? ? ? ? ?? ?? CBSE VI | Mathematics Sample Paper 4 – Solution 6. Correct answer: C Every quadrilateral has four pairs of adjacent angles. Example: For the quadrilateral ABCD, the pairs of adjacent angles are (i) ? A, ? B (ii) ? B, ? C (iii) ? C, ? D (iv) ? D, ? A. 7. Correct answer: A Starting from zero, a jump of 4 units is made to the right to reach 4. Then, 3 jumps (each of 1 unit) are taken to the right to reach 7. So, this number line represents 4 + 3. 8. Correct Answer: A If the number can be divided by the numbers 2 and 3, then that number is divisible by 6. 9. Correct answer: B CCC stands for 300 And XL stands for 40 So, CCCXL stands for 300 + 40 = 340 10. Correct answer: A When hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 180º. Fraction = 180º 1 360º 2 ? 11. Correct answer: A 1 + 0 = 1 ? It does not represent zero 12. Correct answer: B The given shape is cuboid. CBSE VI | Mathematics Sample Paper 4 – Solution Section B 13. Using distributive property of multiplication over addition, we have: 101 × 33 = (100 + 1) × 33 = 3300 +33 = 3333 101 × 333 = (100 + 1) × 333 = 33300 + 333 = 33633 101 × 3333 = (100 + 1) × 3333 = 333300 + 3333 = 336633 101 × 33333 = (100 + 1) × 33333 = 3333300 + 33333 = 3366633 14. (74 × 126) – (74 × 32) + (74 × 16) = 74 × (126 – 32 + 16) = 74 × 110 = 8140 15. 21397 can be estimated as 21000 27807 can be estimated as 28000. 42305 can be estimated as 42000. On adding, we get 21000 + 28000 + 42000 = 91000. 16. 4 × [10 + (-12)] = 4 × (-2) = -8 17. The arcs which can be formed in the given circle are as follows: arc LMN, arc MNP, arc LNP and arc LMP. 18. There are unlimited number of integers both to the left and the right of zero, hence we cannot determine the biggest or the smallest integer. 19. Angles which are neither angles of the triangle nor its exterior angles are ?AXB, ?EYF and ?CZD. 20. A triangle with all three sides of different lengths is called a scalene triangle. ? ?DEF is a scalene triangle. 21. Line segments QR and ST are the chords of the circle. CBSE VI | Mathematics Sample Paper 4 – Solution 22. ? ? ? ? 3 4 2 3 4 1 21 43 3 4 3 4 ? ? ? ? ? ? ? ? ? ? ? 14 13 34 14 4 13 3 12 56 39 12 95 12 ?? ? ? ? ? ? ? ? 23. (a) It is not a polygon as it is not a closed figure (b) Yes it is a polygon made of 6 sides. (c) No it is not made of line segments. (d) No it is not made of only line segments. 24. Since the number is divisible by 12, it will also be divisible by its factors i.e. 1, 2, 3, 4, 6, 12. Clearly, 1, 2, 3, 4, and 6 are the numbers other than 12 by which this number is also divisible. Section C 25. Number of circles in step 1 = 3 = 1 × 2 + 1 Number of circles in step 2 = 5 = 2 × 2 + 1 Thus, we can observe that the number of circles is obtained by multiplying the step number by 2 and then adding 1. Therefore, the number of circles in the 100 th step = (100 × 2) + 1 = 201 26. (a) (-52) + (-36) + 42 + 8 + (-22) + 46 = -(52 + 36+22) + (42 + 8+46) = -110 + 96 = -14 (b) The largest 4-digit positive integer is 9999 and the smallest 3-digit negative integer is -999. ? 9999 + (-999) = 9999 – 999 = 9000 (c) Two integers between 2 and -5 that are inverses of each other are -1 and 1. The sum of 1 and -1 is 0. CBSE VI | Mathematics Sample Paper 4 – Solution 27. To solve using the number line start with -8, move 12 steps right and then back 2 steps as shown below: So, we reach at 2; therefore, (-8 + 12 - 2) = 2 28. We have: 2 (9 3) 2 29 19 19 3 57 9 and 19 3 3 3 1 1 3 3 ? ? ? ? ? ? ? ? ? The required number can be calculated by subtracting 29 57 from 33 . 57 29 57 29 3 3 3 28 3 1 9 3 ? ?? ? ? Hence, 1 9 3 should be added to 2 9 3 to get 19. 29. Mark point A. Take point A as the centre and draw a circle with radius 3 cm using a compass. The radius is the distance between the centre and any point on the circumference. ? AB is the radius of the circle. The diameter is the chord which divides the circle into two halves. ? XY is the diameter of the circle. A line segment which joins any two points on the circumference of a circle is called a chord. ? XZ is a chord of the circle.Read More

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