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MT/MATH6/23-24 DELHI PUBLIC SCHOOL VADODARA Academic Session 2023-24 Mid Term Examination Class : VI Time : 3 hr. Subject: Ma...

MT/MATH6/23-24 DELHI PUBLIC SCHOOL VADODARA Academic Session 2023-24 Mid Term Examination Class : VI Time : 3 hr. Subject: Mathematics (041) M.M : 80 General Instructions: Total no. of pages: 08 1) This question paper has 5 Sections A-E. 2) Section A has 20 multiple choice questions carrying 1 mark each. 3) Section B has 5 questions carrying 2 marks each. 4) Section C has 6 questions carrying 3 marks each. 5) Section D has 4 questions carrying 5 marks each. 6) Section E has 3 case based integrated units of assessment (04 marks each) with subparts. 7) All questions are compulsory. However, an internal choice in 2 questions of 5 marks, 2 questions of 3 marks and 2 questions of 2 marks have been provided. _____________________________________________________________________________________ SECTION A Questions 1 to 20 carry 1 mark each. 1. The correct numeral for forty two lakh seventy thousand eight is: (a) 427008 (b) 4270080 (c) 4207008 (d) 4270008 2. Which of the following number is not prime? (a) 33 (b) 17 (c) 83 (d) 97 3. Which of the following numbers is expressed as a product of prime factors? (a) 62 = 2 × 31 (b) 56 = 7 × 4 × 2 (c) 42 = 2 × 21 (d) 54 = 2 × 3 × 9 4. Greatest number formed by digits 7, 5, 0, 3, 8, 9 without repetition is _______. (a) 0357980 (b) 305789 (c) 987530 (d) 987350 5. By observing the number line, state which of the following statements true? (a) B is greater than 10 (c) A is greater than 0 (b) B is greater than A (d) B is greater than 0 1 6. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 3 to 6? 1 3 1 1 1 (a) 2 (b) 4 (c) 4 (d) 4 7. Which of the following number is equal to one billion? (a) 10 lakh (b) 1 crore (c) 10 crore (d) 100 crore 8. The predecessor of one more than the smallest 4-digit number is _____. (a)100 (b) 9999 (c) 999 (d) 1000 9. Which number is not greater than (6000 ÷ 6000)? (a) 1 (b) 2 (c) 3 (d) 4 10. Which number is between (100 ÷ 20) and (15 × 1)? (a) 14 (b) 16 (c) 17 (d) 18 11. In the figure angle ∠XYZ cannot be written as: (a)∠ZYX (b) ∠PYX (c) ∠XYP (d) ∠ZXY 12. Which digit of the number 9308 has the greatest face value? (a) 8 (b) 9 (c) 3 (d) 0 13. Number of two digit numbers that can be formed are: (a) 90 (b) 99 (c) 91 (d) 98 14. 889500 comes just after: (a) 889400 (b) 889501 (c) 889499 (d) 889489 15. Which of the following is a perfect number? (a) 8 (b) 28 (c) 12 (d) 9 2 16. A quadrilateral with all sides and angles equal is a _________. (a) rhombus (b) trapezium (c) rectangle (d) square 17. Which of the following number is the least common multiple of 8 and 9? (a) 28 (b) 72 (c) 36 (d) 24 18. The smallest 4-digit number that can be formed using the digits 8, 5, 0, 3 without repetition is ______. (a) 0358 (b) 5308 (c) 3058 (d) 83580 DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. 19. Statement A (Assertion): After placing comma in the number 56943821 according to International System of Numeration, the number is written as 56,943,821. Statement R (Reason): To write a numeral in the Indian System, commas are first put after three digits from the right and then after every two digits. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of Assertion (A) (c) Assertion (A) is true but reason(R) is false. (d) Assertion (A) is false but reason(R) is true. 20. Statement A (Assertion):. The factors of 16 are 1, 2, 4 and 8. Statement R (Reason) :. Every factor is less than or equal to the given number. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. SECTION B Questions 21 to 25 carry 2 marks each. 21. Evaluate the difference between the place values of two 5’s in the number 85105863. 22. The L.C.M of two co-prime numbers is 500. If one of the numbers is 25, find the other number. 23. Draw a number line to represent 4 + 5. 24. Simplify: (− 13) + (− 18) + 92 3  OR Simplify: 40 − (− 26) − (− 4) 25. Write the greatest number and the smallest number of four digits that can be formed by the digits 3, 6 and 8 with the condition that digit 5 always in tens place. OR Write 4 possible 2–digit numbers that can be formed by using the digits 3, 7 and 9, if repetition of digits is allowed. 26. Do as directed: (a) Find the sum of (− 52), (− 36), 42 and 8. (b) Write two integers between (− 4) and (− 7). (c) Find the sum of largest 4-digit positive integer and smallest 3-digit positive integer. 27 Name the angles marked by letters a, b, c, x ,y and (a+b). OR Draw a rough diagrams of two angles such that they have (a) One point in common (b) Two points in common. (c) Three points in common. 28. There are 36 apples, 54 mangoes and 72 oranges. These are to be arranged in heaps containing the same number of fruits. Find the greatest number of fruits possible in each heap. OR A milk vendor has 21 litres of cow milk, 42 litres of toned milk and 63 litres of double toned milk. If he wants to pack them in cans so that each can contains same litres of milk and does not want to mix any two kinds of milk in a can, then find the least number of cans required. 29. Where will the hour hand of a clock stop if it starts: 4  (a) from 6 and turn through 1 right angle? (b) from 8 and turn through 2 right angle? (c) from 10 and turn through 3 right angle? 30. An engine pumps out 850 litres of water in one minute. How many hours will it take to pump out 13,77,000 litres of water? 31. Do as directed: (a) Find the difference between 795 and the number obtained by reversing its digits. (b) How many whole numbers are there between 51 and 102? (c) Write the successor of one lakh. SECTION D Questions 32 to 35 carry 5 marks each. 32. A farmer has 945 cows and 2475 sheep. He arranges them into flocks, keeping cows and sheep separated and having the same number of animals in each flock. Answer the question based on the given information: (a) If he want maximum number of cows and sheep, then find the maximum number of animals. (b) Find the number of flocks required for arranging cows. (c) Find the total number of flocks required. 33. Name the types of the following triangles: (i) Triangle with lengths of the sides 7 cm, 8 cm and 9 cm. (ii) ∆ABC with sides AB = 8.7 cm, AC = 7 cm and BC = 6 cm. (iii) ∆PQR such that side PQ = QR = PR = 5 cm. (iv) ∆DEF with ∠D = 90° (v) ∆XYZ with ∠Y = 90° and XY = YZ. OR Give reasons for the following: (i) A square can be thought of as a special rectangle. (ii) A rectangle can be thought of as a special parallelogram. (iii) A square can be thought of as a special rhombus. 5  (iv) Squares, rectangles, and parallelograms are all quadrilaterals. (v) A square is also a parallelogram. 34. One day Om went to explore a hill. When he reached the hill top, he started looking at the things around. School Bridge Farm Om Tree Answer the following question based on the given information: (i) In what direction is Om facing if he looks at the tree? (a) North (b) South (c) North (d) South (ii) What angle does Om turn through, if he turns clockwise from looking at the school to the farm? (a) 45 ° (b) 90° (c) 180° (d) 270° (iii) What angle does Om turn through, if he turns anticlockwise from looking at the school to the bridge? (a) 45 ° (b) 90° (c) 180° (d) 270° (iv) How many right angles are formed, if Om start facing North and turn clockwise to West? (a) 1 (b) 2 (c) 3 (d) 4 (v) What part of a revolution Om will complete, if he was facing West and turn clockwise to East? 1 3 (a) of a revolution (c) of a revolution 4 4 1 (b) of a revolution (d) 1 complete revolution 2 35. Use the symbols of < , > or = to make the statement true: 6  (a) – 12 – ( – 9) ________ Additive inverse of 20 (b) – | – 11| – (–3) ________ 22 (c) Successor of (– 19) ________ predecessor of (– 14) (d) 4 more than (– 2) ________ 3 less than (– 2) (e) ( – 10) + 25 ________ 25 – 10 OR Fill in the blanks: (a) The two integers greater than (– 17) are _______ and _______. (b) On subtracting (– 9) from (– 7) we get _______. (c) The opposite of 7 km North is_______. (d) All positive integers are _______ than zero. (e) The predecessor of integer zero is_______. SECTION –E (Case Study Based Questions) Questions 36 to 38 carry 4 marks each. 36. Case Study – 1 A carpenter marks the points A, B, C and D with a nail to specify the position where he would make hole with a drilling machine for wall painting. Answer any four of the following questions: (i) How many pairs of parallel lines are there? (a) 1 (b) 2 (c) 3 (d) 4 (ii) How many lines pass through point A? (a) 1 (b) 2 (c) 3 (d) 4 (iii) What is the number of pairs of intersecting lines? (a) 1 (b) 2 (c) 3 (d) 4 (iv) Name the lines whose point of intersection is B. (a) AB and BC (b) DC and BC (c) AB and AD (d) AD and DC (v) Which of the following statement is false? (a) There are 4 angles in the given figure. (c) The above figure is not a polygon. (b) ∠BCD can be written as ∠DCB. (d) There are four meeting points in the given figure. 37. Case Study – 1I Mathematics teacher of Class VI draws a straight line AB´ on the white board and marks a point Z on it. She asks one student to draw ray ⃗ ZC passing through point Z. Then she asks other student to draw another ray ⃗ZD passing through Z. At last she asks one more student to place the points U,V, X and Y anywhere on the board as shown below: 7  Answer any four of the following questions: (i) How many angles are formed in the given figure? (a) 3 (b) 4 (c) 5 (d) 6 (ii) How many points are in the interior of ∠ DZB ? (a) 2 (b) 3 (c) 4 (d) 5 (iii) How many points are in the exterior of ∠ CZA ? (a) 2 (b) 3 (c) 4 (d) 5 (iv) Which is the common point in three angles ∠ DZA , ∠ DZC and ∠ CZB ? (a) point D (b) point Z (c) point A (d) point C (v) Which points lie on ∠ DZA ? (a) points D, Z, A (b) points Z, A, B (c) points A, X, Y (d) points C, X, Y 38. Case Study – 1II A teacher told the students to draw a number line on the ground of a school. She asked the students to mark integers between -20 and 20 with an equal and sufficient gap between two consecutive numbers so that they can stand comfortably at any position representing an integer. The teacher called the children by the integers they represent and gave instructions. Ans wer any four of the following questions: (i) What is the position of a student if he starts from zero, moves 15 steps to the right and then 7 steps to the left on number line? (a) 5 (b) 6 (c) 7 (d) 8 (ii) What is the position of a student when he reaches the number which is the greatest negative integer on number line? (a) - 20 (b) -19 (c) - 1 (d) 0 (iii) What is the position of the student on number line when he takes the position of a number which is neither positive nor negative? (a) - 20 (b) 0 (c) 20 (d) none of these (iv) What is position of a student if he starts from number 20 moves 19 steps to the left and then 2 numbers to the right on number line? (a) 1 (b) 2 (c) 3 (d) 4 (v) How many integers lie between -20 and 20 on number line? (a) 37 (b) 38 (c) 39 (d) 40 -----End----- 8