8 QUESTIONS × 1 MARK = 8 MARKS ACA D E M I C AS S ES S M E N T S E R I ES MATHEMATICS QUESTION PAPER CLASS VI • HIGHER ORDER THINKING ASSESSMENT Time Allowed: 2 Hours Total Questions: 25 Maximum Marks: 50 SYLLABUS / CHAPTERS COVERED Natural Numbers & Whole Numbers | Factors & Multiples | Ratio, Proportion & Unitary Method | Percentage & Its Applications | Basic Geometrical Concepts | Line Segments GENERAL INSTRUCTIONS All questions are compulsory unless an internal choice is specified. Show neat and clear working steps wherever required. Calculators or electronic gadgets are strictly not permitted. Some questions integrate multiple mathematical concepts. Read each question carefully. Case Study questions must be answered based on the provided contexts. SECTION A — MULTIPLE CHOICE QUESTIONS 1. A number is both a multiple of 12 and a factor of 144. Which of the following could be the number? a) 18 b) 24 c) 36 d) 48 2. Starting with 0, a student writes every second whole number: 0, 2, 4, 6, 8, ... Which statement is definitely true? a) Every number written is a prime number. b) Every number written is a factor of 24. c) Every number written after 0 is even. d) Every number written is a natural number. 3. The ratio of boys to girls in a class is 5 : 7 . If 8 more girls join the class, the ratio becomes 5 : 9 . The original number of girls was: a) 21 b) 28 c) 35 d) 42 4. A shopkeeper marks an article at ₹ 800 and gives a discount of 15%. Which expression gives the selling price? a) 800 + 15% of 800 b) 800 - 15% of 800 c) 15% of 800 d) 800 - 15 5. Four points A, B, C and D lie on the same line. How many different line segments can be named using these four points as endpoints? a) 4 b) 5 c) 6 d) 8 6. Three lines pass through the same point. Which statement is correct? a) They are parallel lines. b) They are concurrent lines. c) They are collinear lines. d) They form a line segment. 1. 2. 3. 4. 5. Class VI Mathematics • HOTS Assessment Page 1 of 4 4 QUESTIONS × 1 MARK = 4 MARKS 5 QUESTIONS × 2 MARKS = 10 MARKS 4 QUESTIONS × 3 MARKS = 12 MARKS 7. Which pair represents quantities that can correctly form a ratio? a) 5 apples : 8 kg b) 3 hours : 45 minutes c) 7 boys : 2 metres d) 4 books : 9 litres 8. The LCM of two co-prime numbers 8 and 15 is: a) 23 b) 40 c) 120 d) 60 SECTION B — ASSERTION & REASON Directions: For Questions 9 to 12, select the correct option from the following choices: (A) Both Assertion and Reason are true, and Reason correctly explains Assertion. (B) Both Assertion and Reason are true, but Reason does NOT correctly explain Assertion. (C) Assertion is true, but Reason is false. (D) Assertion is false, but Reason is true. 9. Assertion (A): The HCF of 24 and 36 is a factor of their LCM. Reason (R): The HCF of any two numbers is always a factor of their LCM. 10. Assertion (A): The ratios 3 : 5 and 18 : 30 are in proportion. Reason (R): Multiplying both terms of a ratio by the same non-zero number does not change its value. 11. Assertion (A): One and only one line can be drawn through two distinct given points. Reason (R): An unlimited number of lines can be drawn through a single point. 12. Assertion (A): If an article is sold at a price greater than its cost price, there is always a loss. Reason (R): Profit occurs when the selling price is greater than the cost price. SECTION C — SHORT ANSWER QUESTIONS 13. Find the smallest number which must be added to 3,457 so that the resulting number is divisible by both 9 and 5. 14. Without converting both ratios into decimals, determine which is greater: 7 : 12 or 11 : 18 . Give a valid reason for your answer. 15. The ratio of the number of red, blue and green counters is 3 : 4 : 5 . If there are 48 blue counters, find the total number of counters. 16. A student claims: "If 25% of a number is 30, then 30% of that number must be 36." Is the statement correct? Prove your answer with calculations. 17. Four points P, Q, R and S are drawn such that P, Q and R are collinear, while S does not lie on their line. a) How many line segments can be formed using P, Q and R ? b) Are P, Q, R and S collinear? Give a reason. SECTION D — APPLICATION & HOTS QUESTIONS 18. A school has 720 students. The ratio of boys to girls is 5 : 7 a) Find the number of boys and girls in the school. b) If 10% of the boys participate in a mathematics competition, how many boys participate? 19. Three school bells ring after intervals of 18 minutes, 24 minutes, and 30 minutes respectively. They ring together at 9:00 a.m. a) After how many minutes will they ring together again? b) At what exact time will this happen? Class VI Mathematics • HOTS Assessment Page 2 of 4 2 QUESTIONS × 4 MARKS = 8 MARKS (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) 2 QUESTIONS × 4 MARKS = 8 MARKS (2 Marks) (2 Marks) 20. A shopkeeper buys a school bag for ₹ 600. He spends ₹ 60 on repairing it and then sells it for ₹ 759. Find: a) The actual total cost price after including repair expenses. b) The profit earned. c) The profit percentage. 21. Line segment AB is 8.4 cm long and CD is 5.75 cm long. a) Which comparison method would be most appropriate if two segments drawn on paper were almost equal: observation, tracing, or divider? b) Calculate the length difference AB - CD c) If another segment EF is exactly equal in length to CD , write two different ways in which EF can be compared with AB SECTION E — CASE STUDY QUESTIONS CASE STUDY 1 — SCHOOL CARNIVAL A school carnival committee prepares 240 gift packets. The packets are distributed among three houses in the ratio 3 : 4 : 5 Each packet originally costs ₹ 25 to prepare. To reduce expenses, the committee manages to reduce the preparation cost by 20%. 22. Based on Case Study 1, answer the following questions: a) How many packets does the house having ratio-part 5 receive? b) Find the new cost of preparing one packet after the reduction. c) Find the total cost of preparing all 240 packets at the reduced cost. d) A student claims that reducing the cost by 20% and then increasing the reduced cost by 20% brings it back to ₹ 25. Is the student correct? Show calculations. CASE STUDY 2 — SCHOOL PLAYGROUND A rectangular playground has four corner points named A, B, C and D . Opposite sides are intended to remain parallel. Two diagonal paths AC and BD are drawn and intersect at point O The mathematics teacher asks students to analyse the geometrical layout. 23. Based on Case Study 2, answer the following questions: a) Name one pair of parallel line segments in the layout. b) What kind of lines are AC and BD given that they meet at O ? c) How many line segments are formed on diagonal AC after point O is marked on it? Name them. d) A fifth straight path is drawn through O . Are the three paths ( AC, BD , and the new path) concurrent? Explain. SECTION F — BRAIN TEASERS 24. Find the smallest natural number N such that: N + 8 is divisible by both 12 and 18, and N + 5 is divisible by 7. Show your reasoning clearly. Do not simply list numbers until you find one. 25. Five straight lines are drawn in a plane. a) Suppose no two lines are parallel and no three lines pass through the same point. What is the maximum possible number of points of intersection? b) Now suppose three of the five lines are made concurrent at one point, while the remaining two lines still intersect all other lines separately. What is the new number of points of intersection? • • Class VI Mathematics • HOTS Assessment Page 3 of 4 *** END OF QUESTION PAPER *** Class VI Mathematics • HOTS Assessment Page 4 of 4