Final Exam Paper Mathematics - Set 3

Maximum Marks: 80
Time: 3 Hours

General Instructions:
(i) All questions are compulsory.
(ii) Marks for each question are indicated against it.
(iii) Section A consists of 12 MCQs carrying 1 mark each.
(iv) Section B consists of 12 questions carrying 2 marks each.
(v) Section C consists of 8 questions carrying 3 marks each.
(vi) Section D consists of 5 questions carrying 4 marks each.
(vii) Use of calculators is not allowed.

Syllabus: The Final Examination is based on the following chapters: Geometric Twins, Operations with Integers, Finding Common Ground, Another Peek Beyond the Point, Connecting the Dots..., Constructions and Tilings, and Finding the Unknown.

Section A (12 × 1 = 12 Marks)

Q1. Which triangle congruence condition uses the hypotenuse?
(a) SSS
(b) SAS
(c) RHS
(d) ASA

Q2. Solve the equation 2x + 3 = 4x + 5 using a suitable method.
(a) 1
(b) -1
(c) 4
(d) -4

Q3. The LCM of two different prime numbers m and n is:
(a) 1
(b) m + n
(c) m × n
(d) m - n

Q4. Write 7,89,12,345 in expanded form using powers of 10. The highest place value term is:
(a) 7 × 10⁷
(b) 7 × 10⁸
(c) 7 × 10⁶
(d) 7 × 10⁹

Q5. If a data set has an even number of values, the median is:
(a) The middle value
(b) The total sum
(c) The average of the two middle values
(d) The mode

Q6. When copying an angle ∠A to ∠X, the SSS condition is used because:
(a) A ruler is used
(b) Three corresponding lengths are equal
(c) Angles are equal
(d) Radius is fixed

Q7. A 210 g packet costs ₹70.50 and a 110 g packet costs ₹33.25. Which is cheaper per gram?
(a) 210 g packet
(b) 110 g packet
(c) Both same
(d) Cannot be determined

Q8. The HCF of two consecutive even numbers is always:
(a) 1
(b) 2
(c) 4
(d) Their average

Q9. Dividing a number by 0.1 is equivalent to multiplying it by:
(a) 0.1
(b) 1
(c) 10
(d) 100

Q10. A 60° angle can be constructed using which polygon?
(a) Square
(b) Regular hexagon
(c) Equilateral triangle
(d) Pentagon

Q11. Parag's group has 30 guavas shared among 6 members. What is the fair-share?
(a) 4
(b) 5
(c) 6
(d) 30

Q12. Which term was used by Bhaskaracharya for "Mean"?
(a) Samarajju
(b) Samamiti
(c) Samikarana
(d) Bijaganita

Section B (12 × 2 = 24 Marks)

Q13. Find the prime factorisation of 105.

Q14. How can a 30° angle be constructed from a 60° angle?

Q15. Solve: 4k + 1 = 13.

Q16. State the result of -1 × a.

Q17. Compare 6.78 and 6.87.

Q18. Find the HCF of 84 and 180 using common factor division.

Q19. Describe the historical origin of the "rod" as a unit of length.

Q20. Solve: 2y = 60.

Q21. Evaluate: 0.018 × 0.012.

Q22. What is special about tangram piece number 4?

Q23. Find the HCF of n and 5n.

Q24. Define the RHS congruence condition.

Section C (8 × 3 = 24 Marks)

Q25. Bhaskaracharya's problem: One person owns ₹300 and 6 horses. Another person owns 10 horses but has a debt of ₹100. If both persons are equally rich, find the price of one horse.

Q26. Describe the steps to construct a 6-pointed star using a ruler and compass.

Q27. Find the LCM of 14 and 35 using the prime factorisation method.

Q28. A dot plot shows most data values clustered between 0 and 2, and one value far away at 25. Describe the nature of the data.

Q29. Solve the equation 3k + 1 = 100 and state the value of k.

Q30. A shopkeeper divides 9.5 kg of sugar equally into 4 bags. Find the weight of sugar in each bag.

Q31. A cricket team scores a total of 407 runs. Can the median score of the team be 0? Give a reason.

Q32. Find the total number of factors of 840 using its prime factorisation.

Section D (5 × 4 = 20 Marks)

Q33. A balanced weighing scale shows the following arrangement: On the left pan, there are 3 identical sacks and a 6 kg weight. On the right pan, there are 2 identical sacks and a 14 kg weight. 
(a) Let the weight of one sack be x kg and frame an equation. 
(b) Solve the equation using the balance method. 
(c) Find the weight of one sack.

Q34. A matchstick pattern is formed such that the first figure has 3 matchsticks, the second figure has 5 matchsticks, and the third figure has 7 matchsticks. 
(a) Write an algebraic expression for the number of matchsticks in the nth figure. 
(b) Frame an equation to find the position of a figure that uses 99 matchsticks. 
(c) Find the position number.

Q35. Prove that adding or subtracting the same number on both sides of an equation does not change its solution. Use the equation: 5x + 4 = 24.

Q36. Two students solve the equation 3y + 2 = 20. Student A uses the trial method, while Student B uses the balance method. 
(a) Solve the equation using the balance method. 
(b) State why the balance method is more efficient.

Q37. In a weighing scale, equal weights are removed from both pans and the scale remains balanced. 
(a) Write the corresponding algebraic principle. 
(b) Use this principle to solve the equation: 2x + 7 = x + 15.

You can access the solutions of this Final Exam here.