ALGEBRA
Date of Exam : 6th Ashoj, 2080
Important Instructions:
Full Marks : 60
Pass Marks : 30
Duration : 2 hrs
All questions are compulsory.
Group A (6 marks)
[ Q. No. 1] Factorize the following: [4]
i) 3x² – 27 ii) a³b – ab³
iii) 4a² – 36b² iv) x² – 1/x²
[ Q. No. 2 ] Find the HCF of (3x – 6) and (x – 3). [1]
[ Q. No. 3 ] Find the LCM of (a-b) and (a²-b²). [1]
Group B (34 marks)
[ Q. No. 4 ] Without initially expanding squares, find the values of : [1×2=2]
i) 99² – 1² ii) 4⁴ – 2⁴
[ Q. No. 5 ] Find the missing terms from each of the following to make it a perfect square. [1×2=2]
i) x² – ………. + 25 ii) ……… + 8a + 4
[ Q. No. 6 ] Left side is given some algebraic expressions. On the right, there are two blanks. Fill in those blanks with appropriate numbers required to factorize the given expressions. ( One is done for you ) [1×2=2]
Example : a² + 5a + 6 2 & 3
i) x² – 7x + 10 ……….. & ………..
ii) a² + 7a + 12 ……….. & ………..
[ Q. No. 7 ] Factorize the following : [2×6=12]
i) 4a²-12a+9 ii) 6-35b-6b²
iii) p²+2p-15 iv) 19+18d-d²
v) x(x+z)–y(y+z) vi) 44x²+19xy+2y²
[ Q. No. 8 ] Resolve the following algebraic expressions into factors. [2×2=4]
i) m³ – m² – 9m + 9
ii) 3(a-b)² + 5(a-b) – 2
[ Q. No. 9 ] The area of a square field is expressed as m² + 18m + 81 cm². Find the expression for its length. [2]
[ Q. No. 10 ] A hardworking farmer has a rectangular field of area y² – y – 12 m². Obtain the possible expressions for the length and the breadth of the field. [2]
[ Q. No. 11 ] Find the HCF of the following expressions : (2×2=4)
i) 5a²-8ab+3b² and 4a²-ab-3b²
ii) 2x²-5xy-3y² and 12x²+8xy+y²
[ Q. No. 12 ] Find the LCM of : (2×2=4)
i) x²-1 and x²+2x-3
ii) x²-7x+12 and x²+3x-18
Group C (20 marks)
[ Q. No. 13 ] Show geometrically that : (2×2=4)
i) (a+b)²= a² + 2ab + b²
ii) (a-b)² = a² – 2ab + b²
[ Q. No. 14 ] Factorize : (4×2=8)
i) 36(a + b)² – 16(a – b)²
ii) x²(2a+3b)+3x(2a+3b)+2(2a+3b)
[ Q. No. 15 ] Find the HCF and LCM of : [2+2=4]
x² + xy, xz + yz and x² + 2xy + y²
[ Q. No. 16 ] Ram owns a rectangular farm whose area is 210 m². One day, Shyam visits his farm and asks about the dimensions of the farm. Ram replies, “The length of the farm is one more than twice its breadth.”
i) Express the area of the farm in terms of its dimensions. [2]
ii) Solve for the length and the breadth of the farm. [2]
* Best Of Luck *
SEE Preparation 2080 