10th Std Maths Midterm Exam 2024-25 (SSSC) PDF

SRI SAI STUDY CENTRE (R) X - State Mid Term Examination September - 2024 Subject: Mathematics [81E] Date: 22.09.2024 Max Marks: 80 Duration: 3 hours...

SRI SAI STUDY CENTRE (R) X - State Mid Term Examination September - 2024 Subject: Mathematics [81E] Date: 22.09.2024 Max Marks: 80 Duration: 3 hours Total No. Questions: 38 I. Four alternatives are given for each of the following questions / incomplete statements. Choose the correct alternative and write the complete answer along with its letter of alphabet. 8X1=8 1. If HCF (P, 8) = 4 and LCM (P, 8) = 24, then the value of P is A) 8 B) 10 C) 12 D) 14 2. Degree of the polynomial p(x) = 7x – 5x + x2 – x + 35 is 4 3 A) 2 B) 3 C) 5 D) 4 3. The value of K, for which the pair of linear equations 4x + 6y – 1 = 0 and 2x – ky = 7 represents parallel lines is A)2 B) - 3 C) 4 D) – 2 4. If the discriminant value of a quadratic equation is – 7, then the equation has A) no real roots. C) Two distinct rational roots. B) Two equal real roots. D) Two distinct irrational roots. 5. The sum of first n natural numbers is 𝑛(𝑛+1) A) 2 B) n(n + 1) C) n2 D) n(n – 1) 6. The nth term of an Arithmetic progression is an = 6n – 1, then the Arithmetic progression is A) 5, 10, 15, … B) 5, 8, 11, … C) 5, 11, 17, … D) 5, 7, 9, … 7. In ∆ ABC, PQ ‖ BC, AP = 2cm, PB = 4cm and BC = 9 cm, then the length of PQ is A) 4.5 cm B) 6 cm C) 3 cm D) 4 cm A 2cm P Q 4cm B 9cm C 8. The lines drawn to the pair of linear equations are coincident to each other. If one of the equation is 2x + 3y – 9 = 0, then the other equation is A) 3x + 5y – 18 = 0 C) 4x + 6y + 18 = 0 B) 4x – 6y – 18 = 0 D) 4x + 6y – 18= 0 II. Answer the following questions: 8X1=8 9. Express 100 as a product of its prime factors. 10. Find the mid points if the co ordinates (2,3) and (4,5) 11. If the pair of linear equations have unique solution, then write the type of lines they have. 12. Find the roots of the quadratic equation: (x – 1) (x + 3) = 0 13. Write the following statement in the standard form of quadratic equation. “product of two consecutive positive integers is 20”. Use E-Papers, Save Tress Above Line Hide When Print Out 14. The sum of first six terms of an Arithmetic progression is 42, and the sum of first five terms of the same Arithmetic progression is 30. Find its sixth term. 15. State Thales theorem. 16. ∆ ABC ~ ∆ DEF, write the (i) Corresponding angle of E (ii) Corresponding side of AC III. Answer the following Questions: 8 X 2 = 16 Prove that 3 + 5 is an irrational number. Find the distance between the point's (2,3) and (6,6) using distance formula OR Find the co ordinates of line joining the points A(-1,7) and B(4,-3) are in the ratio 2:3. Solve the equations by elimination method 3x + 2y = 12 x – 2y = 4 Find the values of K, in which the quadratic equation 9x2 – 3Kx + K = 0 has two equal roots. Find the sum of first 20 terms of the Arithmetic progression 7, 13, 19,…. Using formula. 𝐴𝑀 𝐴𝑁 In the figure, LM ‖ CB and LN ‖ CD, prove that 𝐴𝐵 = 𝐴𝐷 B M A C N D OR Using Basic proportionality theorem, prove that “a line drawn through the mid point of one side of a triangle parallel to another side bisect the third side.” In ∆ ABC, D and E are points on sides AB and AC respectively. If AD = 1.4 cm, AB = 5.6 cm, AE = 1.8 cm and AC = 7.2 cm prove that DE ‖ BC A D E B C Find LCM of 12,15,21 by using prime factorisation method Use E-Papers, Save Tress Above Line Hide When Print Out IV. Answer the following questions: 9 X 3 = 27 The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number. OR Find the HCF and LCM of 54 and 306 by the prime factorisation method, hence find their LCM. If α and β are the zeroes of a quadratic polynomial x2 – 7x + 10, find the value of α2 + β2. OR If α and β are the zeroes of a polynomial x2 – 5x + K, such that α – β = 1, then find the value of K. 1 1 If 2 is added to numerator of a fraction it reduces to 2. It becomes 3 , if 1 is subtracted from the denominator find the fraction. OR Find the values of x and y in the following rectangle using substitution method. D x+3y C 3x + y 7 A B 13 Find the discriminant of the quadratic equation 5x2 – 6x – 2 = 0 and Hence find the nature of its roots. In an A. P. Third term is 4 and fourth term is 10.then find sum of 20 terms of A. P ABCD is a trapezium in which AB ‖ DC and its diagonals intersect each other at the point O as shown in the figure. using a similarity criterion for two triangles, show that AO. DO = BO. CO D C A B Find the ratio of in which the line segment joining the points (-3,10) and (6,-8) is divided by (-1,6) OR Use E-Papers, Save Tress Above Line Hide When Print Out  How do you show that points (18,4) (12,12) and (8,4) are the vertices of an isosceles triangle.? For what values of a and b the following pair of linear equations have infinite number of solutions? 2x + 3y = 7 a(x + y) – b(x – y) = 3a + b – 2 (i) What are similar triangles? (ii) State whether the following rectangles are similar or not, give reason. 3cm 5cm D C S R 1.5cm 1.5cm 3cm 3cm A B 3cm P 5cm Q V. Answer the following questions: 4 X 4 = 16 34. Find the solution of the given pair of linear equations by graphical method. 2x + y = 7 x+y=4 35. Prove that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar”. 36. A motor boat whose speed is 11 km / hour in still water takes 2 hours 45 minutes to go 12 km upstream then to return down stream to the same spot. Find the speed of the stream. OR The length of a rectangular field is 3 times its breadth. If the area of the field is 147 sq. m find the length and breadth. 37. Find the zeroes of the quadratic polynomial p(x) = x2+7x+10 and verify the relationship between the zeroes and the co-efficients. VI. Answer the following questions: 1X5=5 38. An arithmetic progression consists of 30 terms. The 17th term of ap is 4 more than thrice its 5th term. If the 10th term is 31.then find last 3 terms of A. P and also find first 3 terms of ap. Use E-Papers, Save Tress Above Line Hide When Print Out