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ICSE Class X Prelims 2024 : Mathematics

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Kritika singh Bais
Rajeshwar Convent Higher Secondary School (RCHSS), Rajgarh
1st to 10th

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FIRST SEMESTER EXAMINATION-2023-2024 TIME-2:30 Hours CLASS- X SUBJECT-MATHEMATICS M.M.80 You will not be allowed to write during first 15 minutes .This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work ,must be clearly shown , and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. SECTION-A (40 MARKS) (Attempt all questions from this section) Question 1 Choose the correct answers to the questions from the given options. (i) (ii) (iii) The mean proportional between 4 and 9 is . (A) 4 (B) 6 (C) 9 (D) 36 if 3 2 < 9 , , then the value of is. (A) < 3 (B) > 3 (C) > 3 (D) < 3 The term of an Arithmetic Progression (A.P.) is = 2 + 5 . 10 . (A) 15 (B) 25 (C) 7 (D) 45 [15] (iv) (v) The printed price of an article is Rs 4020 . if the rate of GST is 10% then the GST charged is. (A) Rs 40 (B) Rs 40.20 (C) Rs 402 (D) None of them 2 If 7 2 + 3 , is divided by (2 + 1) , then the remainder is . (A) 23 4 (B) 25 4 (C) 15 2 (D) None of them if the numbers , 28 , 24 112 are in proportional then the value of . (A) 5 (B) 6 (C) 8 (D) 2 (vii) If a matrix has 18 elements . What are the possible order it can have. (A) 6 (B) 8 (C) 10 (D) 2 (viii) Statement 1 : A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an identity matrix. Statement 2 : A matrix in which the number of rows are equal to the number of columns , is called Row matrix. (A) Both the statements are not correct (B) Both the statements are correct (C) Statement 1 is correct But statement 2 is not correct (D) Statement 2 is correct But Statement 1 is not correct (ix) Shyam deposits Rs 800 every month in a recurring deposit account for 6 months .if he receives Rs 4884 at the time of maturity , then the interest he earns is . (A) Rs 42 (B) Rs 24 (C) Rs 84 (D) Rs 284 (x) The Point A( 5 , 3 ) are mapped on reflection in the x-axis . (A) ( 5 , -3 ) (B) ( -5 , 3 ) (C) ( 5 , 3 ) (D) (-5 , -3 ) 2 2 1 8 8 (xi) If [ ]+3[ ]=[ ] , the value of is. 0 1 4 0 12 1 (A) 2 (B) 3 (C) 4 (D) 5 (xii) for what value of , the points ( , 2 ), (1 , 4 ) ( 3 , 16) in given order are collinear? (A) 3 (B) 5 (C) 1 (D) 2 (xiii) The equation of the is . (A) = (B) = 0 (C) = 0 (D) None of them (xiv) For the given G.P. : 3 , 9 , 27 , 81 , Assertion (A) : in an geometric progression common ratio are equal. Reason (R) : terms of an geometric progression is = + ( 1) . (vi) (A) A is true , R is false (B) A is false , R is true (C) Both A and R are true (D) Both A and R are false Which of the following is/are an Arithmetic Progression (A.P.) 1. 1 , 4 , 9 , 16, (xv) 2. 3 , 2 3 , 3 3 , 4 3 , . 3. 8 , 6 , 4 , 2 , . (A) Only 1 , is correct (B) only 2 , is correct (C) only 2 and 3 is correct (D) all 1 , 2 and 3 are correct Question 2 (i) Soniya had a recurring deposit account in a bank and deposited Rs 600 per month for 3 years . if the rate of interest was 10% p.a. , find the maturity value of this account. [4] The 4th term of a G.P. is 16 and the 7th term is 128 . find the first term and common ratio of the series. [4] Solve the following quadratic equation and given the answer correct to two decimal places figures. 2 7 + 3 = 0 [4] (ii) (iii) Question 3 (i) (ii) (iii) Use factor theorem to factorise f(x) = 6 3 + 17 2 + 4 12 completely. [4] Use graph paper for this question. Use 1cm = 1 unit on both axes.(i) plot the points A(3,5) and B(-2,-4) (ii) is the image of A when reflected in the x-axis . Write down the coordinates of and plot it on the graph paper.(iii) is the image of B when reflected in the y-axis , followed by the reflection in the origin . Write down the coordinates of and plot it on the graph paper.(iv) write down the geometrical name of the figure .(v) name two invariant points under reflection in the x-axis. (vi) find the area of the figure A . [5] . Find the total amount to be paid by the customer for the following bills. [4] MRP Rs 2000 Rs 5500 Rs 3200 Rs 1400 Discount 15% 20% 10% 12% GST is 18% and the sale in intra-state SECTION-B (40 MARKS) (Attempt any four questions from this section) Question 4 (i) (ii) (iii) Find the value of for which the lines 2 + 3 7 = 0 , and 4 12 = 0 , are perpendicular to each other . [3] Prove the following trigonometric identity.(sin + )2 + (cos + sec ) 2 = 7 + 2 + 2 [3] Using the properties of (compoendo and Dividendo) , if X = 2 +1+ 2 1 , 2 +1 2 1 then prove that 2 4 + 1 = 0 [4] Question 5 (i) The MRP of an article is Rs 5,000 , A dealer buys it at a discount of 20% . he sells it to a customer in the same city at a discount of 5% find . (i) the total amount paid by the customer and (ii) the net GST paid by the dealer to the government if GST is charged at 12% . [3] (ii) The slope of a line joining P(6 , k) and Q(1-3k , 3) is 2 . find (i) k (ii) (iii) 1 Midpoint of PQ , using the value of k found in (i). [3] A car covers a distance of 400 km at a Certain Speed . Had the speed been 12km/h more , the time taken for the journey would have been 1 hour 40 minutes less . find the original speed of the car. [4] Question 6 (i) Solve the following inequation . Write down the solution set and represent it on the real number line. 5( 9) 17 9 > + 2 , . [3] (ii) The 5th term and the 9th term of an Arithmetic progression are 4 and 12 respectively . find: (i) the first term (ii) common difference (iii) sum of 20th terms of the A.P. [3] (iii) What number must be added to each of the Numbers 4 , 6 , 8 , 11 in order to get the four numbers in proportion. [4] Question 7 (i) Solve the following inequation and write the solution set on the number line. 3 + 8 3 + 2 14 3 + 2 ; ( ) . [3] (ii) A dealer buys goods worth Rs 7,500 and sells it at a profit of 10% within the same State . if GST is charged at 12% , find the (i) selling price , (ii) CGST , (iii) SGST and (iv) the total amount paid by the customer. [3] 9 16 3 (iii) If = [ ] = [ ] , 2 = . [4] 0 0 1 Question 8 1 tan (i) Prove the identity : ( 1 cot )2 = 2 [3] (ii) A(2,5) , B(-1 , 2) and C(5 , 8) are the vertices of a triangle ABC , M is a point on AB such that AM : MB = 1 : 2 .find the co-ordinates of M . Hence find the equation of the line passing through the points C and M. [3] (iii) In an arithmetic Series, the sum of 10 terms is 310 and the sum of 20 terms is 1020 . find the first term and the common difference. [4] Question 9 (i) (ii) (iii) Find the points of trisection of the line segment joining the points A(-4,2) and B(3,7). [3] Find the equation of the line joining the Points , A(3,4) and B(-2,4). [3] What must be added to the polynomial 2 3 3 2 8 , so that it leaves a remainder 10 when divided by 2 + 1 . [4] Question 10 (i) Prove that the points A(4,-5) , B(1,1) and C(-2,7) are collinear. [3] (ii) Mr .sonu has a recurring deposit account and deposits RS 750 per month for 2 years .if he gets Rs 19125 at the time of maturity .find the rate of interest.[3] 3 0 4 2 (iii) If A = [ ] = [ ] , 2 2 + 2 [4] 5 1 1 0 .............

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