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ICSE Class X Sample / Model Paper 2023 : Mathematics

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10th ICSE Mathematics 2023 Prediction Paper PRIME PRIVATE TUITION ICSE X Marks: 80 Subject: Mathematics Time: 2 Hours 30 Min Section A (Attempt all questions from this section) Question 1. 1. The CGST paid by a customer to a retailer for an article costing Rs. 2,000 is Rs. 180. The rate of GST charged is (a) 5% (b) 9% (c) 12% (d) 18% 2 2. The roots of the quadratic equation 2x 3x + 4 = 0 are (a) Real and equal (b) Real and unequal (c) Not Real 3 (d) Irrational 2 3. If (x 2) is a factor of 3x + 2ax x 2, find a. (a) 2 (b) 2.5 (c) 4 (d) 5 4. A2 3 B3 m = C2 1 then m = (a) 1 (b) 2 (c) 3 (d) Matrices can t be multiplied 5. The 5th term from the end of 3, 7, 11, 15, , 99 is (a) 75 (b) 79 (c) 83 (d) 87 6. The point invariant in the line x = 2 is (a) (3, 2) (b) ( 2, 1) (c) (2, 4) (d) (0, 2) 7. If ABC ~ DEF, find DF (a) 5 cm (b) 18 cm (c) 30 cm (d) 40 cm 8. Volume of a cylinder with same radius and height as a cone is 30 cm3, then the volume of cone is (a) 10 cm3 (b) 15 cm3 (c) 30 cm3 (d) 90 cm3 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 1 9. The solution set for the given inequation is: 5 < 3x + 1 < 13, x Z (a) {1, 2, 3, 4} (b) {0, 1, 2, 3, 4} (c) { 1, 0, 1, 2, 3} (d) { 1, 0, 1, 2, 3, 4} 10. Which of the following cannot be probability of an event? (a) 20% (b) 3 7 (c) 0.5 (d) 0.75 1 5 2 3 11. If [ ]+ 2[ ]=[ ] then x is 1 0 4 1 7 2 (a) 4 (b) 1 (c) 1 (d) 4 12. The midpoint of line joining points (2a, 3) and (4, a 3b) is ( 6, 2) then b is (a) 2 (b) 1 (c) 3 (d) 2 13. In the given figure, PQ = QR, RQP = 68 , PC & CQ are tangents to the circle with centre O. PCQ = (a) 56 (b) 68 (c) 72 (d) 112 14. If tn = 2n 3, then the first three terms of the AP are (a) 3, 1, 1 (b) 1, 3, 7 (c) 1, 1, 3 (d) 2, 0, 2 15. In grouped frequency distribution mode is found using (a) Bar Graph (b) Histogram (c) Ogive (d) Both (b) and (c) Question 2. (a) A man had a recurring deposit account for 1 year at 14% p.a. simple interest. If he gets Rs. 6,455 at the time of maturity, find the monthly installment. [4] (b) If 2, 6, p, 54 and q are in continued proportion, find the values of p and q. [4] (c) [4] Question 3. (a) A toy is in the shape of a cone surmounting a hemisphere. The height and radius of the base of the conical part are 4 cm and 3 cm respectively. Find the volume of the toy correct to four significant figures. 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts [4] 2 (b) A line AB meets X axis at A and Y axis at B. P (4, 1) divides AB in the ratio 1 : 2. (i) Find the co-ordinates of A and B. (ii) Find the equation of the line through P and perpendicular to AB. (iii) Find the equation of line through origin and parallel to AB. (c) Use graph paper to answer the following questions: (i) Plot P (3, 1) and Q (0, 5). Reflect Q in the origin to get Q . (ii) Reflect P in the y axis to get R. (iii) Reflect P and R in the x axis to get P and R . (iv) Give a name to the figure PQRR Q P . [4] [5] Section B (Attempt any 4 questions from this section) Question 4. (a) The following bill shows the rates and the marked price of articles: P2T Medical Centre Articles Marked Price Rate of GST DOLO 650 (For Trigo) Rs. 15,500 18% Poison (For Circles) Rs. 1,900 28% Find the total amount on the bill. (b) Solve the quadratic equation and give your answer correct to two decimal places: x (x + 1) = 3. [3] [3] (c) [4] 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 3 Question 5. 4 1 (a) If A = [ ], show that A2 6A + 9I = 0 1 2 [3] (b) [3] (c) Given that (x + 1) and (x 2) are factors of x3 + ax2 bx 6. Find the value of a and b. Hence factorise completely. Question 6. [4] (a) The vertices of parallelogram ABCD taken in order are A(-1, 0), B(3, 1) and C(2, 2) find: (i) the coordinates of the fourth vertex D. (ii) equation of the diagonal BD. [3] (b) [3] (a) The first term, common difference and the last term of an AP are 12, 6 and 252 respectively. Find the sum of all the terms of this AP. [4] Question 7. (a) A bag contains some blue, green, red and white balls. One ball is drawn at random 1 1 1 from the bag. The probability of getting a blue, green and red balls is 2 , 4 , 8 respectively. If the number of white balls is 4, find: (i) the probability of getting a white ball (ii) the total number of balls in the bag [3] (b) A hemi-spherical bowl of internal radius 9 cm is is melted and recasted into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles can be made? [3] 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 4 (c) [4] Question 8. (a) [3] (b) Find the mean of the following distribution using step deviation method: Price (Rs.) 80 90 90 100 100 110 110 120 120 130 No. of days 12 10 8 15 5 [3] (c) [4] Question 9. (a) If the speed of an aeroplane is reduced by 40 km per hr it takes 20 mins more to cover 1200 km. Find the speed of the plane. [4] (b) [6] 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 5 Question 10. (a) If 3 + 1 + + 1 3 + 1 + 1 = 4, use properties of proportion to find x. (b) Using ruler and compasses, construct a regular hexagon of side 4 cm. Hence construct a circle inscribing the hexagon. Measure and write down the length of in-radius. [3] [3] (c) As observed from the top of a 80 m tall light house, the angles of depression of two ships on the same side of the light house in horizontal line with its base are 30 and 40 respectively. Find the distance between the two ships. Give your answer correct to the nearest meter. [4] In case of any doubts whatsapp on 9819547699 All the Best 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 6

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