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ICSE Class X Prelims 2025 : Mathematics (Bombay Scottish School, Mahim, Mumbai)

9 pages, 42 questions, 5 questions with responses, 7 total responses,

Nandani Bajaj
The Assam Valley School, Balipara, Sonitpur

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Bombay Sotl Sclool, malim ASSES8MENT 3 MATHEMATIC8 Grade : 10 Date :04.11.2024 Max. Marks No. of questions Duration: 3 hours 80 : 10 No of printed sldes :09 You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the The time given at the head of this Paper is thequestion paper. time allowed for writing the answers. Attempt all questions from section A and any four questions from Section B. Al working, including rough work, must be clearly done on the same sheet as the rest of the shown, and must be answe. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [J Mathematical tables are provided. SECTION A (Attempt all questions from this section) Question 1 Choose the correct answers to the questions from the given options: (Do not copy the question, write the correct answers only.) (1) The money required to buy 50, 240 shares quoted at 38-50 is: (a) 1920 (b) 1952 (c)1924 (d) 1925 (i) Fill in the missing entries for the following transaction within the same city for a dress having GST= 18%, Listed price = 1200, Discount = 20% Discount price -x CGST = y SGST =z, (a) x =* 900, y = 43.20,2 = 86.40 (b) x =* 960, y=* 86.40, z =86.40 (c) x = 860,y =z=172.80 (d) x =*240, y = 43.20,z = 43.20 1 [15] (ii) Assertion (A): A locus of points which are at equal distance from three non collincar points docsn't exit Reason (R) : Locus of three non collinear points A, B and C is the circumcircle of triangle ABC (a) Both A and R are true and R is the explanation for A. (b) Both Aand Rare true and R is not correct the correct (c) A is true but R is explanation for A. (d) A is false but R is false. true. (iv) If the discriminant of quadratic equation ax? + bx + c= 0 is equal to zero,then two equal roots are: (a) - b/2a (v) (b) b/2a (c) b/a (d) - a/2b Assertion: The probability of an event that cannot happen or which is impossible, is equal to zero. Reason: The probability lies between 0 and 1. Hence, it negative. cannot be (a) Both A and R are (b) Both A and R are true and R is the correct (c) A is true but R true and R is not the correct is (d) A is false but R false. is explanation for true. (vi) If (3, 6) is the Find a? explanation A. for A. midpoint of the line segment joining (1, a) and (5, 9.5). (a) 3.5 (b) 1.5 (c) 2.5 (d) 7.5 (vii) The (a) (b) (c) (d) general form of linear inequations in one variable is: ax + b > 0, ax + ax +b >0, ax +b<0, ax +b> 0, ax + bs0 where a, be W b<0, ax + b20, ax + bs0 where a, beN, a and b both ax +b > 0, ax + b< 0, cannot be zero ax + b > 0, ax + bs0 a#0 where a, b EI and ax + b> 0, ax + b<0, ax +b 0, ax + a #0 bs0where a, b eR and 2 (vin) XI and x, 3,y.12, y are in continued proportion, then what are the values of (a) (b (c) (d (ix) X 1.3, y 36 X36, y4 X0.7S, y 48 x1.3, y 48 The (n - l)th term of an A.P. is given by 7, 12,17, 22,... is (a) 5n + 2 (b) 5n +3 (c) 5n -5 (d) 5n -3 (x) A flagpole 15 meters high is casting a shadow that has a length of 9 meters. Find the closest angle of elevation of the sun? (a) 30 (b) 45 (c) 60 (d) 75 (xi) Study the given figure and find the correct statements from the following: A B 5 3 12 AAOB ~A COD by SAS test of similarity. (i) (iii) (iv) A AOB a) only (iv) (c) (ii) and (ii) ACOD as two right triangles are always similar. A AOB ~ A COD implies that CD = 15 The given data is insufficiernt (b) (d) 3 (i) and (iii) (i), ( ) and (iii) (Kii) Assertion: Acvlinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone. Reanon: If the radius of the cylinder is doubled and height is halved the volume will be doubled. la) Both Aand Rare true and Ris the correct explanation for A. () Both Aand Rare true and Ris not the correct explanation for A. () A is true but R is false. (d) A is false but R is true. (xiii) The 11th term of the G.P. 1/8, -1/4, 1/2, -1 .....is (a) 184 (b) 192 (c) 128 (d) 1024 (xiv) The probability of an event A js 0.7. what is the probability of the complement of A? (a) 0.7 (b) 0.3 (c) 1.7 (d) 1.4 (xv) Assertion (A) : PA and PB are tangents to a circle with centre O such that zAOB =110, then LAPB 90 Reason (R): The length of two tangents drawn fromn an external point are equal. la) BothA and R are true and R is the correct explanation for A. (b) Both A and R are true and R is not the correct explanation for A. (c) A is true but R is false. (d) A is false butR is true. 4 Question 2 consecutive terms in Geometric four are 3x+3,0 2x+2, (a) If x, progression. Find (i) first term (ii) common ratio (1) G (b) In AARC, ZABC DAC, AR 8 cm, AC4 cm, AD5 cm. (i) Prove that AACD is similar to ABCA. (i ) Find BC and CD (iii) Find the arca of AACD: area of AABC. (c axis respectively. Mand N are two points on the X axis and Y ratio 2 :3. Find: the in P(3, 2) divides the line segment MN (i) the coordinates of Mand N ( ) slope of the line MN. Question 3 of the circle. Calculate (a) In the figure, 2DBC- 58 . BD is the diameter (i) ZBDC (i) ZBEC (ii) 2BAC [4 (b) Find x : y, if 2x -5y: xy = 1: 3 ifx and y are positive values. (c) Use graph paper for this question (Take 2 cm = 1 unit along both x and [4 yaxis). Plot quadrilateral ABCD whose vertices are A(2, 2), B2, -2), (5] (i) Reflect quadrilateral ABCD on the y-axis and name it as A'BCD. c(0, -1) and D (0,1). (ii) Write down the coordinates of A' and B'. (iij) Name two points which are invariant under the above reflection. (iv) Give the geometric name of ABCD. 5 SECTION B (Attempt any 4 questlons from this section) Question 4 (a) (b) (3] Simplify : Find the value of p for which the lines 2x+ 3y -7 -0 and. 4y - px - 12-0 are perpendicular to each other. [3] (C) From two points Aand B on the same side of a building, the angles of elevation of the top of the building are 30 and 60 respectively. If the height of the building is 10m, find the distance between A and B correct to two decimal places. [4] Question 5 (a Using step deviation method, calculate the mean marks of the following distribution. [3] Marks Number of students 50- 55 5 55 - 60 20 60 - 65 65- 70 10 70- 75 9 75- 80 80- 85 6 12 85 - 90 8 (b) Amit Kumar invests 36,000 in buying 100 shares at premium.If the dividend is 15% per annum, Find: () The number of shares he buys 20 (ii) His yearly dividend (iii) The percentage return on his investment. Give your answer correct number. to the nearest whole [3] 6 (c) In an Arithmetic 14 respectively. Find Progression (A.P) the fourth and sixth terms are o a the: (i) first term (ii) common difference (iii) sum of the first 20 (41 terms. Question 6 (a) Solve the following quadratic equation 4x?-7% + 2 0 and give the correct answer to two significant figures. (3] (b) Amap of a square plot of land is drawn a scale of 1:25000. If the arca of the plot in the map is 72 cm, find : (i) the actual area of the plot of land in km ( ) the length of the diagonal in the actual plot of land. [3] (c) In a School, 100 pupils have heights as tabulated below,Find the median height by drawing an ogive. Height (in cm) [4) No. of pupils 121 - 130 12 131- 140 16 141 - 150 30 151 - 160 20 161 - 170 14 171- 180 8 Question 7 (a) In a class of 40 students, marks obtained by the students (out of 10) are given below : a class test (3 Marts Number of Students 3 Calculate the following for the given distribution: (i) Median (ii) Mode 7 3 (b) Shawn openeda Recurring Deposit Account in a bank and deposited t800 per month for 1.5 years. If he reccived 15,084 at the time of maturity, find the rate of interest per annum (c) Two pipes AAnd Bnunning togcther can fill a tank in Ihour If pipe A takes 1hour more than the other to fill it, find 12minutes. the time in which cach pipe would fill the tank. Question 8 (a) A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder corect to 3 significant figures. (b) Prove that: sec A-tan A sec A + tan A (c) [3 (3] cos A (1+ stn A) Find the equation of the straight line passing the origin and the point of intersection of the lines x + 2y = 7 through and x -y= 4. (4 Question 9 (a) If (x +2) and (x + 3) are factors of x+ ax + b, find the values of 'a' and b'. [3 (b) Draw a circle of diameter of 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given circle from this (3 exterior point. Measure the length of each tangent. (c) Using a graph paper, draw a histogram for the given showing the number of runs scored by 50 batsmen. distribution Estimate the mode of the data: Runs scored No. of batsmen 3000- 4000 4 4000- 5000 18 5000 -6000 6000- 7000 9 6 7000-8000 7 8000-9000 2 9000 - 10000 4 Question 10 (a) The marked price of an article is 12500, A dealer in Kolkata sells the article to a consumer in the same city at a profit of 8%. If the rate of GST is 18%, find (i) the selling price (excluding tax) of the article. (11) CGST and SGST paid by the dealer to the Central and State Governments. (11) The amount which the consumer pays for the article. [3 (b Using properties of proportion, solve for x: +1+-1 4x-1 a+i-r-i [3] (c) The diagram, given below, represents two inequations P and Q on real number line: P= 32 10 1 2 3 456 23 4 6 (1) Write down P and Q in set builder notation. (i) Represent each of the following sets PUQ & PnQ on diferent number lines. (4]

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