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RYAN GROUP OF SCHOOLS STD: SUB: ACADEMICYEAR 2023-24 ICSE, SECOND PRE-BOARD EXAMINATION X MARKS: MATHEMATICS DURATION: RYAN 80 2 HRS 30 MINS Answer to this Paper must be written on the paper provided separately. Youwill 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. . 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 theanswer. 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 (15 MARKS] Select the correct option for each of the following questions. Question 1. Choose the correct answers to the questions fromn the given options. (Do not copy the question, Write the correct answer only.) [15] 1.Apoint P is reflected in the x-axis. Co-ordinates of its image are (-4, 5). Find the co-ordinates of P. a. The origin b. (-4,-5) c.(-4,5) d. (4,-5) 2.Calculate the co-ordinates of the centroid of the triangle ABC, if A= (7,-2), B= (0,1), C= (-1,4). a. (2,1) b. (-2,-1) c. (2, -1) d. (-2,1) 3. In the given figure, BC isa diameter of circle with Centre '0'. If ZAOB =70 then the value of L0AC is a. 35 C. 110 b. 70 d, 140 STD: X 4. cot x V1-cos MATHS -2 ICSE is C. tan a. cos d. cot 0 b. sin probability of winning of Rajesh is the Joseph, and Rajesh between 5. In a badminton match 0.58. Find the probability of not winning of Rajesh. a. 0.42 C. 1 b. 0.58 d. 0 is: quadraticequation 2x3x + 1 =0, the of roots of nature The 6. c. imaginary a. real and equal b. real and unequal d. none of these kx +10,then the value of kis: 2xx + of factor a is 2 7. If xc. 13 a. 3 d. 26 b. 8. 8. by which of the following In the given figure, AAPC~ABPD B A a. SAS b. SSS C. ASA d. AA similarity criterion? STD: X MATHS -3 ICSE 9. The SGST paid by a customer to the shopkeeper for a toy which is priced at 1000 is 50. The rate of GST charged is. a. 5% c. 15% b. 10% d. 6% is 10. If the first term of AP is 2 and common difference is 8, then 10h term c. 88 tC a. 154 d. 160 b. 72, 14 B is 11. If matrix A is of order 3x2 and matrix AB is of orders 3x2, then order of matrix a. 3 x 2 c. 2 x 3 b. 2 x 2 d. 1x3 surface area of 12. If the radius of acone is r and its slant height ([) is halved, then curved the cone is C. Tl d. r(r + )r b. 2Tr 313. I6 + The value of 'xis a. 2 C. 4 b. 3 d. 5 14. The median of a grouped frequency distribution is. found a. Linear graph b. A histogram c. A polygon d. A cumulative frequency curve 15. The third proportional to 1.2 and a. 9 2. b. 6 3 Question 2. 1. Mohan graphically by drawing 1.8 is c. 3 d. 1.5 in a bank for 2 years at 6% account deposit recurring has.a he gets of maturity, find 1200 as interest at the time p.a. simple interest. It 14] STD: X ICSE a. themonthly b. the -4 MATHS instalment amount of maturity. 2. In the figure given below, O is the centre of the circle and SP is a tangent. If LSRT = 65 find the values ofx, y and z [4] P 65 3. Prove 1+sin A 1-sin A R =s c A + tan A [4] Question 3. (4] 1. Use the figure given: a. Write the coordinates ofA and B. b. P divides AB in the ratio 2:3. Find the coordinates of P c. Find the equation of the line parallel to AB passing through origin. 2 2. The inner circumference of the rim of a circular metal tub is 44 cm. find [4) STD: X -5 ICSE MATHS a. The inner radius of the tub. b.The volume of material ofthe tub if its outer radius is 8cm. give your answer to three significant figures. 8Cm 3. Using a graph paper, plot the points A (6, 4) and B (0,4). a. Reflet A and B in the origin to get the images A' and B' b. Write the co-ordinates of A' and B' c. State the geometrical name of the figure ABA'B'. d. Find its perimete. SECTION B Attempt any Four questions fromthis section. Question. 1.In the figure, the circle. Calculate: DBC = 58 , BD is a diameter of a. ZBDC b. LBEC C. ZBAC paper. The 2. Use a graph daily pocket school are expenses of200 students in a given below: [3] STD: X Pocket expense (in ) MATHS -6 ICSE 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 10 14 28 42 50 30 14 12 No. of students Draw a histogram and estimate the mode from graph. 3. Solvethe following inequation & represent solution set on number line 44] 4r- 19 <-2s+x; XER. Question 5. 1. If.8a-5b 8c-5d 8a+5b 8 +5d Rrove that b [3] d 2. Using Remainder theorem, Factorise the expression x3 + 10x2 -37x + 26 completely. 3| (4| 3. In an A.P, the fourth and the sixth terms are 8 and 14 respectively. Find a. First term b. Common difference c. Sum of first 20terms. Question 6. points A (-4, 6) andB (8, -3), Find 1. Given a line segment AB joining the the y-axis a. the ratio in which AB is divided by point of intersection b. find the co-ordinate of the 2. toBC. If AB=9 cm, DE-3 AB and DE are perpendicular cm, AC=24 cm findAD A D B E C 3] MATHS -7 ICSE STD: X the mean weight to 3. The weights of50 apples were recorded as given below. Calculate nearest gram, by step- Deviation fnethod. 105-110 110-115 Weights in grams 80-85 85-90 90-9595-100 100-105 No of Apples 5 12 10 8 (4] 4 8 Question 7. The 1. Abox contains the same green, yellow and white tennis ball. probability of selecting a 1 balls, then find green ballis and yellow ballis -.3 If the box contains 10 white [3) a. Total Number of balls in the box b. Probability of selecting a white ball sells the shares when the price of 2. Sachin invests .8500 in 10 %, 100 shares at.170. He (31 .100shares at .125.find each share rises by .30. He invests the proceeds in l2% a. the sale proceeds. b. the number of 125 shares he buys. c. the change in hisannual income. and B meet at C. 3. '0' is the centre of the circle tangent at A IfLACO=30 find [3] a. zBCO b. LAOB 30 C. ZAPB C B Question8. 1. Prove: 31 + tan A = Sec A 1+sin A cos A 2. The first term and last termof G.P is 3 and 96 a. the number of terms'n' respectively. If the common ratio is 2. Find 31 b. sum of 'n'terms 3. Find the matrix m,such that M 3 =-2 16] STD: X MATHS -8 ICSE Question 9. 1. The sum of the ages of Vivek and his younger brother Amit is 47 years. The produetof their age in years is 550. Find their ages. 2. The daily wages of 80 workers in a Project are given below: Wages in ? No. of Workers 400-450 450-500 500-550 550-600 2 6 12 18 [41 [6] 600-650 650-700 24 700-750 13 Use a graph paper to draw a give for above distribution use a scaie pf 2cm =50 on x-axis and 2 cm = 10 workers on y - axis. Use gives to estimate. a. Median wages of the workers b. Lower quartile wage of workers c. The number of workers who earn more than 625 daily. Questioy10. 1. Construct a regular hexagon of side4 cm. Construct a circle circumscribing the hexagon. [3] 2. The following billshows that GST rates & marked price of articles. (3] Bill:Toy Articles Marked Price Rate of GST Car 1500 18% Bike 9500 28% Find the total amount to be paid for the above bil. 3. The length of the shadow of vertical toweron level ground increases by 1Om, when the altitude of the sun changes from 45 to 30 . Calculate the height of the tower correct to two decimal places. .141 *****
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