Formatting page ...
This paper contains 6 printed pag Attempt all the questions from Section I and any four questions from Section II The intended marks for the questions or parts of questions are given alongside the questions SECTIONA(40 marks) (Attempt all questions) Question 1 a) Find the tenth term from the end of an AP: 4, 9, 14, - b) Solve the 254 following inequation -5-x c) Show that 2x + 3x 7 is a 131 and represent your solution on real number line: 3-xxeR 13] factor of 2x3+ 5x2- 11 x-14. Hence, factorise the given expression completely, using factor theorem. [41 Question 2 a) If A find = the matrix B such that A2 2B 3A + 5, where Iis a 2x2 131 identity matrix. b) The marked price of an article is 9000 and rate of GST on it is 18%. A shopkeeper buys this article at reduced price and sells it at its marked price. If the shopkeeper paid R162 to the govermment, find the amount (inclusive of [31 GST) paid by the shopkeeper. c) Following table gives marks scored by students in an examination: Marks 0-5 No. of 3 5-10 10-15 15-20 20-25 25-30 30-35 35-40 15 24 16 8 5 2 students Calculate the mean marks correct to 2 decimal places. 41 Question3 a) Using properties of proportion, solve for x. Given that x is positive 2x+4x 4 2x-v4x2-1 131 b) Prove that: 2( sin$0+ cos 0)-3(sin 0 +cos 0)+ 1 0 131 c) Sonal can row a boat at a speed of 5 km/h. Ifit takes her 1 hour more to row the boat 5.25km upstream than to return downstream, find the speed of the stream. Oucction A 141 Question3 a) Using properties of proportion, solve for x. Given that x is positive 2x+ V4x2-1 2x-V4x2-1 131 4 b) Prove that: 131 2( sin0+ cos0)-3( sin 0 +cos 0)+ 1=0 c) Sonal can row a boat at a speed of 5 km/h. If it takes her 1 hour more to row the boat 5.25km upstream than to return downstream, find the speed of the 141 stream. Question 4 a) In the given figure, O is the centre of the circle and PQ is a tangent to a circle at point C. Given 4DCO and ABD 400 40 D =60, find the measure of the following angles: () DBC P 600 i) BCP (ii) LAOD b) There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box. Find the probability that the number on the disc is: 131 VIBGYOR GROUP OF SCHOOLS () an odd number (Gi) divisible by 2 and 3 both. c) From (ii) multiple of 3 or 5. a solid cylinder whose height [3] is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume [41 and total surface area of the remaining solid. SECTION B (40 marks) (Attempt any 4 questions.) Question 5 a) In the given figure, POR = PST = 90 , PQ = 5 cm and PS i. Prove that APQR APST 2 cm. R ii. Find Area of APQR: Area of quadrilateral SRQT b) Prove that:. tan-0 cos20 13] SECTIONB(40 marks) (Attempt any 4 questions.) Question 5 a) In the given figure, 2PQR =ZPST= 90 , PQ =5 cm and PS 2 cm. P Prove that APQR APST ii. (3 Find Area of APQR: Area of quadrilateral SRQT b) Prove that. tan-0 cose sin20-cos201-2cos20 c) Use graph paperfor this question Use 1 cm 131 tan20-1 1 unit on both axes. Plot points A(0,5), B(4,1), C(-2,1), D(-2, -1) B'is the image of B when reflected in the x-axis, followed by the reflection in the origin. C' is the image of C when reflected in the y-axis. D' is the image of C when reflected in the origin. () Write the coordinates of B, C' and D' and plot it on the graph paper. (i) Write the geometrical name of ABCDD'CB'A. (iii) Find the area of the fiaure formed 141 Prove i. that APQR APST Find Area of APQR: Area of quadrilateral SRQT I31 b) Prove that:. tan 0 cos-0 tan20-1 sin20-cos20 1 1-2cos20 3] c)Use graph paperfor this question. Use 1 cm=1 unit on both axes. Plot points A(0,5), B(-4,1), C(-2,1), D(-2, -1) B'is the image of B when reflected in the x- axis, followed by the reflection in the origin. C' is the image of C when reflected in the y-axis D' is the image of C when reflected in the origin. ) Write the coordinates of B'. C' and D' and plot it on the graph paper. (i) Write the geometrical name of ABCDD'C'B'A (Gii) Find the area of the figure formed. Question 6 [4 Data/Local/Temp/Temp1 OneDrive 2020-12-14.zip/Prelim%201%20Exam%20QP/CISCE GRADE%2010 MATHEM rowser? Set as default + A Read aloud Draw Question 6 VIBGYOR GROUP OF SCHOOLS 2 a) Write the equation of a line whose slope isand which passes through P, where P divides the line segment joining A(4,-8) and B(12,0) in the ratio 3:1. 131 b) Using Quadratic Formula, solve for x, and give your answer correct to 2 significant figures x-3(X+3) =0 c) In the adjoining figure, 2 BQR 131 450 and x 2y. Calculate the values of x and y. [41 R B Question 7 Question 7 a) A hollow metallic cylindrical tube has an internal radius of 3 cm and height 14 cm. The thickness ofthe metal of the tube iscm. The tube is melted and cast into a 2 right circular cone of height 6.5 cm. Find the radius of the cone correct to one [41 decimal place. b) The weight of 60 workers is given below Weight( in Kg) 50-60 60-70 No. of workers 6 9 70-80 80-90 13 16 90-100 8 100-110 110-120 5 3 Using a graph paper draw an ogive for the above distribution. Use your ogive to estimate: i The median ii Upper Quartile ii. If weighing 95 Kg and above is considered overweight, find the number of workers who are overweight. [6] Question 8 a) Three vertices of a parallelogram ABCD taken in order are A(3,6), B(5,10) and C(3.2). Find ) The co-ordinates of the fourth vertex D (i)Equation of side AB of parallelogram ABCD [31 VIBGY OR GROUP OF SCHOOLS b) Find the value of k for which x2+ 4kx + (K?-k+2) =0 has equal roots. c 131 An aeroplane at an altitude of 250m observes the angle of depression of 2 boats on the opposite banks of the river to be 420 and 600 respectively. Find the width of the river and write the answer to nearest whole number 4] Question 9: a) Ms Shetty opened a recurring deposit account in a bank. She deposited 2500 per month for 2 years. At the time of maturity, she got T67,500. Find: i) The total interest earned by Ms. Shetty. 13] i) The rate of interest per annum. b) Theline joining the points (2, 1) and (5,-8) istrisected at the points P and Q. If Point P lies on the line 2x-y+k= 0, find the value of k. Also, find the co [31 ordinates of point Q c) The sum of first m terms of an AP is 4m2- m. If its nth term of n. is 107, find the value Also find the 21st term of this AP 4 Question 10: a) When divided by x-3, the polynomials x- px+x+6and 2x-x- (p+3)x-6 leave the same remainder. Find the value of p' b) The marks of 10 students of a class in an examination arranged in ascending9 Aer ie foIlWc [3] she got T67,500. Find: per month for 2 years. At the time of maturity, ) The total interest earned by Ms. Shetty. (ii) The rate of interest per annum. b) The line joining the points (2, 1) and (5,-8) is trisected at the points P and Q. Point P lies on the line 2x-y+k 0, find the value of k. Also, find the co- [3 If = 13 ordinates of point Q. The c) sum of first m terms of an AP is 4m2- m. If its nth term is 107, find the value [41 of n. Also find the 21st term of this AP. Question 10: a) When divided byx-3, the polynomials x- px2+x+6 and 2x3- x- (p+3)x - 6 [31 leave the same remainder. Find the value of 'p'. b) The marks of 10 students of a class in an examination arranged in ascending order is as follows: 13, 35, 43, 46, x, x +4, 55, 61, 71, 80 If the median marks is 48, find the value of x. Hence, find the mean and mode 131 of the given data. c) Given matrix B Find given XA Question 11 a) Ifa h d d prove that: the matrix X, if X B2- 4B. Hence, Find matrix A = [41 Question 11 a If a: b c:d, prove that: 5a+7b:5a-7b 5c +7d:5c-7d. 31 VIBG Y OR GROUP OF SCHOOLSs b) Priyanka has a recurring deposit account of R1000 per month at 10% per annum. If she gets 5550 as interest at the time of maturity, find the total time for which the account was held. 131 c) In the given figure, the median BD and CE of a triangle ABC meet at G. Prove that: () A EGDA CGB, and hence (i) Prove that BG 2GD [41 GROUP OF SCHOOLS b) Priyanka has annum. If she a per month at 10% per recurring deposit account of 1000 find the total time R5550 as interest at the time of maturity, gets for which the account c) In the given figure, was held. the median BD and CE of a triangle ABC meet at 13 G. Prove that: ) (i) () A EGD A CGB, and hence 141 2GD Prove that BG A E D C B *** *
|
