
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

ICSE Class X Board Practice 2025 : Mathematics (Competency-Focused Questions)

49 pages, 0 questions, 0 questions with responses, 0 total responses,

Biswajit Maity
City English School, Sundargarh

+Fave Message

Profile Timeline Uploads

Home > maitybiswajit884 >

Formatting page ...

PREFACE With a growing emphasis on competency-based education globally, the educational landscape in India has also steered towards high-quality learning experiences that allow learners to incorporate critical thinking and problem-solving approaches. This approach goes beyond rote memorisation and focuses on developing the skills and knowledge that students need to apply in their real-world scenarios. The Council for the Indian School Certificate Examinations (CISCE), as a national-level progressive examination board, has taken several steps to infuse competency-based education in CISCE schools through teacher capacity-building on item development for competencybased assessments and the incorporation of competency-focused questions at the ICSE and ISC levels from the examination year 2024. To further facilitate the adoption of competency-based assessment practices in schools and to support teachers and students towards the preparation for attempting higher-order thinking questions in future board examinations, Item Banks of Competency-Focused Practice Questions for selected subjects at the ICSE and ISC levels have been developed. This Item Bank consists of a rich variety of questions, both objective and subjective in categories, aimed at enhancing the subject-specific critical and analytical thinking skills of the students. In this Item Bank, each question is accompanied by the topic and cognitive learning domain/s that it intends to capture. The cognitive domains reflected in these questions include understanding, analysis, application, evaluation and creativity, along with some questions of the higher-order recall domain. The Answer Key at the end presents the possible answers to a given question, but it is neither limiting nor exhaustive. These practice questions are also meant to serve as teacher resources for classroom assignments and as samplers to develop their own repository of competency-focused questions. Apart from offering a good practice of higher-order thinking skills, engaging with these questions would allow students to gauge their own subject competencies and use these assessments for learning to develop individual learning pathways. During the development of this Item Bank, a large pool of questions was prepared by a team of experienced CISCE teachers. The questions that were finalised by the internal and external reviewers as being higher-order competency-focused questions have been collated in this item bank. I acknowledge and appreciate all the ICSE and the ISC subject matter experts who have contributed to the development and review of these high-quality competency-focused questions for CISCE students. We are hopeful that teachers and students will utilise these questions to support their teachinglearning processes. August 2024 Dr. Joseph Emmanuel Chief Executive & Secretary CISCE Mathematics ICSE - Class X Table of Contents S.No Type of Questions Page No. I. Multiple-Choice Questions 2-14 II. Short Answer Questions -1 15-21 III. Short Answer Questions -2 22-29 IV. Long Answer Questions -1 (Graph-based) 30-31 Long Answer Questions -2 32-36 V. Answer Key ICSE Competency-Focused Practice Questions 37-46 1 Mathematics ICSE - Class X COMPETENCY-FOCUSED PRACTICE QUESTIONS ICSE CLASS X Mathematics I: Multiple Choice Questions Type (1 Mark Each) S.No. 1. Questions [Commercial Mathematics] A retailer buys an article at its listed price from a wholesaler and sells it to a consumer in the same state after marking up the price by 20%. The list price of the article is 2500, and the rate of GST is 12%. What is the tax liability of the retailer to the central government? (a) (b) (c) (d) 2. 0 15 30 60 [Analysis & Evaluate] [Commercial Mathematics] Dev bought an electrical fan which has a marked price of 800. If the GST on the goods is 7%, then the SGST is: (a) (b) (c) (d) 3. 24 28 56 80 [Evaluate] [Commercial Mathematics] P is deposited for n number of months in a recurring deposit account which pays interest at the rate of r % per annum. The nature and time of interest calculated is: (a) (b) (c) (d) compound interest for n number of months. simple interest for n number of months. compound interest for one month. simple interest for one month. [Understanding & Application] ICSE Competency-Focused Practice Questions 2 Mathematics ICSE - Class X S.No. 4. Questions [Commercial Mathematics] Anwesha intended to open a Recurring Deposit account of 1000 per month for 1 year in a Bank, paying a 5% per annum rate of simple interest. The bank reduced the rate to 4% per annum. How much must Anwesha deposit monthly for 1 year so that her interest remains the same? (a) (b) (c) (d) 5. 12325 1250 1200 1000 [Analysis & Evaluate] [Commercial Mathematics] Mr. Das invests in 100, 12% shares of Company A available at 60 each. Mr. Singh invests in 50, 16 % shares of Company B available at 40 each. Use this information to state which of the following statements is true. (a) (b) (c) (d) The rate of return for Mr. Das is 12% The rate of return for Mr. Singh is 10% Both Mr. Das and Mr. Singh have the same rate of return of 10% Both Mr. Das and Mr. Singh have the same rate of return of 20% [Application & Evaluate] 6. [Commercial Mathematics] Amit invested a certain sum of money in 100 shares, paying a 7.5% dividend. The rate of return on his investment is 10%. The money invested by Amit to purchase 10 shares is: (a) (b) (c) (d) 7. 250 750 900 1100 [Application & Evaluate] [Algebra] If -3 -4x+5 and x W, then the solution set is: (a) (b) (c) (d) 8. { .-3,-2,-1,0,1,2,3 } { 1, 2 } { 0,1,2} { 2, 3 4,5} [Understanding & Application] [Algebra] If -4x > 8y, then (a) (b) (c) (d) x > 2y x > -2y x < -2y x < 2y ICSE Competency-Focused Practice Questions [Understanding & Application] 3 Mathematics ICSE - Class X S.No. 9. Questions [Algebra] The value/s of k for which the quadratic equation 2 2 + = 0 has equal roots is(are): (a) (b) (c) (d) 10. 0 only 4,0 8 only 0,8 [Understanding & Application] [Algebra] If x = -2 is one of the solutions of the quadratic equation 2 + 3 -x = 0, then the value of a is: (a) (b) (c) (d) 11. -8 -2 -1/3 1/3 [Understanding & Application] [Algebra] In solving a quadratic equation, one of the values of the variable x is 233.356. The solution rounded to two significant figures is: (a) (b) (c) (d) 233.36 233.35 233.3 230 A B C [Understanding & Application] 12. [Algebra] In the adjoining diagram, AB = x cm, BC=y cm and x y = 7 cm. Area of ABC = 30 2. The length of AC is: (a) (b) (c) (d) 13. 10 cm 12 cm 13 cm 15 cm [Analysis & Evaluate] [Algebra] If p, q, and r are in continued proportion, then: (a) (b) (c) (d) p : q = p: r q : r = 2 : 2 p : 2 = r : 2 p : r = 2 : 2 ICSE Competency-Focused Practice Questions [Understanding & Application] 4 Mathematics ICSE - Class X S.No. 14. Questions [Mensuration] The ratio of diameter to height of a Borosil cylindrical glass is 3:5. If the actual diameter of the glass is 6cm, then the curved surface area of the glass is: (a) (b) (c) (d) 15. 120 60 30 18 [Analysis & Evaluate] [Algebra] If the polynomial 2 3 + 3 2 2 3 is completely divisible by (2x + a), and the quotient is equal to ( 2 1), then one of the values of a is: (a) (b) (c) (d) 16. -3 -1 1 3 [Analysis] [Algebra] A polynomial in x is 3 + 5 2 kx -24. Which of the following is a factor of the given polynomial so that the value of k is 2? (a) (b) (c) (d) 17. (x + 2) (x 3) (x + 4) (x 4) [Analysis & Evaluate] [Algebra] ] = [ ], then: only matrix AB is possible. only matrix BA is possible. both matrices AB and BA are possible. both matrices AB and BA are possible, AB = BA. If = [ (a) (b) (c) (d) [Understanding & Application] 18. [Algebra] 6 9 0 0 Matrix = [ ] such that 2 = [ ].Then k is: 4 0 0 (a) 6 (b) -6 (c) 36 (d) 6 [Analysis & Evaluate] ICSE Competency-Focused Practice Questions 5 Mathematics ICSE - Class X S.No. 19. Questions [Algebra] If the sum of n terms of an arithmetic progression Sn = n2 n, then the third term of the series is: (a) (b) (c) (d) 20. 2 4 6 9 [Understanding & Application] [Algebra] Which of the following is NOT a geometric progression? (a) (b) (c) (d) 21. 1/3, 1, 3, 9 1/5, 1/5,1/5,1/5 -2, 4, -8, 16 2,0,4,0,8,0 [Understanding] [Algebra] In the adjoining diagram, G is the centroid of ABC. A (3,-3), B (2,-6), C (x, y) and G (5,-5). The coordinates of point D are: (a) (b) (c) (d) (2,- 6 ) (3,- 6 ) (6,- 6 ) (10,- 6 ) A (3, -3) G (5, -5) B (2, -6) D C (x, y) [Analysis & Application] 22. [Algebra] In the given diagram, O is the origin, and P is the midpoint of AB. The equation of OP is: (a) (b) (c) (d) y=x 2y = x y = 2x y = -x [Analysis & Application] ICSE Competency-Focused Practice Questions 6 Mathematics ICSE - Class X S.No. 23. Questions [Algebra] In the given figure Line l1 is a parallel to Line l2. If line l3 is perpendicular to Line l1, then the slopes of lines l2 and l3 respectively are: (a) (b) (c) (d) Yaxis Line l3 1, 1 -1, -1 1, -1 -1, 1 Line l1 45 0 Xaxis Line l2 [Analysis & Application] 24. [Algebra] Which of the following lines cut the positive x-axis and positive y-axis at equal distances from the origin? (a) (b) (c) (d) 25. 3x+3y=6 5x +10y = 10 -x + y = 1 10x +5y = 5 [Understanding & Application] [Geometry] In the given diagram (not drawn to scale), railway stations A, B, C, P and Q are connected by straight tracks. Track PQ is parallel to BC. The time taken by a train travelling at 90km/hr to reach B from A by the shortest route is: A (a) 8 minutes (b) 12 minutes (c) 16.8 minutes (d) 20 minutes P B ICSE Competency-Focused Practice Questions 20 50 km km Q C [Analysis & Application] 7 Mathematics ICSE - Class X S.No. 26. Questions [Geometry] D A B C E F In the given diagram, ABC and DEF (not drawn to scale) are such that = F and = , then (a) (b) (c) (d) 27. ABC ~ DEF BCA ~ DEF CAB ~ DEF the similarity of given triangles cannot be determined. [Geometry] In the adjoining diagram, ST is not parallel to PQ. The necessary and sufficient conditions for PQR ~ TSR is: (a) (b) (c) (d) 28. [Analysis] PQR= STR QPR= TSR PQR= TSR PRQ= RST R T Q S P [Understanding & Application] [Geometry] The scale factor of a picture and the actual height of Sonia is 20cm: 1.6m. If her height in the picture is 18cm, then her actual height is: (a) (b) (c) (d) 14.4m 2.25m 1.78m 1.44m ICSE Competency-Focused Practice Questions [Analysis & Application] 8 Mathematics ICSE - Class X S.No. 29. Questions [Geometry] In the adjoining figure, O is the centre of the circle, and a semicircle is drawn on OA as the diameter. APQ=20 .The degree measure of OAQ is: (a) (b) (c) (d) 25 40 50 65 [Analysis & Application] 30. [Geometry] In the given diagram, O is the centre of the circle, and DE is a tangent at B. If ABC=50 , then values of x,y and z respectively are: (a) (b) (c) (d) 500 , 1000 , 400 500 , 500 , 650 400 , 800 , 500 500 , 250 , 780 [Analysis & Evaluation] ICSE Competency-Focused Practice Questions 9 Mathematics ICSE - Class X S.No. 31. Questions [Geometry] In the given figure, PT and QT are tangents to a circle such that TPS = 450 and TQS = 300. Then, the value of x is: (a) (b) (c) (d) 300 450 750 1050 [Analysis & Evaluation] 32. [Mensuration] A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching? (a) (b) (c) (d) 33. Its curved surface area. Its total surface area. Its volume. Its radius. [Understanding] [Mensuration] A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is: (a) (b) (c) (d) 21cm 42cm 21 7 cm 2 7 cm. [Use = 22/7] ICSE Competency-Focused Practice Questions [Understanding & Application] 10 Mathematics ICSE - Class X S.No. 34. Questions [Mensuration] A solid sphere with a radius of 4cm is cut into 4 identical pieces by two mutually perpendicular planes passing through its centre. Find the total surface area of onequarter piece. (a) (b) (c) (d) 24 32 48 64 [Understanding & Application] 35. [Mensuration] Two identical solid hemispheres are kept in contact to form a sphere. The ratio of the total surface areas of the two hemispheres to the surface area of the sphere formed is: (a) (b) (c) (d) 1:1 3:2 2:3 2:1 + = [Analysis & Application] 36. [Trigonometry] 2 + 2 is equal to: (a) (b) (c) (d) 37. 2 + 2 + ( + )2 1 [Application] [Trigonometry] Given = 3 2 and = 3 2 2. The value of (a b) is: (a) (b) (c) (d) 1 2 3 5 ICSE Competency-Focused Practice Questions [Application] 11 Mathematics ICSE - Class X S.No. 38. Questions [Trigonometry] At a certain time of day, the ratio of the height of the pole to the length of its shadow is 1 : 3, then the angle of elevation of the sun at that time of the day is: (a) (b) (c) (d) 39. 30 45 60 90 [Understanding & Application] [Trigonometry] A man standing on a ship approaching the port towards the lighthouse is observing the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the lighthouse changes from to . Then: (a) (b) (c) (d) 40. > < = [Analysis & Evaluation] [Statistics] Assertion (A): The difference in class marks of the modal class and the median class of the following frequency distribution table is 0. Class interval Frequency 20 30 30 40 40 50 50 60 60 -70 1 3 2 6 4 Reason (R): Modal class and median class are always the same for a given frequency distribution. (a) (b) (c) (d) 41. Both A and R are correct, and R is the correct explanation for A. Both A and R are correct, and R is not the correct explanation for A. A is true, but R is false. Both A and R are true. [Analysis] [Statistics] Assertion(A): For a collection of 11 arrayed data, the median is the middle number. Reason (R): For the data 5, 9,7, 13,10,11,10, the median is 13. (a) (b) (c) (d) Both A and R are correct, and R is the correct explanation for A. Both A and R are correct, and R is not the correct explanation for A. A is true, but R is false. Both A and R are true. [Analysis] ICSE Competency-Focused Practice Questions 12 Mathematics ICSE - Class X S.No. 42. Questions [Commercial Mathematics] Ankit had the option of investing in company A, where 7%, 100 shares are available at 120 or in company B, where 8%, 1000 shares are available at 1620. Assertion (A): Investment in Company A is better than Company B. Reason (R): The rate of income in Company A is better than in Company B. (a) (b) (c) (d) 43. Both A and R are true, and R is the correct explanation. Both A and R are true, but R is not the correct explanation. A is false, but R is true. Both A & R are false. [Analysis] [Algebra] Assertion (A): 3 + 2 2 2is a polynomial of degree 3. Reason (R): x + 2 is a factor of the polynomial. (a) (b) (c) (d) 44. Both A and R are correct, and R is the correct explanation for A. Both A and R are correct, and R is not the correct explanation for A. A is true, but R is false. Both A and R are true. [Analysis] [Algebra] Assertion(A): The point ( -2, 8) is invariant under reflection in line x = - 2. Reason (R): If a point has its x-coordinate 0, it is invariant under reflection in both axes. (a) (b) (c) (d) 45. Both A and R are correct, and R is the correct explanation for A. Both A and R are correct, and R is not the correct explanation for A. A is true, but R is false. Both A and R are true. [Analysis] [Algebra] When a die is cast with numbering on its faces, as shown, the ratio of the probability of getting a composite number to the probability of getting a prime number is _______. (a) (b) (c) (d) 2:3 3:2 1:3 1:2 ICSE Competency-Focused Practice Questions [Analysis] 13 Mathematics ICSE - Class X S.No. 46. Questions [Algebra] 1 2 2 The product of A = [ ] and matrix M, AM = B where B = [ ], then the 3 4 24 order of matrix M is ____________. (a) (b) (c) (d) 47. 2x2 2x1 1x2 4x1 [Understanding & Application] [Algebra] Given, 1 , 2 , 3 , .and 1 , 2 , 3 , . are real numbers such that 1 1 = 2 2 = 3 3 = . are all equal. 1 1 , 2 2 , 3 3 . forms a ______________ progression. (a) (b) (c) (d) 48. Geometric (r=1) Arithmetic (d=1) Geometric (r<1) Arithmetic (d=0) [Analysis & Application] [Geometry] Locus of a moving point is _______________ if it moves such that it keeps a fixed distance from a fixed point. (a) (b) (c) (d) 49. Circle Line Angle Line segment [Recall & Understanding] [Geometry] The point of concurrence of the angle bisectors of a triangle is called the _________ of the triangle. (a) (b) (c) (d) centroid incentre circumcentre orthocentre ICSE Competency-Focused Practice Questions [Recall & Understanding] 14 Mathematics ICSE - Class X II. Short Answer Questions - 1 (3 Marks) S.No. 50. Questions [Commercial Mathematics] A shopkeeper marked a pressure cooker at 1800.The rate of GST on pressure cooker is 12%. The customer has only 1792 with him and he requests the shopkeeper to reduce the price so that he can buy the cooker in 1792. What percent discount must the shopkeeper give? [Application & Evaluation] 51. [Commercial Mathematics] A man opened a recurring deposit account in a branch of PNB. The man deposits certain amount of money per month such that after 2 years , the interest accumulated is equal to his monthly deposits. Find the rate of interest per annum that the bank was paying for the recurring deposit account. [Application & Evaluation] 52. [Commercial Mathematics] Akshay buys 350 shares of 50 par value of a company. The dividend declared by the company is 14%. If his return percent from the shares is 10%, find the market value of each share. [Application & Evaluation] 53. [Algebra] Solve the following inequation and answer the questions given below. 1 2 (2 1) 2x + 1 2 1 52 + (a) Write the maximum and minimum values of x for x R. (b) What will be the change in maximum and minimum values of x if x W. [Evaluate & Analysis] 54. [Algebra] Solve for x, if 55. 5 + 4 3 = 2 3 2 , x 0 [Application & Evaluate] [Algebra] The marked price of a toy is same as the percentage of GST that is charged. The price of the toy is 24 including GST. Taking the marked price as x, form an equation and solve it to find x. [Application & Evaluate] 56. [Algebra] The mean proportion between two numbers is 6 and their third proportion is 48. Find the two numbers. [Application & Evaluate] ICSE Competency-Focused Practice Questions 15 Mathematics ICSE - Class X S.No. 57. Questions [Algebra] Pamela factorized the following polynomial: 2 3 + 3 2 3 2 She found the result as (x+2)(x-1)(x-2). Using remainder and factor theorem, verify whether her result is correct. If incorrect, give the correct result. [Analysis & Application] 58. [Algebra] A=[ 1 0 6 0 ] and B = [ ] . 1 3 4 2 Find matrix M, if M = 1 2 A -2B + 5l, where l is the identity matrix. [Application & Evaluate] 59. [Algebra] (a) Write the nth term (Tn) of an Arithmetic Progression (A.P.) consisting of all whole numbers which are divisible by 3 and 7. (b) How many of these are two-digit numbers? Write them. (c) Find the sum of first 10 terms of this A.P. [Application & Evaluate] 60. [Algebra] Write the first five terms of the sequence given by ( ) , n N. (a) Is the sequence an A.P. or G.P? (b) If the sum of its first ten terms is p(3+ 3),find the value of p. [Application & Evaluate] ICSE Competency-Focused Practice Questions 16 Mathematics S.No. 61. ICSE - Class X Questions [Algebra] ABC is a triangle as shown in the figure below. (a) Write down the coordinates of A, B, and C on reflecting through the origin. (b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively. [Analysis & Evaluate] 62. [Algebra] Determine the ratio in which the line y = 2 + 3x divides the line segment AB joining the points A (-3, 9) and B (4 , 2 ). [Understanding & Application] 63. [Algebra] Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at (-3,-1) and the diagonal DB produced is equally inclined to both the axes.The diagonals AC and BD meets at P (-2,-2). Find the: (a) slope of BD (b) equation of AC 64. [Analysis, Create & Evaluate] [Geometry] ABCD is a rectangle where side BC is twice side AB. If ACQ~ BAP, find area of BAP: area of ACQ. [Analysis & Evaluate] ICSE Competency-Focused Practice Questions 17 Mathematics S.No. 65. ICSE - Class X Questions [Geometry] Given a triangle ABC, and D is a point on BC such that BD = 4cm and DC = x cm. If BAD = C, and AB = 8cm, then, (a) prove that triangle ABD is similar to triangle CBA. (b) find the value of x . [Understanding, Application & Evaluate] 66. [Geometry] In the extract of Survey of India map G43S7, prepared on a scale of 2cm to 1 km,a child finds the length of the cart track between two settlements is 7.6 cm. Find: (a) the actual length of the cart track on the ground. (b) actual area of a grid square,if each has an area of 4 2 . [Understanding & Evaluate] 67. [Geometry] Construct a triangle ABC such that AB = 7cm, BC = 6cm and CA = 5cm. (use ruler and compass to do so). (a) Draw the locus of the points such that (i) it is equidistant from BC and BA. (ii) it is equidistant from points A and B. (b) Mark P where the loci (i) and (ii) meet , measure and write length of PA. [Analysis & Create] ICSE Competency-Focused Practice Questions 18 Mathematics S.No. 68. ICSE - Class X Questions [Geometry] In the given figure O is the centre of the circle. ABCD is a quadrilateral where sides AB, BC, CD and DA touch the circle at E, F, G and H respectively. If AB = 15 cm, BC= 18 cm and AD=24 cm , find the length of CD. [Application & Evaluate] 69. P [Geometry] In the given diagram, ABCDEF is a regular hexagon inscribed in a circle with centre O. PQ is a tangent to the circle at D. Find the value of: O F (a) FAG (b) BCD (c) PDE D E G A C Q B [Application & Evaluate] 70. [Geometry] AB and CD intersect at the centre O of the circle given in the above diagram. If EBA=33 and EAC=82 , find (a) BAE (b) BOC (c) ODB [Application & Evaluate] ICSE Competency-Focused Practice Questions 19 Mathematics ICSE - Class X S.No. 71. Questions [Mensuration] A famous sweet shop Madanlal Sweets sells tinned rasgullas. The tin container is cylindrical in shape with diameter 14cm, height 16cm, and it can hold 20 spherical rasgullas of diameter 6cm and sweetened liquid such that the can is filled and then sealed. Find out how much sweetened liquid the can contains. Take =3.14. [Analysis, Application & Evaluate] 72. [Mensuration] The ratio of the radius and the height of a solid metallic right circular cylinder is 7 : 27. This is melted and made into a cone of diameter 14 cm and slant height 25cm. Find the height of the: (a) cone (b) cylinder 73. [Analysis, Application & Evaluate] [Trigonometry] An inclined plane AC is prepared with its base AB which is 3 times its vertical height BC.The length of the inclined plane is 15 m.Find: (a) value of . (b) length of its base AB,in nearest metre. C 15m A B [Analysis, Application & Evaluate] 74. [Trigonometry] Prove that 2 + 2 1 = 2 . 2 [Analysis & Application] ICSE Competency-Focused Practice Questions 20 Mathematics S.No. 75. ICSE - Class X Questions [Statistics] The class mark and frequency of a data is given in the graph. From the graph, Find: (a) the table showing the class interval and frequency. (b) the mean. [Analysis, Application & Evaluate] 76. [Statistics] The mean of 5,7, 8 , 4 and m is n and the mean of 5, 7 , 8 , 4 , m and n is m. Find the values of m and n. [Understanding & Application] 77. [Probability] The probability of selecting a blue marble and a red marble from a bag containing red,blue and green marbles is 1/3 and 1/5 respectively. If the bag contains 14 green marbles,then find: (a) number of red marbles. (b) total number of marbles in the bag. ICSE Competency-Focused Practice Questions [Analysis & Evaluate] 21 Mathematics ICSE - Class X III. Short Answer Questions - 2 (4 Marks) S.No. 78. Questions [Commercial Mathematics] The following bill shows the GST rate and the marked price of items: S. No. 1. 2. 3. Wheat Flour (unpacked) Basmati Rice (Branded & Packed) Surf Excel Quick Wash Detergent ( ) 35.00 5 % 180.00 5 5% 220.00 18 % Find: (a) the value of x if the total GST on wheat flour and basmati rice is 45. (b) the value of y, if CGST paid for detergent powder is 39.60. (c) total amount to be paid (including GST) for the above bill. [Understanding, Analysis & Evaluate] 79. [Commercial Mathematics] Amit deposited 600 per month in a recurring deposit account. The bank pays a simple interest of 12% p.a. Calculate the: (a) number of monthly instalments Amit deposits to get a maturity amount of 11826? (b) total interest paid by the bank. (c) total amount deposited by him. [Application & Evaluate] 80. [Commercial Mathematics] Aman has 500, 100 shares of a company quoted at 120, paying a 10% dividend. When the share price rises to 200 each, he sells all his shares. He invests half of the sale proceeds in 10, 12% shares at 25, and the remaining sale proceeds in 400, 9% shares at 500. Find his: (a) (b) (c) (d) sales proceeds. investment in 10, 12% shares at 25. original income. change in income. ICSE Competency-Focused Practice Questions [Application & Evaluate] 22 Mathematics ICSE - Class X S.No. 81. Questions [Commercial Mathematics] Solve the following inequation. 11 + 3 3 3 > , R 5 2 (a) Write the solution set. (b) Represent the solution on the number line. 82. [Application & Create] [Algebra] Determine whether the following quadratic equation has real roots. 5 2 9 + 4 = 0 (a) Give reasons for your answer. (b) If the equation has real roots, identify them. 83. [Analysis & Application] [Algebra] The profit in rupees in a local restaurant and the number of customers who visited the restaurant are tabulated below for each week for one month. Week number Number of customers Profit in Week 1 1400 28000 Week 2 5600 112000 Week 3 x 32140 Week 4 3212 y Find: (a) if the number of customers and profit per week in continued proportion or not? Justify your answer. (b) the value of x and y. [Analysis & Evaluation] 84. [Algebra] Given, 9 2 4 is a factor of 9 3 2 + 8: (a) find the value of m and n using the remainder and factor theorem. (b) factorise the given polynomial completely. [Understanding & Application] ICSE Competency-Focused Practice Questions 23 Mathematics ICSE - Class X S.No. 85. Questions [Probability] The marks scored by 100 students are given below: Marks scored 0-10 10- 20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 No. of students 4 5 9 7 13 12 15 11 14 10 A student in the class is selected at random. Find the probability that the student has scored: (a) (b) (c) (d) 86. less than 20. below 60 but 30 or more. more than or equal to 70. above 89. [Algebra] Given, matrix A = [ 1 ] and B = [ ] such that AB is a null matrix. Find: 2 2 (a) order of the null matrix. (b) possible values of x and y. 87. [Analysis & Evaluation] [Understanding & Application] [Algebra] The sum of a certain number of terms of the Arithmetic Progression (A.P.) 20, 17, 14, . is 65. Find the: (a) number of terms. (b) last term. 88. [Understanding & Application] [Algebra] (a) Point P (2, -3) on reflection becomes P (2,3). Name the line of reflection (say 1 ). (b) Point P is reflected to P along the line ( 2 ), which is perpendicular to the line 1 and passes through the point, which is invariant along both axes. Write the coordinates of P . (c) Name and write the coordinates of the point of intersection of the lines 1 and 2 . (d) Point P is reflected to P on reflection through the point named in the answer of part I of this question. Write the coordinates of P . Comment on the location of the points P and P . [Analysis & Create] ICSE Competency-Focused Practice Questions 24 Mathematics ICSE - Class X S.No. 89. Questions [Algebra] In the given figure, if the line segment AB is intercepted by the y-axis and x-axis at C and D, respectively, such that AC: AD = 1: 4 and D is the midpoint of CB. Find the coordinates of D, C and B. [Understanding & Application] 90. [Algebra] Find the equation of the straight line perpendicular to the line x+2y=4, which cuts an intercept of 2 units from the positive y-axis. Hence, find the intersection point of the two lines. [Analysis & Application] 91. [Geometry] While preparing a PowerPoint presentation, ABC is enlarged along the side BC to AB C , as shown in the diagram, such that BC B C is 3 5. Find: (a) (b) (c) (d) AB BB length AB, if BB = 4 cm. Is ABC ~ AB C ? Justify your answer. ar ( ABC): ar (quad. BB C C). C C A B B [Understanding & Evaluate] ICSE Competency-Focused Practice Questions 25 Mathematics S.No. 92. ICSE - Class X Questions [Geometry] The approximate volume of a human eye is 6.5 cm3. The volume of a laboratory model (excluding base and stand) of the human eye is 1404 cm3. (a) State whether the scale factor k is less than, equals to or greater than 1. (b) Calculate the: (i) value of k (ii) diameter of the human eye if the radius of the model is 7.2 cm. (iii) the external surface area of the human eye if the surface area of the model is 651.6 cm2. [Analysis & Evaluate] 93. [Geometry] P In the adjoining diagram PQ, PR and ST are the tangents to the circle with centre O and radius 7 cm. Given OP=25 cm. Find: (a) length of ST (b) value of OPQ, i.e. (c) QUR, in nearest degree (use mathematical tables) 25 cm T S Q R 7 cm O U [Application & Evaluate] 94. [Geometry] Use ruler and compass to answer this question Construct a triangle ABC where AB=5.5 cm, BC= 4.5 cm and angle ABC=135o. Construct the circumcircle to the triangle ABC. Measure and write down the length of AC. [Create & Evaluate] ICSE Competency-Focused Practice Questions 26 Mathematics S.No. 95. ICSE - Class X Questions [Mensuration] The curved surface area of a right circular cone is half of another right circular cone. If the ratio of their slant heights is 2:1 and that of their volumes is 3:1, find ratio of their: (a) radii (b) heights 96. [Understanding & Application] [Trigonometry] A cylindrical drum is unloaded from a truck by rolling it down along a wooden plank. The length of the plank is 10 m and it is making an angle of 10o with the horizontal ground. Find the height from which the cylindrical drum was rolled down. Give your answer correct to 3 significant figures. [Analysis & Evaluate] 97. [Statistics] The data given below shows the marks of 12 students in a test, arranged in ascending order: 2, 3, 3, 3,4, x, x+2, 8, p, q,8, 9 If the given value of the median and mode is 6 and 8 respectively, then find the values of x, p, q. [Understanding & Evaluate] 98. [Algebra] Solve the linear inequation, write down the solution set and represent it on the real number line: 5(2 - 4x) > 18 - 16x > 22 - 20x , x R [Application & Create] 99. [Algebra] If a polynomial x3 + 2x2 ax + b leaves a remainder -6 when divided by x +1 and the same polynomial has x 2 as a factor, then find the values of a and b. [Application & Evaluate] ICSE Competency-Focused Practice Questions 27 Mathematics ICSE - Class X S.No. 100. Questions [Algebra] 1 3 1 2 4 If A= [ ], B= [ ], C= [1 4] and D = [ ]. 2 0 0 3 1 (a) Is the product AC possible? Justify your answer. (b) Find the matrix X, such that X = AB+ 2 DC [Analysis & Evaluate] 101. [Geometry] A 2 70 G F E 40 C D 3 B In the given figure(not drawn to scale), BC is parallel to EF, CD is parallel to FG, AE : EB = 2:3, BAD= 70 , ACB = 105 , ADC = 40 and AC is bisector of BAD. (a) Prove AEF ~ AGF (b) Find: i. AG: AD ii. area of ACB: area ACD iii. area of quadrilateral ABCD: area of ACB. [Analysis, Application & Evaluate] ICSE Competency-Focused Practice Questions 28 Mathematics ICSE - Class X S.No. 102. Questions [Geometry] In the given figure angle ABC = 700 and angle ACB = 500. Given, O is the centre of the circle and PT is the tangent to the circle. Then calculate the following angles (a) (b) (c) (d) CBT BAT PBT APT [Application & Evaluate] 103. [Geometry] (Use a ruler and a compass for this question.) (a) (b) (c) (d) (e) Construct a triangle ABC such that BC = 8cm , AC = 10 cm and ABC = 90 . Construct an incircle to this triangle. Mark the centre as I. Measure and write the length of the in-radius. Measure and write the length of the tangents from vertex C to the incircle. Mark points P, Q and R where the incircle touches the sides AB, BC, and AC of the triangle respectively. Write the relationship between RIQ and QCR. [Analysis & Create] 104. [Statistics] The daily wages of workers in a constuction unit were recorded as follows: Class Marks (Wages) 425 275 525 575 625 675 No. of workers 6 12 15 17 7 13 Form a frequency distribution table with class intervals and find modal wage by plotting a histogram. [Analysis & Create] 105. [Probability] A bag contains 13 red cards , 13 black cards and 13 green cards. Each set of cards are numbered 1 to 13. From these cards, a card is drawn at random. What is the probability that the card drawn is a: (a) green card? (b) a card with an even number? (c) a red or black card with a number which is a multiple of three? [Understanding & Evaluate] ICSE Competency-Focused Practice Questions 29 Mathematics ICSE - Class X IV. Long Answer Questions - 1 (Graph-based) (5 Marks) S.No. 106. Questions [Algebra] (For this question, use a graph paper. Scale: 2cm = 1 unit along both x and y-axis.) Plot the points A(2,2), and B (6, -2) in the graph and answer the following: (a) Reflect points A in origin to point D and write the co-ordinates of point D. (b) Reflect points A in line y = - 2 to point C and write the co-ordinates of points C. (c) Find a point P on CD which is invariant under reflection in x = 0, write its coordinates. (d) Write the geometrical name of the closed figure ABCD. (e) Write the co-ordinates of the point of intersection of the diagonals of ABCD. [Understanding & Create] 107. [Algebra] (For this question, use a graph paper. Scale: 1cm = 1unit along both x and y-axis.) Plot points A ( 0,3 ) , B ( 4,0 ) , C ( 6,2 ) and D ( 5,0 ). Reflect the points as given below and write their coordinates: (a) (b) (c) (d) (e) 108. Reflect A on x-axis to A . Reflect B on y- axis to B . Reflect C on x-axis to C . D remain invariant when reflected on the line whose equation is _______. Join the points A, B, C, D,C ,B,A , B and A to form a closed figure. Name the closed figure BCDC . [Understanding & Create] [Statistics] The following data represents the daily wages in rupees of a certain number of employees of a company: Daily wages (in ) No. of Employees 30 40 40 -50 50 60 60 -70 70-80 80-90 90-100 100-110 8 14 12 17 20 26 13 10 Use a graph to answer the following questions: (a) Represent the above distribution by an ogive. (b) Find the following on the graph drawn: (i) median wage. (ii) percentage of employees who earn more than 84 per day. (iii) number of employees who earn 56 and below. [Create & Evaluate] ICSE Competency-Focused Practice Questions 30 Mathematics ICSE - Class X S.No. 109. Questions [Statistics] Study the graph and answer the questions that follow (a) (b) (c) (d) (e) Make a frequency table for the information provided in the graph. The number of students whose height is less than 150 cm. The total number of students. The modal height. The difference in the modal height and the mean height, if the average height of the students is 145.5 cm. [Analysis & Application] ICSE Competency-Focused Practice Questions 31 Mathematics ICSE - Class X V. Long Answer Question - 2 (5 Marks) S.No. 110. Questions [Commercial Mathematics] On seeing the above display board outside Pearl Stationary Shop, Chetan enters the shop to buy the following items: Price Discount Premium Items purchased GST Pen Pencil 5 each 5% on a dozen pens 1 dozen 18% 7 each 10% on 20 pencils 20 pencils 12% Rainbow Cover Notebook 200 each - 50 on each notebook 5 12% The shopkeeper handed over the bill to Chetan saying that he has given further discount of 2% on total bill. Chetan became so happy hearing about the discount that he did not check the bill until he reached home. He later found out that though shopkeeper has given 2% discount as promised, he had also mcharged uniform 18% GST on all the items. (a) Calculate : (i) total selling price of all the items as per the offers displayed on the board. (ii) total amount to be paid by Chetan including GST with correct rates. (iii) actual amount charged by the shopkeeper. (b) Did the shopkeeper overcharge Chetan? Justify your answer. [Application & Evaluate] ICSE Competency-Focused Practice Questions 32 Mathematics ICSE - Class X S.No. 111. Questions [Algebra] Using remainder and factor theorem, show that (2x+3) is a factor of the polynomial 2 2 +11x+12. Hence,factorise it completely. What must be multiplied to the given polynomial so that 2 + 3 4 is a factor of the resulting polynomial?Also,write the resulting polynomial. [Understanding, Application & Evaluate] 112. [Algebra] The sequence 2,9,16, is given. (a) Identify if the given sequence is an AP or a GP. Give reasons to support your answer. (b) Find the 20th term of the sequence. (c) Find the difference between the sum of its first 22 and 25 terms. (d) Is the term 102 belong to this sequence? (e) If k is added to each of the above terms, will the new sequence be in A.P. or G.P.? [Analysis & Evaluate] 113. [Algebra] Given the equations of two straight lines, L1 and L2 are x y = 1 and x + y = 5 respectively . If L1 and L2 intersects at point Q ( 3, 2).Find : (a) the equation of line L3 which is parallel to L1 and has y-intercept 3. (b) the value of k, if the line L3 meets the line L2 at a point P (k,4). (c) the coordinate of R and the ratio PQ: QR, if line L2 meets x-axis at point R. [Analysis & Evaluate] 114. [Geometry] D E C F A G B In the figure given above (not drawn to scale), AD GE BC,DE = 18 cm, EC = 3cm, AD = 35 cm. Find : (a) (b) (c) (d) AF:FC length of EF area(trapezium ADEF ) : area( EFC) BC GF ICSE Competency-Focused Practice Questions [Application & Evaluate] 33 Mathematics S.No. 115. ICSE - Class X Questions [Geometry] (Use a ruler and a compass for this question.) (a) Construct the locus of a moving point which moves such that it keeps a fixed distance of 4.5 cm from a fixed-point O. (b) Draw line segment AB of 6 cm where A and B are two points on the locus (a). (c) Construct the locus of all points equidistant from A and B. Name the points of intersection of the loci (a) and (c) as P and Q respectively. (d) Join PA. Find the locus of all points equidistant from AP and AB. (e) Mark the point of intersection of the locus (a) and (d) as R. Measure and write down the length of AR. [Create & Analysis] 116 [Constructions] (Use a ruler and a compass for this question.) Construct a regular hexagon ABCDEF of side 4.3 cm and construct its circumscribed circle. Also, construct tangents to the circumscribed circle at points B and C which meets each other at point P. Measure and record BPC. [Create & Analysis] 117. [Mensuration] A mathematics teacher uses certain amount of terracotta clay to form different shaped solids. First, she turned it into a sphere of radius 7cm and then she made a right circular cone with base radius 14 cm. Find the height of the cone so formed. If the same clay is turned to make a right circular cylinder of height 7/3 cm, then find the radius of the cylinder so formed. Also,compare the total surface areas of sphere and cylinder so formed. [Understanding, Application & Evaluate] ICSE Competency-Focused Practice Questions 34 Mathematics S.No. 118. ICSE - Class X Questions [Trigonometry] A tree (TS) of height 30 m stands in front of a tall building (AB). Two friends Rohit and Neha are standing at R and N respectively, along the same straight line joining the tree and the building (as shown in the diagram). Rohit, standing at a distance of 150 m from the foot of the building, observes the angle of elevation of the top of the building as 30o. Neha from her position observes that the top of the building and the tree has the same elevation of 60o. Find the: (a) height of the building (b) distance between (i) Neha and the foot of the building (ii) Rohit and Neha (iii) Neha and the tree (iv) building and the tree. ICSE Competency-Focused Practice Questions [Analysis, Application & Evaluate] 35 Mathematics ICSE - Class X S.No. 119. Questions [Statistics] A life insurance agent found the following data of age distribution of 100 policy holders, where f is an unknown frequency. Age in years 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 No. of Policy Holders 7 12 15 22 14 8 4 (a) If the mean age of the policy holders is 35.65 years, find the unknown frequency f. (b) Find the median class of the distribution. [Application & Evaluate] ICSE Competency-Focused Practice Questions 36 Mathematics ICSE - Class X Answer Key S.No Expected Answer 1. (c) 30 2. (b) 28 3. (d) simple interest for one month. 4. (b) 1250 5. (d) Both Mr. Das and Mr. Singh have same rate of return of 20%. 6. (b) 750 7. (c) { 0,1,2} 8. (c) x < - 2y 9. (d) 0 , 8 10. (b) 2 11. (d) 230 12. (c) 13 cm 13. (d) p : r = 2 : 2 14. (b) 60 15. (d) 3 16. (c) (x+4) 17. (d) both matrices AB and BA are possible, AB=BA. 18. (b) -6 19. (b) 4 20. (d) 2, 0, 4, 0, 8, 0 21. (c) (6, -6) 22. (b) 2y = x ICSE Competency-Focused Practice Questions 37 Mathematics S.No ICSE - Class X Expected Answer 23. (c) 1, -1 24. (a) 3x + 3y = 6 25. (d) 20 minutes 26. (d) the similarity of given triangles cannot be determined. 27. (c) = 28. (d) 1.44m 29. (c) 50 30. (a) 500 , 1000 , 400 31. (d) 105 32. (c) Its volume 33. (b) 42cm 34. (b) 32 35. (b) 3 : 2 36. (c) ( + )2 37. (d) 5 38. (a) 30 39. (b) < 40. (c) A is true, but R is false. 41. (c) A is true, but R is false. 42. (a) Both A and R are true, and R is the correct explanation. 43. (d) Both A and R are true. 44. (c) A is true, but R is false. 45. (a) 2:3 46. (b) 2 x 1 47. (d) Arithmetic (d=0) ICSE Competency-Focused Practice Questions 38 Mathematics ICSE - Class X S.No Expected Answer 48. (a) Circle 49. (b) incentre 50. 11.11% 51. 4% 52. 70 53. -1 x 5 (a) 5, -1 (b) No change in maximum value, minimum value will change to 0. 54. = 2 3 , = 3 4 55. x = 20 and GST rate = 20% 56. 3 and 12 57. (x+2) (x-1) (2x+1) 58. [ 59. (a) Tn = 21+ (n-1)21 or 21n 0 0 ] 0 0 (b) Four are two-digit numbers. 21, 42,63,84 (c) 1155 60. (a) G.P. (b) p=121 61. (a) (- 4, -5), (0, -3), (-3, 0) (b) For x-axis C (3,0); for y-axis B (0,3) 62. 4:3 63. (a) m=1 (b) x+y+4=0 64. 1:5 ICSE Competency-Focused Practice Questions 39 Mathematics ICSE - Class X S.No 65. Expected Answer (a) In ABD and CBA, B is common to both triangles, BAD = BCA (given) ABD ~ CBA (by A.A.A. postulate) (b) Since the triangles are similar, their corresponding sides are proportional. = = 8 4+ 4 8 = = 2x8=4+x 16 = 4 + x x = 16 - 4 66. x = 12cm (a) 3.8 km (b) 1 2 67. 68. 27 cm 69. (a) 60 (b) 120 (c) 30 ICSE Competency-Focused Practice Questions 40 Mathematics ICSE - Class X S.No 70. Expected Answer (a) 57 (b) 50 (c) 17 71. 200.96 cm3 72. (a) 24 cm (b) 18 cm 73. (a) 30 (b) 8 m 74. L.H.S. = 2 + 2 1 = 2 (1 2 ) = = = 2 2 2 2 (1 2 ) 2 2 2 x 2 = 2 . 2 = . . 75. (a) Class interval 12-14 14-16 16-18 18-20 20-22 22-24 frequency 8 2 3 4 5 6 (b) Mean = 18 76. m= 6; n= 6 77. (a) 6 (b) 30 78. (a) 0% (b) y = 2 kg (c) 1639.20 ICSE Competency-Focused Practice Questions 41 Mathematics ICSE - Class X S.No 79. Expected Answer (a) 18 instalments (b) 1026 (c) 10800 80. (a) 100000 (b) 50000 (c) 5000 (d) 4600 (gain) 81. 82. {x: 1 9 x < , x R} 2 2 (a) Discriminant is positive and a perfect square. Hence, roots are real and rational. (b) 1 and 4/5 83. (a) No. 1400 = 5600 = 1 28000 112000 20 Hence the numbers are in proportion. Number of customers and profit per week are not continued in proportion. (b) x = 1607, y = 64240 84. (a) m = 18, n = 4 (b) (3x - 2) (3x + 2) (x - 2) 85. (a) 9/100 (b) 32/100 = 8/25 (c) 35/100 = 7/20 (d) 10/100 = 1/10 86. (a) Order of the null matrix is 2 x 1. (b) x = 1, y = 2 and x = -2, y = -4 87. (a) 10 (b) -7 88. (a) x-axis. (b) P'' (-2, 3) (c) Origin (0,0); P'''(-2,3) (d) P'' & P'' are coincident points. ICSE Competency-Focused Practice Questions 42 Mathematics ICSE - Class X S.No 89. Expected Answer D (6,0), C (0,9/2) B (12, - 9/2) 90. 2x y + 2 = 0 (0, 2) : =3:2 = 6 , 9: 16 91. (a) (b) (c) (d) 92. (a) k>1 (b) (i) k=6 (ii) 2.4 cm (iii) 18.1cm2 93. (a) 10.5 cm (b) =16 16' (c) 73 44' = 74 94. AC = 9.1 cm Radius = 6.5 cm 95. (a) 1:4 (b) 48:1 96. 1.74 m 97. x = 5 and p = 8, q = 8 98. {x : x<-2 or x >1, x R} 99. a = 3, b = -10 100. No, number of columns in A is not equal to number of rows in C. b) [ 4 1 19 ] 9 ICSE Competency-Focused Practice Questions 43 Mathematics ICSE - Class X S.No 101. Expected Answer (a) In AFE, AFE = 105 (corresponding angle) 70 EAF = 2 = 35 ( AC is the bisector) AEF = 180 -(105 - 35 ) = 40 (sum of angles of triangle) AGF = ADC = 40 (corresponding angles) In AEF, and AGF, EAF = GAF = 35 (AC being the bisector) AEF = ACF = 40 (as shown above) AEF ~ AGF (A.A.A.) (b) i. 2:5 ii. 1:1 iii. 2:1 102. (a) 900 (b) 300 (c) 200 (d) 100 103. (b) 2cm (c) 5.8cm (d) RIQ + QCR=180 104. Frequency table Wages in f 400-450 6 450-500 12 500-550 15 550-600 17 600-650 7 650-700 3 Mode = 557.50 105. (a) 1/3, (b) 6/13 (c) 8/39 ICSE Competency-Focused Practice Questions 44 Mathematics ICSE - Class X S.No 106. Expected Answer (a) D (-2, -2) (b) C (2, -6) (c) P (0, -4) (d) square (e) (2, -2) 107. (a) (0, -3) (b) (-4,0) (c) (6, -2) (d) Y = 0 (e) Concave quadrilateral 108. (b) i) 74 ii) 32.5% iii) 30 109. (a) Class 120-130 130-140 140-150 150-160 160-170 f 6 29 34 22 12 cf 6 35 69 91 103 (b) 69 (c) 103 (d) 143 cm (e) 2.5 cm 110. (a) (i) 1433 (ii) 1608.38 (iii) 1657.12 b) Yes, the shopkeeper overcharged an amount of 48.78 111. (x + 4) (2x + 3) to multiplied by (x - 1) 2x 3 + 9x 2 + x - 12 ICSE Competency-Focused Practice Questions 45 Mathematics S.No 112. ICSE - Class X Expected Answer (a) AP as d = 7 (b) 135 (c) 489 (d) No (e) A.P. 113. (a) x y + 3 = 0 (b) k = 1 (c) R (5,0); 1:1 114. (a) 6:1 (b) 5 cm (c) 48:1 (d) 7:6 115. (e) AR 8.8cm or 4.8cm 116. BPC=120 117. hcone=7 cm rcylinder =14 cm TSA sphere 3 = TSA cylinder 7 118. (a) 86.6 m (b) i. 50 m ii. 100 m iii. 17.32 m iv. 32.68 m. 119. (a) 18 (b) 30-35 ICSE Competency-Focused Practice Questions 46 Mathematics ICSE Competency-Focused Practice Questions ICSE - Class X 47

Formatting page ...

Related ResPapers
ICSE Class X Board Exam 2024 : Mathematics
by sanvigowda01

ICSE Class X Board Exam 2020 : Mathematics
by srijanchowdhury22

ICSE Class X Board Exam 2023 : Mathematics
by theakshatgypta

ICSE Class X Board Specimen 2024 : Mathematics
by dkp2023

Formatting page ...

maitybiswajit884 chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: