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

ICSE Board Exam 2003 : Mathematics

7 pages, 43 questions, 42 questions with responses, 102 total responses,

ICSE
Indian Certificate of Secondary Education (ICSE), New Delhi

+Fave Message

Profile Timeline Uploads Q & A

Home > icse > F Also featured on: mehdi_momin

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

MATHEMATICS (Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the 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 and any four questions from Section B. All working, i ncluding rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. S ECTION A (40 Marks) Attempt all questions from this Section. Question 1 (a) The price of a washing machine, inclusive of sales tax is Rs. 13,530/-. If the sales tax is 10%, find its basic price. [3] (b) What sum of money will amount to Rs. 3,630/- in two years at 10% per annum compound interest? [3] (c) Solve using the quadratic formula x2 4x + 1 = 0. (Type in the answers separated by commas. Copy and paste the (square root) symbol from the question. Leave no spaces in your answer.) [3] Question 2 (a) If 3a + 4b 3c + 4d = 3a 4b 3c 4d , prove that a b = c d [3] (b) Find the value of a, if (x a) is a factor of x3 a2x + x + 2. [3] Question 3 [6] Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axes). Plot the points P (3, 2) and Q ( 3, 2) from P and Q, draw perpendiculars PM and QN on the x-axis. (a) Name the image of P on reflection in the origin. (b) Assign the special name to the geometrical figure PM QN and find its area. (c) Write the co-ordinates of the point to which M is mapped on reflection in (i) x-axis. (c) Write the co-ordinates of the point to which M is mapped on reflection in (ii) y-axis. (c) Write the co-ordinates of the point to which M is mapped on reflection in (iii) origin. Question 4 (a) Find the value of cos 75 sin 15 + sin 12 cos 78 cos 18 [3] sin 72 (b) Solve 2 2x 3 5, x R and mark it on a number line. [3] Question 5 Given the following details, calculate the simple interest at the rate of 6% per annum up to June 30:- Date Debit Rs. Credit Rs. Balance Rs. Jan 1 -- 24000.00 24000.00 Jan 20 5000.00 Jan 29 -- 10000.00 29000.00 M arch 15 -- 8000.00 37000.00 -- 19000.00 [5] April 3 -- M ay 6 3040.00 M ay 8 -- 7653.00 44653.00 -- 41613.00 5087.00 46700.00 Question 6 [5] If sin x = 3 / 5 and cos y = 12 / 13; evaluate (a) secant 2x (b) tan x + t an y. (Type in the answers separated by commas. Leave no spaces in your answer.) Question 7 PS is a diameter of a circle of radius 6 cm. Q and R are points on the diameter such that PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the figure. Find the perimeter of the shaded region. ( = 3.14) [3] S ECTION B (40 Marks) Attempt any four questions from this Section. Question 8 (a) The work done by (x 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio of 3 : 10. Find the value of x. [3] (b) If f (x) = 2x 5 / 4x + 1, find:(i) f (3) [1] (b) If f (x) = 2x 5 / 4x + 1, find:- [1] (ii) f (x2) (b) If f (x) = 2x 5 / 4x + 1, find:- [1] (iii) f (2x + 1) (c) Find the mean of the following frequency distribution:- [4] Class Interval Frequency 0 - 50 4 50 - 100 8 100 - 150 16 150 - 200 13 200 - 250 6 250 - 300 3 Question 9 [10] (a) A man invests Rs. 20,020/- in buying shares of nominal value Rs. 26/- at 10% premium. The dividend on the shares is 15% per annum. Calculate:(i) The number of shares he buys. (a)(ii) The dividend he receives annually. (a)(iii) The rate of interest he gets on his money. (Type in the answers separated by commas. Leave no spaces around the commas.) (b) Prove that Question 10 cos A 1 tan A + sin A 1 cot A = cos A + sin A [10] (a) A straight line passes through the points P ( 1, 4) and Q (5, 2). It intersects the co-ordinate axes at points A and B. M is the mid point of the segment AB. Find:(i) The equation of the line. (a) (ii) The co-ordinates of A and B. (a) (iii) The co-ordinates of M . (Type in the answers separated by commas. Leave no spaces in your answer.) (b) In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find:(i) The number of rows in the original arrangement. (b) (ii) The number of seats in the auditorium after re-arrangement. (Type in the answers separated by commas. Leave no spaces around the commas.) Question 11 [5] (a) Draw a histogram and hence estimate the mode for the following frequency distribution:Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 2 8 10 5 4 3 (b) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 . When he moves 50 m away from the bank. He finds the angle of elevation to be 30 . Calculate:(i) the width of the river and (b) (ii) the height of the tree. (Type in the answers separated by commas. Leave no spaces around the commas.) Question 12 (a) Find x and y if:- [4] [ 3 2 ] [ 2x ] + 2 [ 4 ] = 4 [ 2 ] 1 4 1 5 y (Type in the answers separated by commas. Leave no spaces around the commas.) (b) A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top which is open, is 2.5 cm. It is filled with water upto the rim. When lead shots, each of which is a sphere of radius 0.25 cm are dropped into the vessel, 2 / 5 of the water flows out. Find the number of lead shots dropped into the vessel. [4] (c) In the given circle with diameter AB, find the value of x. [2] Q uestion 13 (a) Construct an angle PQR = 45 . M ark a point S on QR such that QS = 4.5 cm. Construct a circle to touch PQ at Q and also to pass through S. [4] (b) Find the value of k for which the lines k x 5y + 4 = 0 and 4x 2y + 5 = 0 are perpendicular to each other. (Leave no spaces in your answer.) [4] (c) If (a, b) R, name the kind of relation between a and b if a R b => b R a. Does also show a relation of this kind? Explain. [2] Question 14 [10] (a) The annual income of M rs. Sharma (excluding HRA) is Rs. 1,68,000. She contributes Rs. 4,500 per month to her P.F. account and pays an annual insurance premium of Rs. 8,000. Calculate the income tax including surcharge M rs. Sharma has to pay in the last month of the year if her earlier deductions as income tax for the first 11 months were at the rate of Rs. 600 per month. Assume the following for calculating income tax. Standard deduction : 1/3rd of the total income subject to a maximum of Rs. 20,000 Tax slab:Upto Rs. 50,000 : No tax. Rs. 50,001 to Rs. 60,000 : 10% of the income exceeding Rs. 50,000. Rs. 60,001 to Rs. 1,50,000 : Rs. 1,000 + 20% of the income exceeding Rs. 60,000. Above Rs. 1,50,000 : Rs. 19,000 + 30% of the income exceeding Rs. 1,50,000. Tax Rebate : Surcharge : 10% of the total tax payable after rebate. 20% of the total savings subject to a maximum of Rs 12,000. (b) In a triangle PQR, L and M are two points on the base QR, such that LPQ = QRP and RPM = RQP. Prove that:(i) PQL RPM (b) In a triangle PQR, L and M are two points on the base QR, such that LPQ = QRP and RPM = RQP. Prove that:(ii) QL RM = PL PM (b) In a triangle PQR, L and M are two points on the base QR, such that LPQ = QRP and RPM = RQP. Prove that:(iii) PQ 2 = QR QL

Formatting page ...

Top Contributors
to this ResPaper
(answers/comments)

Lucky
(17)

Lol Its Me
(12)

hikaru_vishal
(12)

Nivi
(8)

Formatting page ...

Additional Info : Solved ICSE Board exam paper study guide - ICSE 2003 : MATHEMATICS - I.C.S.E. Free Online Question Paper
Tags : mathematics, math, maths, commercial arithmetic, algebra, geometry, trigonometry, coordinate geometry, mensuration, statistics, 2003, icse, i.c.s.e., indian certificate of secondary education, cisce, council for the indian school certificate examinations, solved icse board exam papers, free sample question papers, online model answers, students, teachers, icse schools, india, icse examination results, icse free download, icse papers, pdf download 2020 2021 2022 2023, 2024 icse sample papers, icse books, portal for icse india, icse question bank, indian certificate of secondary education, icse question papers with answers, icse model test papers, solved past board question papers of icse last year, previous years solved question papers, free online icse solved question paper, icse syllabus, india icse board sample questions papers, last 10 years icse papers, icse question papers 2022 - 2023, icse guess sample questions papers, icse important questions, class 10 specimen / guess / mock papers, icse pre board question papers, icse 2022 - 2023 pre-board examination

icse chat

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