Orgnisation : Council For Indian School Certificate Examinations
Exam :ICSE (Class X) Mathematics
Document type : Question Paper
Website : cisce.org
Download Sample/Model Question Papers :https://www.pdfquestion.in/uploads/cisce.org/5883-Mathematics.pdf
CISCE Mathematics Question Paper
(Two hours and a half)
Answers to this Paper must be written on the paper provided separately.
SECTION A (40 Marks)
Related : Council For Indian School Certificate Examinations ICSE/ ISC Physics Question Paper : www.pdfquestion.in/5886.html
Attempt all questions from this Section
Question 1 :
Section – A
(a) Find the value of a and b if x 1 and x 2 are factors of 3 x ax b . [3]
(b) In the figure given below, ABCD is a parallelogram. E is a point on AB. CE intersects the diagonal BD at G and EF is parallel to BC. If AE : EB = 1 : 2 find
(i) EF : AD
(ii) area of triangle BEF : area of triangle ABD [3]
(c) On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs 16. Find the sum lent out, if the rate of interest in both cases is 8 % . [4]
Question 2 :
(a) Plot the points A(9,6) and B(5,9) on the graph paper. These two points are the vertices of a figure ABCD which is symmetrical about x = 5 and y = 6. Complete the figure on the graph. Write down the geometrical name of the figure. [3]
(b) In the diagram given below EDC. The tangent drawn to the circle at C makes an angle of 500 with AB produced. Find the measure of ACB. [3]
(c) PQRS is a square piece of land of side 56 m. Two semicircular grass covered lawns are made on two of its opposite sides as shown in the figure. Calculate the area of the uncovered portion. [4]
Question 3 :
(b) A point P(a, b) is reflected in the Y-axis to P1 (-3, 1) Write down the values of a and b. P11 is the image of P when reflected in the X axis. Write down the coordinates of P11. P111 is the image of P when reflected in the line X = 5. Write down the coordinates of P111. [3]
(c) Given : A {x : 3 2x 1 9, x R} , B {x :11 3x 2 23, x R} where R is the set of real numbers.
(i) Represent A and B on number lines
(ii) On the number line also markA B. [4]
Question 4 :
(a) Without using a trigonometric table calculate
(b) Mr. Jacob has a two years recurring deposit account in State Bank of India and deposits Rs.1500 per month. If he receives Rs.37,875 at the time of maturity, find the rate of interest. [3]
(c) Calculate the arithmetic mean, correct to one decimal place, for the following frequency distribution of marks obtained in a Geometry test.
Marks 0-10 10-20 20-30 30-40 40-50
No of students 7 13 15 12 3
Section – B
40 Marks
Attempt any four questions from this Section
Question 5
(b) In the diagram given below if AF = 21 cm, CE = 30 cm and FB = 7 cm. Find the volume of the figure. [3]
(c) A man bought 200 shares each of face value Rs.10 at Rs. 12 per share. At the end of the year, the company from which he bought the shares declares a dividend of 15%.
Calculate :
(i) the amount of money invested by the man
(ii) the amount of dividend he received
(iii) the percentage return on his outlay. [4]
Question 6 :
(a) Solve the following quadratic equation for x and give your answer correct to three significant figures:
(b) An integer is chosen at random from 1 to 50. Find the probability that the number is:
(i) divisible by 5
(ii) a perfect cube
(iii) a prime number. [3]
(c) Find x from the following equation using properties of proportion:
Question 7 :
(a) Bosco wishes to start a 200 m2 rectangular vegetable garden. Since he has only 50 m barbed wire, he fences three sides of the rectangular garden letting his house compound wall act as the fourth side of the fence. Find the dimensions of the garden. [3]
(b) Construct a triangle ABC, with AB = 6 cm, BC = 7 cm and ABC = 60 . Locate by construction the point P such that
(i) P is equidistant from B and C.
(ii) P is equidistant from AB and BC
(iii) Measure and record the length of PA. [3]