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ICSE Class X Sample / Model Paper 2026 : Mathematics

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Siddhartha debnath
Summit, Kolkata

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ICSE CLASS 10 MATHEMATICS Class Test Time: 1 hour 30 minutes Maximum Marks: 40 Answer all questions. All working, including that needed to justify your answer, must be shown. Mathematical tables and graph paper may be used where necessary. Question 1 [2] Find the slope of the line joining the points P(2, 3) and Q(4, 7). Question 2 [2] Find the equation of the line whose slope is 2 and whose y-intercept is 3. Question 3 [3] Find the equation of the line passing through the points A(1, 2) and B(3, 8). Question 4 [4] A line is given by the equation 2x 3y + 6 = 0. Find its slope and the coordinates of the point where it cuts the y-axis. Hence find the equation of the line parallel to this line and passing through the point (3, 1). Question 5 [4] Find the equation of the line perpendicular to 2x 3y + 6 = 0 and passing through the point (3, 1). Question 6 [4] Find the value of k, given that the line joining the points (k, 3) and (2, 7) is parallel to the line joining the points ( 1, 4) and (0, 6). Hence find the equation of the line joining (k, 3) and (2, 7). Question 7 [3] The following table gives the marks obtained by 20 students in a test: Marks Number of students 10 20 5 20 30 8 30 40 7 Using the direct method, find the mean marks of the students. Question 8 [5] The following table gives the marks obtained by 50 students in a test: Marks Number of students 0 10 5 10 20 8 20 30 12 30 40 15 40 50 7 50 60 3 Using the step-deviation method, calculate the mean marks of the students. (Take the assumed mean as 25.) Question 9 [5] The following table shows the distribution of ages (in years) of 40 members of a club: Age (years) Number of members 10 20 4 20 30 6 30 40 10 40 50 12 50 60 8 Find the median age of the members. Question 10 [3] The following table shows the distribution of ages (in years) of 40 members of a club: Age (years) Number of members 10 20 4 20 30 6 30 40 10 40 50 12 50 60 8 Find the modal age of the members, correct to two decimal places. Question 11 [5] The marks obtained by 100 students in an examination are given below: Marks 0 10 10 20 20 30 30 40 40 50 50 60 60 70 Number of students 2 5 8 10 25 25 15 70 80 10 Draw the ogive for the above distribution, taking marks along the x-axis and cumulative frequency along the y-axis (use a scale of 2 cm = 10 marks and 2 cm = 10 students). Use your ogive to estimate the median mark and the number of students who scored more than 60 marks.

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