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ICSE Class 10 Mathematics Solved Question Paper 2012

Short Answer Type

31.
The line through P(5, 3) intersects y-axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q.

(i) Since the line make 45 $°$ with positive direction of x-axis,

Therefore slope (m) = tan 45° = 1

(ii) Equation of line, using point-slope is

y - y₁ = m(x - x₁)

$\Rightarrow y - 3 = 1 (x - 5)$

$\Rightarrow y - 3 = x - 5$

Thus, y = x - 2

(iii) Since Q is a point on y-axis, its x-coordinate is zero.

Putting x = 0 in the equation of line, we get

y = –2

Hence the point Q is (0, –2).

Long Answer Type

32.

The following distribution represents the height of 160 students of school.

Height (in cm) No. of Students

140 – 145 12

145 – 150 20

150 – 155 30

155 – 160 38

160 – 165 24

165 – 170 16

170 – 175 12

175 – 180 8

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

(i) The median height.

(ii) The interquartile range.

(iii) The number of students whose height is above 172 cm.