Subject

Mathematics

Class

ICSE Class 10

Pre Boards

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Sample Papers

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ICSE Class 10 Mathematics Solved Question Paper 2018

Long Answer Type

31.
The 4^th term of an A.P. is 22 and 15^th term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms.

Let 'a' be the first term and 'd' be the common difference of given A.P.

Now,

4^th term = 22

$\Rightarrow$ a + 3 d = 22 ............( i )

15^th term = 66

$\Rightarrow$ a + 14 d = 66 ............( ii )

Subtracting ( i ) from ( ii ), we have

11 d = 44

$\Rightarrow$ d = 4

Substituting the value of 'd' in ( i ), we get

a = 22 - 3 x 4

= 22 - 12

= 10

$\Rightarrow$ First term = 10.

Now,

$Sum of n terms = \frac{n}{2} [2 a + (n - 1) d]$

$Sum of 8 terms = \frac{8}{2} [2 \times 10 + (8 - 1) \times 4] = \frac{8}{2} [2 \times 10 + 7 \times 4] = 4 [20 + 28] = 4 \times 48 = 192$

32.

Use Graph paper for this question. A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:

Height in cm	135 - 140	140 - 145	145 - 150	150 - 155	155 - 160	160 - 165	165 - 170
No. of boys	4	8	20	14	7	6	1

Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other
axis draw an ogive of the above distribution. Use the graph to estimate the following:

(i) the median

(ii) lower Quartile

(iii) if above 158 cm is considered as the tall boys of the class. Find the number of
boys in the class who are tall.