Using properties of proportion solve for x , given 5 x + 2 x - 6 5 x - 2 x - 6 = 4 .

Given that we have to solve for x , 5 x + 2 x - 6 5 x - 2 x - 6 = 4 . Applying componendo and dividendo rule, that states it is proved that if the ratio of a t o b is equal to the ratio of c t o d , then the ratio of a + b t o a − b is equal to the ratio of c + d t o c − d . 5 x + 2 x - 6 + 5 x - 2 x - 6 5 x + 2 x - 6 - 5 x - 2 x - 6 = 4 + 1 4 - 1 ⇒ 2 5 x 2 2 x - 6 = 5 3 ⇒ 3 5 x = 5 2 x - 6 Squaring on both sides. ⇒ 9 ( 5 x ) = 25 ( 2 x - 6 ) ⇒ 45 x = 50 x - 150 ⇒ 50 x - 45 x = 150 ⇒ 5 x = 150 ⇒ x = 30 Hence, x = 30

Use graph paper for this question. The marks obtained by 120 students in an English test are given below. Marks No. of students 0 - 10 5 10 - 20 9 20 - 30 16 30 - 40 22 40 - 50 26 50 - 60 18 60 - 70 11 70 - 80 6 80 - 90 4 90 - 100 3 Draw the ogive and hence, estimate the median marks.

Given, data of the student and there marks. The cumulative frequency table for the given continuous distribution is given below. Marks No. of students Commutative frequency 0 - 10 5 5 10 - 20 9 14 20 - 30 16 30 30 - 40 22 52 40 - 50 26 78 50 - 60 18 96 60 - 70 11 107 70 - 80 6 113 80 - 90 4 117 90 - 100 3 120 Total 120 With this data, we plot the graph as follows: Here, n = 120 ⇒ n 2 = 120 2 = 60 Taking point 60 on Y - a x i s , draw a horizontal line parallel to X - a x i s , which intersect the curve at point P . Now, draw a line parallel to Y - a x i s from point P , which meets the X - a x i s at M . The distance of point M from O is 43 , which is the required median marks. Hence, from the plot, the required median is 43 .

Use graph paper for this question. The marks obtained by 120 students in an English test are given below. Marks No. of students 0 - 10 5 10 - 20 9 20 - 30 16 30 - 40 22 40 - 50 26 50 - 60 18 60 - 70 11 70 - 80 6 80 - 90 4 90 - 100 3 Draw the ogive and hence, estimate the number of student who did not pass the test if the pass percentage was 50 .

Given, data of the student and there marks. The cumulative frequency table for the given continuous distribution is given below. Marks No. of students Commutative frequency 0 - 10 5 5 10 - 20 9 14 20 - 30 16 30 30 - 40 22 52 40 - 50 26 78 50 - 60 18 96 60 - 70 11 107 70 - 80 6 113 80 - 90 4 117 90 - 100 3 120 Total 120 With this data, we plot the graph as follows: From the cumulative frequency table the students having marks < 50 is 78 . Hence, 78 students didn't pass the test.

Use graph paper for this question. The marks obtained by 120 students in an english test are given below. Marks No. of students Commutative frequency 0 - 10 5 5 10 - 20 9 14 20 - 30 16 30 30 - 40 22 52 40 - 50 26 78 50 - 60 18 96 60 - 70 11 107 70 - 80 6 113 80 - 90 4 117 90 - 100 3 120 Total 120 Draw the ogive and hence, estimate the upper quartile marks.

Given, data of the student and there marks. The cumulative frequency table for the given continuous distribution is given below. Marks No. of students Commutative frequency 0 - 10 5 5 10 - 20 9 14 20 - 30 16 30 30 - 40 22 52 40 - 50 26 78 50 - 60 18 96 60 - 70 11 107 70 - 80 6 113 80 - 90 4 117 90 - 100 3 120 Total 120 With this data, we plot the graph as follows Here, n = 120 , For upper quartile 3 4 n = 3 4 × 120 = 90 Taking point 90 on Y - axis, draw a horizontal line parallel to X - axis, which meets the curve at point L . Further draw a line at point L parallel to Y - axis, which meets the X - axis at point M . Since, the distance from origin to the point M is 57 , Hence, 57 is the required upper quartile marks.

HARD

10th ICSE

IMPORTANT

Earn 100

Using a ruler and a compass only construct a semi-circle with diameter $BC = 7 cm$ . Locate a point $A$ on the circumference of the semi-circle such that $A$ is equidistant from $B$ and $C$ . Complete the cyclic quadrilateral $A B C D$ , such that $D$ is equidistant from $A B$ and $B C$ . Measure $∠ A D C$ and write it down.

Important Questions on Sample Question Paper

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 9

The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method.
Take assumed mean as $45$ . Give your answer correct to $2$ decimal places.

Number of Patients	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of Days	$5$	$2$	$7$	$9$	$2$	$5$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 9

Using properties of proportion solve for

x

, given

\frac{\sqrt{5 x} + \sqrt{2 x - 6}}{\sqrt{5 x} - \sqrt{2 x - 6}} = 4

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 9

Sachin invests

₹ 8500 in 10 %

₹ 100

shares at

₹ 170

. He sells the shares when the price of each share rises by

₹ 30

. He invests the proceeds in

12 % ₹ 100

shares at

₹ 125

. If the sales proceeds is

₹ k

, then find the value of

k

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 9

Sachin invests

₹ 8500 in 10 %

₹ 100

shares at

₹ 170

. He sells the shares when the price of each share rises by

₹ 30

. He invests the proceeds in

12 % ₹ 100

shares at

₹ 125

. Find the number of

₹ 125

shares he buys.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 9

Sachin invests

₹ 8500 in 10 %

₹ 100

shares at

₹ 170

. He sells the shares when the price of each share rises by

₹ 30

. He invests the proceeds in

12 % ₹ 100

shares at

₹ 125

. If the change in annual income is

₹ k

, find the value of

k

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 10

Use graph paper for this question. The marks obtained by $120$ students in an English test are given below.

Marks	No. of students
$0 - 10$	$5$
$10 - 20$	$9$
$20 - 30$	$16$
$30 - 40$	$22$
$40 - 50$	$26$
$50 - 60$	$18$
$60 - 70$	$11$
$70 - 80$	$6$
$80 - 90$	$4$
$90 - 100$	$3$

Draw the ogive and hence, estimate the median marks.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 10

Use graph paper for this question.
The marks obtained by $120$ students in an English test are given below.

Marks	No. of students
$0 - 10$	$5$
$10 - 20$	$9$
$20 - 30$	$16$
$30 - 40$	$22$
$40 - 50$	$26$
$50 - 60$	$18$
$60 - 70$	$11$
$70 - 80$	$6$
$80 - 90$	$4$
$90 - 100$	$3$

Draw the ogive and hence, estimate the number of student who did not pass the test if the pass percentage was $50$ .

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 10

Use graph paper for this question.
The marks obtained by $120$ students in an english test are given below.

Marks	No. of students	Commutative frequency
$0 - 10$	$5$	$5$
$10 - 20$	$9$	$14$
$20 - 30$	$16$	$30$
$30 - 40$	$22$	$52$
$40 - 50$	$26$	$78$
$50 - 60$	$18$	$96$
$60 - 70$	$11$	$107$
$70 - 80$	$6$	$113$
$80 - 90$	$4$	$117$
$90 - 100$	$3$	$120$
Total	$120$

Draw the ogive and hence, estimate the upper quartile marks.

Using a ruler and a compass only construct a semi-circle with diameter BC=7 cm. Locate a point A on the circumference of the semi-circle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.

Important Questions on Sample Question Paper

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