INTERNATIONAL INDIAN SCHOOL, RIYADH

CLASS: X SUBJECT: MATHEMATICS

SURFACE AREAS AND VOLUMES. 1. A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the total surface area of the remaining block (2992.5 cm2 ) 2. A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21cm & 40cm & the height of the cone is 15cm, then find the total surface area of the toy (l = 25cm, total area = 4207.6cm2) 3. The total surface area of a solid cylinder 231 cm2. If the curved surface area of this solid cylinder is two – third of its total surface area , find its radius and height ( r = 3.5 cm, h = 7 cm) 4. A solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder in cubic meters (1.98 m3) 5. A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the Cylinder. The Conical hole has a radius of 3/2 cm and its depth is 8/9 cm. Calculate the ratio of the Volume of metal left in the cylinder to the volume of metal taken out in conical shape (133: 2) 6. A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm3 and its diameter is 7 cm, then find the height of the toy (11cm) 7. A rectangular sheet of paper 40cm x 22cm is rolled to form a hollow cylinder of height 40cm. Find the radius of the cylinder (r = 3.5cm) 8. A well of diameter 4m is dug 14m deep. The earth taken out is spread evenly all around the well to form 40 cm high embankment. Find the width of the embankment (10m) 9 The rain water from a 22m x 20m roof drains into a cylindrical vessel of diameter 2m and height 3.5m. If the rain water collected from the roof fills 4/5th of the cylindrical vessel, then find the rainfall in cm (h = 2cm) 10. A hollow sphere of internal & external diameters 4 cm and 8 cm is melted to form a cone of base diameter 8 cm. Find the height and the slant height of the cone (h = 14 cm, l = 2√53cm) 11. A cone of height 24cm and radius of base 6cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere 12. The dimensions of a cuboid are 4.4m x 2.6m x 1.0m. It is melted and re casted into a hollow cylindrica l pipe of 30cm inner radius and thickness 5cm. Find the length of the pipe. (112m) 13. A solid cylinder of diameter 12 cm and height 15cm is melted and re-casted into 12 toys in the shape of a right circular cone mounted on the hemisphere. Find the radius of the hemisphere and the total height of the toy if height of the cone is 3 times the radius (12cm) 14. Water flowing at the rate of 15km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50m long and 44m wide. In which time will the level of water in the pond rise by 21 cm (2hrs) 15. A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in his field , which is 10m in Diameter and 2.m deep. If water flows through the pipe at the rate of 3km/hr, in how much time will the tank be filled. (100min) 16. Water is flowing at 7m/sec through a circular pipe of internal diameter of 4cm into a cylindrical tank, the Radius of whose base is 40cm. Find the increase in water level in 30 minutes (h = 31.5m) 17. A metal container, open from the top, is in the shape of a frustum of a cone of height 21cm with radii of its lower & Upper circular ends as 8 cm & 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of ₨ 35/litre ( ₨ 480. 50) 18. The radii of the circular ends of a bucket in the form of a frustum of a cone of height 15 cm are 14 cm and r cm ( r < 14) . If the capacity of the bucket is 5390 cm3 , Find r (r = 7 cm)

19. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base .If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made (h = 20cm) 20. The height of a cone is 10cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height . Find the ratio of the volumes of two parts (1: 7)

AREAS RELATED TO CIRCLES 1. Area of a sector of a circle of radius 14 cm is 154 cm2. Find the length of the corresponding arc of the sector (22 cm) 2. A chord 10 cm long is drawn in a circle of radius √50cm. Find the area of minor segment (14.285cm2) 3. The cost of fencing a circular field at the rate of Rs 24 per meter is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m2 . Find the cost of ploughing the field (Π= 22/7) (₨1925) 4. The area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21cm, find the the radius of the inner circle ( r = 14 cm) 5. The area of the shaded region between two concentric circles is 286cm2 .The difference of the radii of two circles is 7 cm , find the sum of their radii. (R + r =13cm) 6. A wheel has diameter 84 cm. Find how many complete revolutions must it take to cover 792 meters (300) 7. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances Travelled by Their tips in 24 hrs ( use Π= 3.14) ( 955. 43 cm) 8. Two circles touch internally. The sum of their areas is 116 Π cm2 and the distance between their centres is 6 cm. Find the radii of the circles 9. Two circles touch externally. The sum of their areas is 130 ᴨ sqcm and the distance between their centres is 14cm. Find the radii of the circles (3cm, 11cm) 10. Find the area of the minor segment of a circle of radius 42 cm, if the length of the corresponding arc is m 44cm 11. If the perimeter of a protractor is 72cm, calculate its area (308cm2) 12. Area of a sector of a circle is 1/6 to the area of circle. Find the degree measure of its minor arc (60°) 13. The area of quadrant is 154sqcm. Find its perimeter. (50cm) 14. Find the area of a quadrant of a circle whose circumference is 44cm (3 8.5cm2) 15. If the circumferences of two concentric circles forming a ring are 88cm and 66cm respectively. Find the

width of the ring (width of the ring = 3.5cm)

15. Construct a circle of radius 4 cm. Mark a point P which is 10 cm away from

its centre. Draw a pair of tangents to the circle from the point P.

16. Draw a circle of radius 4cm. Draw a pair of tangents to it which are inclined 600

to each other.

17. Draw a circle of radius 5cm. Draw a pair of tangents to it which are perpendicular

to each other.

18. Prove that the rectangle circumscribing a circle is a square.

19. ∆ABC is right angled at the vertex B such that AB = 6 cm and BC = 8 cm.

A circle is being circumscribed by the triangle. Find the radius of the circle.

20.d1 and d2 (where d1 < d2) are the diameters two concentric circles and c

is the length of a chord of the outer circle which is a tangent to the inner circle.

Prove that d2 2 = d12 + c2.

CLASS : 10 CHAPTER: ARITHMETIC PROGRESSIONS. 1. Find the 17th term of an A.P 𝟐½ ,𝟓,𝟕½,𝟏𝟎,…. …… 2.Find the 23rd term from the last term of the A.P. 𝟕,𝟗½ ,𝟏𝟐,𝟏𝟒½ ,𝟏𝟕,……….𝟐𝟓𝟕 . 3.The nth term of an A.P is given as 𝒕𝒏=𝟑𝒏+𝟕. Find the common difference . 4. Two A.Ps have the same common difference. The difference between their 70th terms is 140. Find the difference between their 100th terms . 5. 𝟐𝒑+𝟏,𝟏𝟑,𝟓𝒑−𝟑 are three consecutive terms of an A.P.Find the value of p . 6. Find the middle term of the A.P 𝟔,𝟏𝟏,𝟏𝟔,𝟐𝟏……𝟓𝟎𝟔 . 7. Which term of the A.P 𝟑𝟐,𝟑𝟓,𝟑𝟖…… is 120 less than its 80th term.? 8. Find the number of 3 digit numbers which are divisible by 7. 9. Find the number of 3 digit numbers which are not divisible by 5. 10. Find the number of 3 digit numbers which are divisible by both 3 and 5. 11. Find the number of 4 digit numbers which leave the remainder 3 when divided by 5. 12. Find the number of multiples of 6 lying between 75 and 750. 13. The sum of the first 10 terms of an A.P is 100 and the sum of its next 10 terms is 300. Find the 30th term of the A.P. 14.The sum of the first n terms of an A.P. is 4n2 +2n. Find the nth term of the A.P. 15. Find the sum of (4 -1/n) + (7-2/n) + (10 – 3/n) + ………….up to n terms. 16. If m times the mth term of an A.P. is equal to n times the nth term prove that its (m+n) th term is 0. 17. The sum of three numbers in A.P. is 18 and their product is 162. Find the numbers. 18.If S1, S2 and S3 respectively represents the sum of the first n, 2n and 3n terms of an A.P. show that: S3 = 3 (S2 – S1). 19.11th term of an A.P. is 0. Show that its 31st term is twice the 21st term 20. Find the sum:5 + (-41) + 9 + (-39) + 13 + (-37) + 17 + ……………………..+(-5) + 81 + (-3).

LESSON : CO-ORDINATE GEOMETRY

1. Find the distance between each of the following pairs of points :

(i) .

(ii) (

2. Show that the points (3 ,-1) , (3 ,-3 ) and ( 5 ,-1 ) are the vertices of a right angled isosceles triangle.

3. Show that the points A(2 ,-2) , B(14 ,10) , C(13 ,15) and D(1 , 3) are the vertices of a parallelogram.

4. Find the area of a Rhombus ABCD , if its vertices are A(3 ,0) ,B(4 ,5) C(-1 ,4) and D(-2 ,-1).

5. Find the points on Y-axis , which is equidistant from the points (5 ,-2) and (-3 ,2).

6. Find the value of p ,for which the points (-5 ,1) (1 ,p) and (4 ,-2) are collinear.

7. The point R divides the line segment AB ,where (-4 ,0) and (0 ,6) are respectively the co-ordinates of A and B

such that AR = . Find the co-ordinates of R.

8. The midpoints of the sides of a triangle are (3 ,4) ,(4 ,6) and (5 ,7) .Find the co-ordinates of the vertices of the

triangle.

9. Find the relation between x and y , if ( x ,y ) ,(1 ,3) and (8 ,0) are collinear.

10. The area of the triangle with vertices (a ,b+c ) , (b ,c+a) and (c ,a+b) is ....................

11. Three vertices of a parallelogram are (0 ,0) , (a ,0) and (b ,c).Find the co-ordinates of the fourth vertex.

12. Find the co-ordinates of the centroid of the triangle whose vertices are (-4 ,6) ,(2 ,-2) and (2

,5).

13. Find a point on the X-axis which is equidistant from the points (-2 ,5) and (2 ,-3).

14. If the points (a ,0) , (0 ,b) and (1 ,1) are collinear ,show that .

CLASS: 10 CHAPTER:QUADRATIC EQUATIONS

1. Solve for x: 36x2 – 12ax + (a 2 --- b2) = 0.

2.Divide 25 into 2 parts so that the sum of their squares is 325.

3.Solve the quadratic equation 3x2 – 11x + 10 = 0 by completing the square method.

4.A plane left 30 minutes later than the scheduled time. It had to increase the speed by

250km/hr from its usual speed to reach at the destination on time. If the destination is

1500 km away, find its usual speed.

5.The sum of the squares of two positive integers is 208. If the square of the larger

number is 18 times the smaller, find the numbers.

6. If the roots of the quadratic equation (a- b) x2 + (b-c) x + ( c – a ) = 0, are equal prove

that 2a = b + c.

7.Solve for x : .

8. Solve for x:

9.Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes

10 hours less than the smaller one to fill the tank separately. Find the time in which each

tap can separately fill the tank.

10. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km

upstream than to return downstream to the same spot. Find speed of the stream.

11.The hypotenuse of a right triangle is 6m more than twice the shortest side. If the third

side is 2metre less than the hypotenuse, find the sides of the triangle.

12. The hypotenuse of a right triangle is 3√5 cm. If the smaller side is tripled and the

larger side is doubled, the new hypotenuse will be 15 cm. Find the length of each side.

Q13.The lengths of the sides forming right angle of a right angled ∆ are 5x cm and (3x – 1

)cm. The area of the triangle is 60 cm2. Find the length of the hypotenuse.

14. A takes6 days less than the time taken by B to complete a work. If they together

can complete the work in 4 days, find the time taken by each to finish the work.

15.300 apples are distributed equally among a certain number of students. Had there

been 10 more students, each would have received one apple less. Find the number of

students.

16. A person on a tour had Rs. 12000 for his daily expenses. In order to extend his

journey for 2 more days he had to cut down his daily expenses by Rs. 200 . Find the

duration of the tour he planned first.

17.A man sold an article for Rs. 96 gaining as many as percent as the cost price (in

Rupees) is. Find the cost price of the article.

18. A peacock is sitting on the top of a pillar which is 9 m high. From a point 27m away

from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing

the snake, the peacock pounces on it. If their speeds are equal, at what distance from

hole, the snake caught?

19. One fourth of a herd of camels was seen in the forest. Twice the square root of the

herd gone to mountains and the remaining 15 camels were seen on the bank of the river.

Find the total number of camels.

20. Some boys planned a picnic. The budget for food was Rs. 3000 . Five boys could not

go for picnic and thus the cost of food for each member increased by Rs.30 . How many

boys attended the picnic?