CBSE 9th Mathematics Term 2 -Revision

Answer the following questions

Section-A

1. Find the value of the polynomial 2x + 5 at x = – 3.

2. Find the volume of a sphere whose surface area is 616 sq. cm.

3. A joker’s cap is in the shape of a right circular cone with base radius 7 cm and height

24 cm. Find the area of sheet required for 10 such caps.

4. Prove that “A diagonal of a parallelogram divides it into two congruent triangles”

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CBSE Class 9 Mathematics-Important Questions-Surface Area and Volume

Answer the following

1. The total surface area of a cube is 726 cm2. Find the length of its edge. [11cm]

2. How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm ? [154cm3]

3. Find the area of the sheet required to make closed cylindrical vessel of height 1 m and diameter 140 cm. [7.48m2]

4. If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions 8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be carried in the wooden box. [1000000]

5. How many balls, each of radius 2 cm can be made from a solid sphere of lead of radius 8 cm ? [64]

6. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of the sphere [2.1cm]

7. A school provides milk to the students daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk up to a height of 12 cm, find how many litres of milk is needed to serve 1600 students. [739.2 litres]

8. A rectangular piece of paper is 22 cm long and 10 cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder. [385cm3]

9. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find it volume. If 1cm3 wheat cost is Rs 10, then find total cost. [Rs866.25]

10. The curved surface area of a cylinder is 176 cm2 and its area of the base is 38.5 cm2. Find the volume of the cylinder. [Ans:98 cm3]

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CBSE 9th Mathematics Worksheet - Probability

Answer the following

1. A bag contains 50 coins and each coin marked from 51 to 100. One coin is
picked up at random. The probability that the number on the coin is not a prime
number is…………………

2. Eleven bags of wheat flour, each marked 5 kg actually contained the following weights of flour (in kg):

4.97    5.05   5.08   5.03   5.00    5.06     5.08     4.98    5.04    5.07     5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

3. The record of a weather station shows that out of the past 250 consecutive days,
its weather forecast correct 175 times. What is the probability that on a given
day.
(i) it was correct.
(ii) it was not correct.

4. A die having six faces is tossed 80 times and the data is as below:
Outcome    1      2      3     4      5   6
Frequency 10    20    10   28    8   4
Find (i) P (1) (ii) P (4) (iii) P (6) (iv) P (5).

5. The blood groups of 30 students of class IX are recorded as follows:

A,

B,

O,

O,

AB,

O,

A,

O,

B,

A,

O,

B,

A,

O,

O,

A,

AB,

O,

A,

A,

O,

O,

AB,

B,

A,

O,

B,

A,

B,

O

A student is selected at random from the class from blood donation. Find the probability that the blood groups of the student chosen is:
(i) A (ii) B (iii) AB (iv) O

6. Given below is the frequency distribution of wages (in Rs.) of 30 workers in a certain factory

Wages
(in Rs.)            110-130     130-150      150-170     170-190    190-210    210-230    230-250

No. of
workers                 3               4                  5                6                5               4               3
A worker is selected at random. Find the probability that his wages are:

(i) less than Rs. 150

(ii) at least Rs. 210

(iii) more than or equal to 150 but less than 210.

7. Three coins tossed simultaneously 100 times with the following frequencies of
different outcomes.Out come           No head one head        two head three head
Frequency               14 38               36 12
If the coin tossed again then find the probability.
(i) two heads coming up
(ii) 3 heads coming up
(iii) getting more tails than heads
(iv) at least one head coming up

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CBSE Class 9th Mathematics Worksheet - Areas of Parallelograms and Triangles-2

Answer the following

1. In the given figure ABCD is a parallelogram AE ⊥ DC and CF ⊥ AD. If AB = 18 cm, AE = 8 cm and CF = 16 cm, find AD.


2. In the below figure AD is the median, and E is mid-point on AD. If the area of triangle is 16 cm2, what is the area of the triangle BED

3. Two parallelograms are on the same base and between the same parellels. The ratio of their areas is:
a) 1:2
b) 1:1
c) 1:4
d) None of these

4. Show that a median of a triangle divides it into two triangle of equal area.

5. Point P and Q are on the sides DC and AD of a parallelogram respectively. Show that                        
6. If E, F, G & H are mid points of sides of parallelogram ABCD, then show that
                          
7. In given figure ABCD is a quadrilateral and BE||AC is such that BE meets at E on the extended CD. Show that area of triangle ADE is equal to the area of quadrilateral ABCD.

                          

8. ABCD is a trapezium in which AB||CD and diagonals AC and BD intersect at 0. Prove that


9. Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show that perimeter of the parallelogram is greater than that of rectangle.

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CBSE 9th Mathematics Worksheet - Mixed Questions-1

Answer the following

1. 
   

    

2. 
   

    

3. 
   

   

4. 
   

  

5. 
   

    

6. 
   

    

7. 
   

    

8. 
   

    

9. 
   

    

10. 
    

    

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IGCSE Mathematics Worksheet- Sets & Venn Diagrams

Answer the following  

1. 
   

    

2. 
   

    

    

     

3. 
   

     

      

               4. 

    

       

5. 
   

   

6. 
   

    

   

    

    

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CBSE 9th Mathematics Important Questions/ Worksheet - Heron's Formula

Answer the following

1. Find the area of a triangle, two sides of which are 60 cm and 100 cm and the perimeter is 300 cm.

2. In the figure, find the area of the quadrilateral PQRS.
 

3. Find the cost of leveling a ground in the form of a triangle with sides 16m, 12m and 20m at Rs.4 per sq. meter.

4. The sides of a triangular field are 41m, 40m and 9m. Find the number of flower beds that can be prepared in the field, if each flower bed needs 900cm^2 space.

5. An umbrella is made by stitching 10 triangular pieces of cloth of 5 different colour each piece measuring 20cm, 50cm and 50cm. How much cloth of each colour is required for one umbrella? (Use√6 = 2.45)  

6. If area of the hexagon is 24√3cm^2, find its perimeter

7. A park in the shape of a quadrilateral ABCD has C = 90°. AB = 18 m, BC = 24 m, CD = 10 m and AD = 16 m. How much area does it occupy?

8. Anu  has a piece of land which is in the shape of a rhombus (see fig.) She wants her daughter and son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonal is 160 m, how much area each of them will get for their crops?              

9. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area Of grass field will each cow be getting?

10. Find the height of a trapezium in which parallel sides are 25 cm 77 cm and non-parallel sides and 26 cm and 60 cm. Given the area of the trapezium as 1644 cm^2

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CBSE 9th Mathematics Important Questions/Worksheet- Triangles

Answer the following

1. In the figure below, ABC is a triangle in which AB = AC. X and Y are points on AB and AC such that AX = AY. Prove that ΔABY ≌ ΔACX



2. In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side.

3. In the given figure, triangles PQC and PRC are such that QC = PR and PQ = CR. Prove that ∠PCQ = ∠CPR.



4. In the given figure, PS is median produced upto F and QE and RF are perpendiculars drawn from Q and R, prove that QE = RF.



5. In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR. Then prove that

(a) ΔPTR ≌ ΔRMP

(b) RT || PM and RT = RM



6. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that

(i) ΔABD ≌ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

7. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (see figure). Show that

(i) ΔDAP ≌ ΔEBP

(ii) AD = BE



8. ABC and DBC are two isosceles triangles on the same base BC (see figure). Show that ∠ABD = ∠ACD.



9. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see figure). Show that

(i) ΔABM ≌ ΔPQN (ii) ΔABC ≌ ΔPQR



10. In the adjoining figure, sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.



11. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see figure). Show that ∠A > ∠C and ∠B > ∠D.



12. In the figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR > ∠PSQ.



13. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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CBSE 9th Mathematics worksheet- Surface area and volume

Answer the following

1. Three cubes of each side 4cm are joined end to end. Find the surface area of resulting cuboid. 

2. The dimensions of a cubiod are in the ratio of 1 : 2 : 3 and its total surface area is 88m². Find the dimensions. 

3. A cuboidal oil tin is 30cm X 40cm X 50cm. Find the cost of the tin required for making 20 such tins if the cost of tin sheet is Rs. 20/m². 

4. The diameter of a garden roller is 1.4m and it is 2m long. How much area will it cover in 5 revolutions? (π= 22/7) 

5. A cone of height 24cm and slant height 25cm has a curved surface area 550cm². Find its volume (π= 22/7) 

6. A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form an embankment. Find the height of embankment.

7. A semi circular sheet of metal of diameter 28cm is bent into an open conical cup. Find the depth and capacity of cup. 

8. A hollow cylindrical pipe is 210cm long. Its outer and inner diameters are 10cm and 6cm respectively. Find the volume of the copper used in making the pipe. 

9. Water in a canal, 30dm wide and 12dm deep is flowing with a velocity of 20km per hour. How much area will it irrigate in 30min, if 9cm of standing water is desired?  (10dm = 1 meter) 

10. A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 6cm and its height is 4cm. Find the cost of painting the toy at the rate of Rs. 5 per 1000cm². 

11. Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14cm. 

12. A hemispherical bowl of internal diameter 36cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. How many bottles are required to empty the bowl?

13. If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of second sphere? 

14. Find the lateral curved surface area of a cylindrical petrol storage tank that is 4.2m in diameter and 4.5m high. How much steel was actually used, if 1/12 of steel actually used was wasted in making the closed tank.

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