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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CBSE 9th Mathematics Worksheet - Statistics

Answer the following

1. Find the mean of first 10 even natural numbers

2. Calculate the mean for the following distribution.
   

3. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32

4. The following marks were obtained by the students in a test.
81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62
What is the range?

5. Find the mode of following series.
25, 23, 22, 22, 24, 27, 27, 25, 23, 22, 26, 32

6. Find the median of the following data
19, 25, 59, 48, 35, 31, 30, 32, 51. If 25 is replaced by 55, what will be the new
median.

7. The following observations have been arranged in ascending order. If the median
of the data is 63, find the value of x.
29, 32, 48, 50, x, x+2, 72, 78, 84, 95

8. Find the value of x and y in following distribution if it known that the mean of the
distribution is 1.46.



9. The mean monthly salary of 10 members of a group is Rs. 1445, one more
member whose monthly salary is Rs. 1800 has joined the group. Find the mean
monthly salary of 11 members of the group.

10. For the following data, draw a histogram and frequency polygon


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CBSE 9th Mathematics Worksheet - Constructions

Answer the following 

1. Construct ∆ABC in which BC = 6.4 cm, B = 45° and AB – AC = 3.5 cm

2. Construct a ∆ABC in which BC = 5 cm, B = 75° and AB + AC = 9 cm

3. Construct a triangle XYZ in which ∠Y = 30°, Z = 90° and XY + YZ + ZX = 11 cm

4. Construct a Construct a ∆PQR with its perimeter = 10.4 cm and base angles of 75° and 30°

5. Construct an equilateral triangle, given its one side = 5 cm

6. Construct a right triangle whose base is 6 cm and the difference of its hypotenuse and the other side is 8 cm

7. Construct a right triangle whose base is 12 cm and sum of its hypotenouse and other side is 18 cm.

8. Construct a rhombus whose diagonals are 4 cm and 6 cm in lengths.

9. Construct a triangle ABC such that AB = BC = 6 cm and median AD = 4 cm.

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CBSE 9th Mathematics Worksheet - Coordinate Geometry

Answer the following

1. Three vertices of a rectangle are (– 4, 5), (– 4, 2) and (3, 2). Plot these points and find the co-ordinates of the fourth vertex.

2. Points A (5, 3), B (–2, 3) and D (5, –4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

3. (i) Plot each of the points A (–2, 4), B (–2, – 3), C (4, –3) and D (4, 4).

    (ii) Draw the segments AB, BC, CD and DA. What is the name of the figure ABCD ?

    (iii) What are the coordinates of the point where the segment AD cuts the y-axis ?

    (iv) What are the coordinates of the points where the segment CD cuts the x-axis ?

4. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant.

5. In the figure, PQR is an equilateral triangle with the co-ordinates of Q and R as (0, 4) and (0, – 4). Find the co-ordinates of the vertex P.
                             
6. The following table gives the number of pens and their corresponding costs. Plot these as ordered pairs and join them. What type of graph do you get ?
      

7. On a graph paper sketch the parallelogram whose vertices are (–3, 2), (–4, –2), (3, –2) and (4, 2).

8. Abscissa of a point is positive in -------------quadrants

9. The point (–5, 2) and (2, –5) lie in the--------------------------
(a) same quadrants (b) II and III quadrants respectively
(c) II and IV quadrants respectively (d) IV and III quadrants respectively

10. The distance of a point (0, –3) from the origin is :
(a) 0 units (b) –3 units (c) cannot be determined (d) 3 units

11. The area of triangle OAB with O(0,0), A(4,0) & B(0,6) is
(a) 8 sq. unit (b) 12 sq. units (c) 16 sq. units (d) 24 sq. units

12. Draw the graph of the following equations

      (i) y=3x + 2 (ii) y=x

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CBSE 9th Mathematics Worksheet- Areas of Parallelograms and Triangles

Answer the following

1. Prove that parallelograms on the same base and between the same parallels are equal in area.
2. PQRS and ABRS are parallelograms and X is any point on side BR. Show that : 

         (i) area PQRS = area ABRS
        (ii) area AXS = ½ area PQRS.

      3. In the figure, M is a point in the interior of a parallelogram PQRS. Show that

       

     

4. In the figure, diagonals AC and BD of quadrilateral ABCD intersect at O, such that OB = OD. If AB = CD, show that

i)ar (DOC) = ar (AOB)
ii)ar (DCB) = ar (ACB)
iii)ABCD is a parallelogram.

     

       5. In given figure ABCD, DCFE and ABFE are parallelogram show that ar (ADE) = ar (BCF)

       6. 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  

  7. P and Q are mid-points of sides AB and AC respectively. Of triangle ABC. R is mid-point of AP, prove that:

           1 ) ar(PRQ)=1/2 ar(ARC)

           2 ) ar(RQC)=3/8 ar(ABC)

           3 ) ar(PBQ)=ar(ARC)

8. In adjoining figure ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that

                                

                               

9. D, E & F are mid points of sides of triangle BC, CA & AB respectively. Show
   that
                       

        10. 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.

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CBSE 9th Mathematics Worksheet - Quadrilaterals

Answer the following

1. In a parallelogram ABCD, E and F are the midpoints of AB and CD respectively. Show that the linesegments AF and EC trisect the diagonal BD.

2. Show that the quadrilateral formed by joining the mid-points of the sides of a rectangle is a rhombus.

3. In a ΔABC, D, E and F are mid-points of sides AB, AC and BC respectively. If DE and DF are joined, find the perimeter of BDEF.

4. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

(i)MD ⊥ AC

(ii) D is mid-point of AC

(iii) MC = MA = 1/2 AB

5. In the adjoining figure QR=RS Find ∠PSR

                                       

6. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

7. In the adjoining figure, D, E and F are mid-points of the sides BC, CA and AB of ∆ABC If AB = 4.3cm, BC = 5.6cm and AC = 3.5cm, find the perimeter of ∆DEF
                      

8. AD is a median of ∆ABC and E is the mid-point of AD. BE Produced meets AC in F. Prove that AF= 1/3 AC

9. Show that the bisectors of angles of a parallelogram form a rectangle.

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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 - Lines and Angles

Answer the following

1.      If an angle differs from its complement by 10°, find the angle

2.      The supplement of an angle is one third of itself. Determine the angle and its supplement.

3.      Two complementary angles are such that two times the measure of one is equal to three times measure of the other. Find the measure of the large angle.

4.      If x : y : z = 5 : 4 : 6. if XOY is a straight line find the values of x, y and z

             

5.      If  AB║DF, AD║FG, ∠BAC = 65°, ∠ACB = 55°. Find ∠FGH

             

6.      AB║ED and ∠ABC = 30°, ∠EDC = 70° then find x°

                 

7.      If lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠DOE and ∠BOF

                                                        

8.    The angles of a triangle are (x-40°), (x-20°) and ( 1/2 x - 10°) find the value of x.

9.      In the given figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

 

10. Find x and y in the following figure.

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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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