IX SAII MATHS STATISTICS ASSIGNMENT

1.       The relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1	98.6	99.2	90.3	86.5	95.3	92.9	96.3	94.2	95.1
89.2	92.3	97.1	93.5	92.7	95.1	97.2	93.3	95.2	97.3
96.2	92.1	84.9	90.2	95.7	98.3	97.3	96.1	92.1	89

                (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc.

                (ii) Which month or season do you think this data is about?

                (iii) What is the range of this data?

2.       100 surnames were randomly picked up from a local telephone directory and a frequency             distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters	1 - 4	4 - 6	6 - 8	8 - 12	12 - 20
Number of surnames	6	30	44	16	4

                (i) Draw a histogram to depict the given information.

                (ii) Write the class interval in which the maximum number of surnames lie.

3.       The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:                      

Length (in mm)	118 - 126	127 - 135	136 - 144	145 - 153	154 - 162	163 - 171	172 - 180
Number of leaves	3	5	9	12	5	4	2

                (i) Draw a histogram to represent the given data.

                (ii)Also represent by a polygon ( Separately )

                (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

4.       Find out mean, mode  ( Calculate).

Marks	10	20	30	40	50	60	70
Number of students	7	10	10	17	23	15	8

5.       Find the value of p if mean is 7.5

Marks	3	5	7	9	11	13
Number of students	6	8	15	p	8	4

6.       Find the value of  ‘m’ and ‘n’  if mean is 50 and total observations are 90.

Class Marks	10	30	50	70	90
Number of students	17	m	32	n	19

7.       Find median of 

20,26,8,18,24,18,46,23,62,55,70,44

8.       The class mark for a certain continuous frequency distribution are . find class intervals and draw hisrogram.

Class Marks	6	12	18	24	30
Number of students	12	15	20	9	16

9.       The mean of a data is 46. Find the new mean if  each of the observation of a data is

(a) increased by 3   (b) decreased by 2         (c) multiplied by 0.5

10.   Find less than and more than cumulative frequency.

Number of letters	0 - 4	4 - 8	8 - 12	12 - 16	16 - 20
Number of surnames	6	17	23	13	11

IX M SAII QUADRILATERALS ASSIGNMENT 3

IX M SAII QUADRILATERALS ASSIGNMENT 2

IX M SAII QUADRILATERALS ASSIGNMENT 1

Prove the followings:

1. A diagonal of a parallelogram divides it into two congruent triangles. 
2. In a parallelogram, opposite sides and angle are equal. 
3. If each pair of opposite sides of quadrilateral is equal, then it is a parallelogram. 
4. If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. 
5. The diagonals of a parallelogram bisect each other. 
6. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. 
7. A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. 
8. The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side. 
9. The line segment joining the mid- points of the two sides of a triangle is parallel to the third side. 
10. Show that each angle of a rectangle is a right angle. 
11. Show that the diagonal of a rhombus are perpendicular to each other. 
12. Show that the bisectors of the angles of a parallelogram form a rectangle. 
13. ABCD is a parallelogram (||gm) in which P and Q are mid-points of opposite side AB and CD. If AQ intersects DP at S and BQ intersects CO at R, show that

(i) APCQ is ||gm                              (ii)DPBQ is ||gm                             (iii) PSQR is ||gm

14. In Triangle ABC, D, E and Fare respectively the mid points of sides AB, BC and CA. Show that triangle ABC is divided into four congruent triangle by joining D, E and F
15. If the diagonal of a parallelogram are equal, then show that it is a rectangle. 
16. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. 
17. Show that the diagonals of a square are equal and bisect each other at right angles. 
18. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. 
19. In Δ ABC and Δ DEF, AB=DE, AB||DE, BC=EF and BC||EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that:

(i) Quadrilateral ABCD is a parallelogram.

(ii) Quadrilateral BEFC is a parallelogram.

(iii) AD||CF and AD=CF

(iv) Quadrilaterals ACFD is a parallelogram

(v) AC=DF

(vi) Δ ABC ≅ Δ DEF. 

20. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that:

(i) SR||AC and SR =1/2 AC                          (ii) PQ=SR                          (iii) PQRS is a parallelogram. 

21. ABCD is a rhombus and P, Q, R and S are the mid- point of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. 
22. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. 
23. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. 
24. ABC is a triangle right angle at C. A line through the mid-points M of hypotenuse AM and parallel to BC intersects AC at D. Show that

(i) D is the mid –point of AC                      (ii) MD ┴ AC                      (iii) CM=MA=1/2 AB.

IX SAII: QUADRILATERALS ASSIGNMENT

IX SAII:TEST: QUADRILATERALS

IX M SAII ASSIGNMENT: LINEAR EQUATION IN TWO VARIABLES

                                                                       Class- IX  ( Linear equations )         

Q1.         Express y  in terms of x , given that 2x -5y =7 .Check whether the point (-3,-2) is on the given                line .

Q2.         Express x in terms of  y , given that 3x +4y =6 . Check whether the point (3,2) is on given line .

Q3.         Express x in terms of y , it is being given that 7x-3y=15. Check  if the line represented by the given equation intersects the y- axis at y=-5.

Q4.         Find the point of intersection of the line represented by the equation  7x+y=-2 with y-axis . Check whether the point (2,1) is a solution of the given equation.

Q5.         A part of monthly expenses of a family on milk is fixed which is Rs.500 and the remaining varies with the quality of milk taken extra the rate of Rs.20 per kg. Taking the quantity of milk required extra as x kg and the total expenditure on milk Rs y. Write a linear equation for this information and draw its graph.

Q6.         When 5 times the larger of the two numbers is divided by the smaller , the quotient and remainder are 2 and 9 respectively . Form a linear equation in two variable  for  above and give its two solutions.

Q7.         Draw the graph of 2x+y =7 . Write the points where line meets x and y-axis.

Q8.         Draw the graph of the equation x -3y =4 . From the graph find the value of x when y=-2.

Q9.         Draw the graph of the equation 2x +5y =13 . Find the points where the line meets two axis.

Q10.     Plot the graph of the following linear equation 2( x+3) -3 (y+1) =0 . Also answer the following questions:

 a) Write the quadrant in which the line segment intercepted between the axes lie .

b) Shade the triangular region formed by the line and the axes.

c) Write the vertices of the triangle so formed.

Q11.     “ Two years later a father will be 8 years more than three times the age of the son” taking the present age of father and son as x and y respectively . Write a linear equation for above and draw its graph .From the graph ,find the age of the father when the son’s age is 10 years.

Q12.     The taxi fare in a city is also follows:

For the first kilometer, the fare is Rs.8 and for the subsequent distance it is Rs5.per km .Taking the distance covered as x km. and the total fare as Rs y , write a linear equation for this information and draw its graph.

Q13.     If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body . Express this in the form of an equation  in two variables and draw the graph of the same by taking the constant force as 5 units .Also read from the graph the work done when the distance travelled by the body is (a) 2 units (b) 0 unit.

Q14.     Yamini and Fatima , two students of Class IX of a school , together contributed Rs.100 towards the Prime Minister’s Relief Fund  to the help the earthquake victims . Write a linear equation which satisfies this data .( You may take their contributions as Rs x and Rs. y ) Draw the graph of the same.

Q15.     Draw the graphs of the linear equations  y  =  x and y = - x on the same Cartesian plane .What do you observe.

Q16.     Draw the graph of the equation represented by a straight line which is parallel to the x-axis and at a distance 3 units below it .

Q17.     Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10  units.

Q18.     Draw graph of the equation 3 (x+2y) -2(x+3y) =3. Also find the point where the line meets x-axis.

Q19.     If “ the cost of 5 tables exceed the cost of eight chairs by Rs. 150”. Write the linear equation  in two variable to represent the statement . Also find  the cost of one table if cost of one chair is Rs.240.

Q20.     Draw straight lines 2x-y =3 and 3x +2y =1 on the same graph paper . Find the point intersection of      these lines.

Q21.     Draw the lines x =4 , y=2 and x=y , on the same graph paper and then identify what type of figure obtained ?Also write the point of vertices of this figure formed.

Q22.     Ram is half of his father’s age .Twenty years ago the age of father was six times age of Ram . Find the age of Ram and his father.

Q23.     For the first kilometer , the fare is Rs. 5 and for successive distance it is Rs2 per km . Taking distance covered as x and total fare Rs. y . Write a linear equation and draw its graph.

Q24.     The cost of a pen is 5 times the cost of a pencil. Write  a linear  equation in two variable to represent the statement.