# CBSE Board Class 9 Math Previous Year Question Papers 2009

## CBSE Board Previous Year Question Papers 2009 for Class 9 Math

MATHEMATICS

class 9

Max Marks – 90

General Instructions :

1.All questions are compulsory.

2.The question paper consists of 34 questions divided in to Four sections A, B, C and D. Section–A comprises of 8 questions of 1 mark each, Section–B comprises of 6 questions of 2 marks each, Section–C comprises of 10 questions of 3 marks each and Section–D comprises of 10 questions of 4 marks each.

3.Question numbers 1 to 8 in Section – A are multiple choice questions where you are to select one correct option out of the given four.

4.There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four mark each. You have to attempt only one of the alternatives in all such questions.

5.Use of calculator is not permitted.

6.An additional 15 minutes time has been allotted to read this question paper only.

SECTION – A

Questions Number 1 to 8 carry 1 mark each. For each question Four alternate choices have been provided of which only one is correct. Choose the correct one.

1.Any point on the line y=x is of the form :

(A) (a, a) (B) (0, a) (C) (a, 0) (D) (a, -a)

2.Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is :

(A) 95° (B) 90° (C) 105° (D) 120°

3.The equation of x-axis is of the form :

(A) x = 0 (B) y = 0 (C) x = y (D) x + y = 0

4.A quadrilateral having only one pair of opposite sides parallel is called a :

(A) square (B) parallelogram (C) rectangle (D) trapezium

5.If each side of a cube is doubled, the total surface area becomes :

(A) 2 times (B) 12 times (C) 4 times (D) 6 times

6.In fig, O is the centre for the circle. If reflex a ∟AOC=230º then x is equal to :

(A) 65° (B) 50°

(C) 130° (D) 115°

7.Which of the following can not be the empirical probability of an event?

(A) 2/3 (B) 1 (C) 3/2 (D) 0

8.The median of a triangle divides it into two :

(A) triangles of equal area (B) congruent triangles

(C) right triangles (D) Isosceles triangles

SECTION - B

Questions Number 9 to 14 carry 2 marks each.

9.Find median and mode of the following data

7, 9, 12, 13, 7, 12, 7, 12, 15, 7, 18, 20, 7, 13

10. The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find all the angles of the quadrilateral.

11.In fig, a circle with centre at O is given. If ∟ABO= 20° and ∟ACO = 35°, then find the value of x.

12. Find the volume of a right circular cone with radius 6 cm and height 14 cm. (Take π = 22/7)

13.The diameter of the moon is one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

14.The cost of a table is seven times the cost of a chair. Write a linear equation is two variables in the form ax + by + c = 0 to represent this statement. Write also the values of a, b and c.

OR

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. Write one solution also.

SECTION – C

Questions Number 15 to 24 carry 3 marks each.

15.In a circle of radius 5 cm, AB and CD are two parallel chords of lengths 8 cm and 6 cm respectively. Calculate the distance between the chords if they lie on the opposite sides of the centre.

OR

In a fig, PQ=QR are chords of a circle equidistant from the centre O. Prove that the diameter passing through Q bisects ∟PQR. Also, prove that PQ=PR.

16.1.1 cm3 of gold is drawn into a wire of 0.1 mm in diameter. Find the length of the wire in metres.

17.Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus

18.Find the mean of the following frequency distribution.

x : 4 6 9 10 13

f : 5 10 10 7 8

19.A conical tent is 10 m high and the radius of its base is 24 m. Find

i)Slant height of the cone

ii)Cost of the canvas required to make the tent, if the cost of 1 m2 canvas is 70

OR

There metal cubes, whose edges measure 3 cm, 4 cm and 5 cm respectively, are melted to form a single cube. Find its edge. Also find the total surface area of the new cube formed.

20.Solve the equation 4x – 3 = x + 21 and represent the solutions(s) on

i)The number line

ii)The Cartesian plane.

21.1500 families with 2 children were selected randomly and the following data was recorded.

Number of girls in a family : 0 1 2

Number of families : 475 804 221

Compute the probability of a family, chosen at random having

i) 2 girls ii) 1 girl iii) No girl.

Also check whether the sum of these probabilities is 1.

22.Express the following statement as linear equation in two variables :

‘The cost of 2 oranges and 3 apples is 45. From the equation find the cost of an apple if the cost of an orange is 7.50

OR

Find two solutions for each of the following equations.

i) 2x + y = 8 ii) x – 3y = 18

23.In a parallelogram ABCD, P & Q are the mid points of sides DC & AB respectively. Show that the diagonal BD is trisected by line segments AP&CQ.

24.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 91.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

Construct a grouped frequency distribution table with classes 84–86, 86–88 etc.

SECTION – D

Questions Number 29 to 34 carry 4 marks each.

25. P is any point on the chord BC of a circle such that AB=AP. Prove that CP=CQ.

OR

In a circle with centre O, chord SR=chord SM. Radius OS intersects the chord RM at P. Prove that RP = PM.

26.The following is the distribution of weights (in kg) of 50 persons :

Weight (in kg) : 55 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 85

Number of persons : 10 10 8 6 9 5

Draw a histogram for the above data.

27.A closed cylindrical petro storage tank is made up of steel sheet, find

i)the lateral or curved surface area of the tank that is 4.2 m in diameter and 4.5 m high.

ii)how much steel was actually used, if (1/12) of the steel actually used was wasted in making the tank.

28.ABCD is a trapezium with AB║DC. If AD=BC then prove that ∟BCD=∟ADC.

OR

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that

i)ΔAPB ~ ΔCQD

ii)AP = CQ

29.Draw the graph of the linear equation 2x – y = 4. From the graph, find the co-ordinates of the point where the line intersects y – axis.

30.Prove that the parallelograms on the same base and between the same parallels are equal in area.

31.Draw histogram and frequency polygon on the same graph for the following data :

Weight Numver of student

(in kg)

124–128 5

128–132 8

132–136 17

136–140 24

140–144 16

144–148 12

32.Two circles of radii 10 cm and 17 cm intersect at two points and distance between their centres is 21 cm. Find length of common chord.

33.A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

class 9

Max Marks – 90

General Instructions :

1.All questions are compulsory.

2.The question paper consists of 34 questions divided in to Four sections A, B, C and D. Section–A comprises of 8 questions of 1 mark each, Section–B comprises of 6 questions of 2 marks each, Section–C comprises of 10 questions of 3 marks each and Section–D comprises of 10 questions of 4 marks each.

3.Question numbers 1 to 8 in Section – A are multiple choice questions where you are to select one correct option out of the given four.

4.There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four mark each. You have to attempt only one of the alternatives in all such questions.

5.Use of calculator is not permitted.

6.An additional 15 minutes time has been allotted to read this question paper only.

SECTION – A

Questions Number 1 to 8 carry 1 mark each. For each question Four alternate choices have been provided of which only one is correct. Choose the correct one.

1.Any point on the line y=x is of the form :

(A) (a, a) (B) (0, a) (C) (a, 0) (D) (a, -a)

2.Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is :

(A) 95° (B) 90° (C) 105° (D) 120°

3.The equation of x-axis is of the form :

(A) x = 0 (B) y = 0 (C) x = y (D) x + y = 0

4.A quadrilateral having only one pair of opposite sides parallel is called a :

(A) square (B) parallelogram (C) rectangle (D) trapezium

5.If each side of a cube is doubled, the total surface area becomes :

(A) 2 times (B) 12 times (C) 4 times (D) 6 times

6.In fig, O is the centre for the circle. If reflex a ∟AOC=230º then x is equal to :

(A) 65° (B) 50°

(C) 130° (D) 115°

7.Which of the following can not be the empirical probability of an event?

(A) 2/3 (B) 1 (C) 3/2 (D) 0

8.The median of a triangle divides it into two :

(A) triangles of equal area (B) congruent triangles

(C) right triangles (D) Isosceles triangles

SECTION - B

Questions Number 9 to 14 carry 2 marks each.

9.Find median and mode of the following data

7, 9, 12, 13, 7, 12, 7, 12, 15, 7, 18, 20, 7, 13

10. The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find all the angles of the quadrilateral.

11.In fig, a circle with centre at O is given. If ∟ABO= 20° and ∟ACO = 35°, then find the value of x.

12. Find the volume of a right circular cone with radius 6 cm and height 14 cm. (Take π = 22/7)

13.The diameter of the moon is one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

14.The cost of a table is seven times the cost of a chair. Write a linear equation is two variables in the form ax + by + c = 0 to represent this statement. Write also the values of a, b and c.

OR

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. Write one solution also.

SECTION – C

Questions Number 15 to 24 carry 3 marks each.

15.In a circle of radius 5 cm, AB and CD are two parallel chords of lengths 8 cm and 6 cm respectively. Calculate the distance between the chords if they lie on the opposite sides of the centre.

OR

In a fig, PQ=QR are chords of a circle equidistant from the centre O. Prove that the diameter passing through Q bisects ∟PQR. Also, prove that PQ=PR.

16.1.1 cm3 of gold is drawn into a wire of 0.1 mm in diameter. Find the length of the wire in metres.

17.Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus

18.Find the mean of the following frequency distribution.

x : 4 6 9 10 13

f : 5 10 10 7 8

19.A conical tent is 10 m high and the radius of its base is 24 m. Find

i)Slant height of the cone

ii)Cost of the canvas required to make the tent, if the cost of 1 m2 canvas is 70

OR

There metal cubes, whose edges measure 3 cm, 4 cm and 5 cm respectively, are melted to form a single cube. Find its edge. Also find the total surface area of the new cube formed.

20.Solve the equation 4x – 3 = x + 21 and represent the solutions(s) on

i)The number line

ii)The Cartesian plane.

21.1500 families with 2 children were selected randomly and the following data was recorded.

Number of girls in a family : 0 1 2

Number of families : 475 804 221

Compute the probability of a family, chosen at random having

i) 2 girls ii) 1 girl iii) No girl.

Also check whether the sum of these probabilities is 1.

22.Express the following statement as linear equation in two variables :

‘The cost of 2 oranges and 3 apples is 45. From the equation find the cost of an apple if the cost of an orange is 7.50

OR

Find two solutions for each of the following equations.

i) 2x + y = 8 ii) x – 3y = 18

23.In a parallelogram ABCD, P & Q are the mid points of sides DC & AB respectively. Show that the diagonal BD is trisected by line segments AP&CQ.

24.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 91.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

Construct a grouped frequency distribution table with classes 84–86, 86–88 etc.

SECTION – D

Questions Number 29 to 34 carry 4 marks each.

25. P is any point on the chord BC of a circle such that AB=AP. Prove that CP=CQ.

OR

In a circle with centre O, chord SR=chord SM. Radius OS intersects the chord RM at P. Prove that RP = PM.

26.The following is the distribution of weights (in kg) of 50 persons :

Weight (in kg) : 55 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 85

Number of persons : 10 10 8 6 9 5

Draw a histogram for the above data.

27.A closed cylindrical petro storage tank is made up of steel sheet, find

i)the lateral or curved surface area of the tank that is 4.2 m in diameter and 4.5 m high.

ii)how much steel was actually used, if (1/12) of the steel actually used was wasted in making the tank.

28.ABCD is a trapezium with AB║DC. If AD=BC then prove that ∟BCD=∟ADC.

OR

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that

i)ΔAPB ~ ΔCQD

ii)AP = CQ

29.Draw the graph of the linear equation 2x – y = 4. From the graph, find the co-ordinates of the point where the line intersects y – axis.

30.Prove that the parallelograms on the same base and between the same parallels are equal in area.

31.Draw histogram and frequency polygon on the same graph for the following data :

Weight Numver of student

(in kg)

124–128 5

128–132 8

132–136 17

136–140 24

140–144 16

144–148 12

32.Two circles of radii 10 cm and 17 cm intersect at two points and distance between their centres is 21 cm. Find length of common chord.

33.A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

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