Provide CBSE previous year SA2 question paper of Mathematics [Class 9]
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Points : 25 ☺
Subject : Math
Class : 9 (CBSE)
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SUMMATIVE ASSESSMENT - II
MATHEMATICS
CLASS - IX
General instructions :
i) All questions are compulsory.
ii) The paper is divided into 4 sections- A,B,C,D.
iii) Attempt all sections separately.
iv) Use of calculator not permitted.
SECTION - A (1 x 4 = 4)
1) If the line (2k - 1)x + 5y + 7k - 3 = 10 passes through the origin,find k.
2) Find the coordinates of the point of intersection of the graph of its line 3x - 7y = 11 and x-axis.
3) A triangle and a parallelogram are on same base and between same parallels.Find the ratio of their areas.
4) The circumference of the base of a cone is 20 cm and its slant height is 11 cm. Find its LSA.
SECTION - B (2 x 6 = 12)
5) Find the length of the chord of a circle of diameter 34 cm given that the distance of the chords from the center is 8 cm.
6) (REFER TO THE PICTURE GIVEN BELOW)
In the figure, "O" is the center of the circle.If ∠PAO = 20° and ∠PBO = 25°.Find ∠AOB and ∠APB.
7) In parallelogram ABCD, the bisectors of ∠B and ∠D meet the sides of AD and BC at points P and Q. Prove that BP║DQ.
8) Five cubes of edge 10cm each are joined face to face.Find the TSA of the resulting cuboid.
9) 1000 families with 2 children were selected randomly and following data was recorded.
No. of boys in the family 1 0 2
No. of families 450 300 Rest
If a family is chosen at random,find the probability that it has (i) 1 girl (ii)no girl
10) Find the mean of first 13 prime numbers.
SECTION - C (3 x 8 = 24)
11) Draw the graph of equation 3x + 5y = 15. Write the co-ordinate where the graph intersect 'x' axis and 'y' axis. Find the area of triangle so formed.
12) Construct ΔABC in which BC = 7cm, AB+AC = 13cm, ∠C = 45°
13) 3 metallic spheres of diameters 6cm , 8cm and 10cm are melted to form a bigger sphere.
14) If the non-parallel sides of a trapezium are equal, show that trapezium is cyclic.
15) The median of the following data which is in ascending order is 19.Find the mean and mode.
7,13,18,18,x,x+2,22,25,27
16) In quadrilateral ABCD, AC and BD intersect at 'O'. If BO=DO and AB=CD, prove that ar(AOB) = ar(COD).
17) In ΔABC, AD is the median and E is the midpoint of AD. Prove that BE when produced trisects AC.
18) The volume of a cone of base diameter 14cm is 1232cm³. Find its TSA.
SECTION - D (4 x 10 = 40)
19) Construct ΔXYZ in which YZ = 8cm, ∠Y =60° and XZ - XY = 2cm
20) (REFER THE PICTURE 2 GIVEN BELOW)
From the figure, write the equations of lines L,M,N and P. Also write the coordinates of the vertices of quadrilateral ABCD and find the area.
21) Draw the combined histogram and frequency polygon of the following data.
CI 0-10 10-20 20-30 30-40 40-50
fi 8 12 15 10 5
22) Find the mean of the data in the above question (Q.21).
23) Show that the quadrilateral formed by joining the mid-points of the sides of a quadrilateral is a parallelogram.
24) Prove that the line joining the centers of 2 intersecting circles is the perpendicular bisector of their common chord.
25) A die is rolled 25 times and the outcomes are recorded as follows.
Outcomes 1 2 3 4 5 6
Frequency 9 4 4 7 1 0
Find the probability of getting (a) an even number, (b) a multiple of 3,
(c) a prime number, (d) a number neither prime nor even.
26) Prove that each pair of opposite angles of a cyclic quadrilateral is supplementary.
27) AB is diameter of a circle and chord CD is the radius. If AC and BD intersect at point 'P', outside the circles . Prove that ∠APB = 60.
28) How many bricks of dimension 25cm x 20cm x 10cm are required to build a wall if the dimensions are 5m x 3m x 2m,given that 10% of the wall is made of mortar?
Questions 29),30),31) are based on OTBA material provided to you.
Kindly go through the material provided to you and practice the questions given in the material.
MATHEMATICS
CLASS - IX
General instructions :
i) All questions are compulsory.
ii) The paper is divided into 4 sections- A,B,C,D.
iii) Attempt all sections separately.
iv) Use of calculator not permitted.
SECTION - A (1 x 4 = 4)
1) If the line (2k - 1)x + 5y + 7k - 3 = 10 passes through the origin,find k.
2) Find the coordinates of the point of intersection of the graph of its line 3x - 7y = 11 and x-axis.
3) A triangle and a parallelogram are on same base and between same parallels.Find the ratio of their areas.
4) The circumference of the base of a cone is 20 cm and its slant height is 11 cm. Find its LSA.
SECTION - B (2 x 6 = 12)
5) Find the length of the chord of a circle of diameter 34 cm given that the distance of the chords from the center is 8 cm.
6) (REFER TO THE PICTURE GIVEN BELOW)
In the figure, "O" is the center of the circle.If ∠PAO = 20° and ∠PBO = 25°.Find ∠AOB and ∠APB.
7) In parallelogram ABCD, the bisectors of ∠B and ∠D meet the sides of AD and BC at points P and Q. Prove that BP║DQ.
8) Five cubes of edge 10cm each are joined face to face.Find the TSA of the resulting cuboid.
9) 1000 families with 2 children were selected randomly and following data was recorded.
No. of boys in the family 1 0 2
No. of families 450 300 Rest
If a family is chosen at random,find the probability that it has (i) 1 girl (ii)no girl
10) Find the mean of first 13 prime numbers.
SECTION - C (3 x 8 = 24)
11) Draw the graph of equation 3x + 5y = 15. Write the co-ordinate where the graph intersect 'x' axis and 'y' axis. Find the area of triangle so formed.
12) Construct ΔABC in which BC = 7cm, AB+AC = 13cm, ∠C = 45°
13) 3 metallic spheres of diameters 6cm , 8cm and 10cm are melted to form a bigger sphere.
14) If the non-parallel sides of a trapezium are equal, show that trapezium is cyclic.
15) The median of the following data which is in ascending order is 19.Find the mean and mode.
7,13,18,18,x,x+2,22,25,27
16) In quadrilateral ABCD, AC and BD intersect at 'O'. If BO=DO and AB=CD, prove that ar(AOB) = ar(COD).
17) In ΔABC, AD is the median and E is the midpoint of AD. Prove that BE when produced trisects AC.
18) The volume of a cone of base diameter 14cm is 1232cm³. Find its TSA.
SECTION - D (4 x 10 = 40)
19) Construct ΔXYZ in which YZ = 8cm, ∠Y =60° and XZ - XY = 2cm
20) (REFER THE PICTURE 2 GIVEN BELOW)
From the figure, write the equations of lines L,M,N and P. Also write the coordinates of the vertices of quadrilateral ABCD and find the area.
21) Draw the combined histogram and frequency polygon of the following data.
CI 0-10 10-20 20-30 30-40 40-50
fi 8 12 15 10 5
22) Find the mean of the data in the above question (Q.21).
23) Show that the quadrilateral formed by joining the mid-points of the sides of a quadrilateral is a parallelogram.
24) Prove that the line joining the centers of 2 intersecting circles is the perpendicular bisector of their common chord.
25) A die is rolled 25 times and the outcomes are recorded as follows.
Outcomes 1 2 3 4 5 6
Frequency 9 4 4 7 1 0
Find the probability of getting (a) an even number, (b) a multiple of 3,
(c) a prime number, (d) a number neither prime nor even.
26) Prove that each pair of opposite angles of a cyclic quadrilateral is supplementary.
27) AB is diameter of a circle and chord CD is the radius. If AC and BD intersect at point 'P', outside the circles . Prove that ∠APB = 60.
28) How many bricks of dimension 25cm x 20cm x 10cm are required to build a wall if the dimensions are 5m x 3m x 2m,given that 10% of the wall is made of mortar?
Questions 29),30),31) are based on OTBA material provided to you.
Kindly go through the material provided to you and practice the questions given in the material.
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