# Class 9- sample paper

Sample questions for 9th Grade ã Mathematics- Paper 1

Questions 1 to 10 are 1 marks each. Each question is provided with 4 choices out of which only one is correct. Choose the correct one.

1. If the mean of the observations x, x+3, x+5, x+7 and x+10 is 9, the mean of last three terms is

(a) 10ã (b) 10ã

(c) 10ã (d) 11ã

1. To draw histogram to represent following distribution
 CI 5ã10 10ã15 15ã25 25ã45 45ã75 F 6 12 10 8 15

the adjusted frequency for class 25ã45 is

(a) 6 (b) 5

(c) 3 (d) 2

1. If every side of cube is doubled, its volume will become

(a) twice (b) four times

(c) eight times (d) thrice

1. A tank 10m û 5m û 6m is full of water. How much water must be taken out to reduce the water level by 1m

(a) 30m2 (b) 100m3

(c) 50m2 (d) none of these

1. If x+3 divides x2 + kx + 12, then k =

(a) 4 (b) 3

(c) 1 (d) 7

1. If a2 + 1 = 7, then a + 1 =

a2 a

(a) ã7 (b) ã5

(c) 3 (d) 2ã2

1. If a + b+ c = 0, then a3 + b3 + c3 =

(a) 3abc (b) 0

(c) abc (d) none of these

1. If x = 9 and y = ã17, then the value of (x2 ã y2)ãã is

(a) ô§ (b) ô¥

(c) ã4 (d) 1

1. A cylindrical tank having internal radius and depth 7cm and 30cm respectively is given. How many litres of milk can be contained by the vessel

(a) 4.62L (b) 4620000L

(c) 46.2L (d) 462L

1. A rational number between ã2 and ã3 is

(a) ã2 + ã3 (b) ã2 .ã3

2 2

(c) 1.5 (d) 1.8

Questions 11 and 12 are 3 marks each

1. Factorize 2x3 ã 5x2 ã 19x + 42
2. The total surface area of right circular cylinder is 231cm2. If its curved surface area is ã of its total surface, determine its radius and height.

Questions 13 is of 4 marks.

1. The number of dolls produced by a factory per day in last 36 days are as follows
 30 32 28 24 20 25 38 37 40 43 16 20 19 24 27 30 32 34 35 42 27 28 19 34 38 39 42 29 15 27 27 22 29 31 19 18
1. Prepare a frequency distribution table with a class size of 5.
2. Find the range.
3. How many days the production was less than 25 dolls. (2ô§ + 1 + ô§ )

Sample questions for 9th Grade Mathematics- Paper 2

SECTION A

(2 marks each)

1. Find the remainder when p (x) = 4x4 - 3x3 – 2x2 + x -7 is divided by (x + ).

2. What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane? Write the name of the point and its coordinates where these two lines intersect?

3. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

4. The class marks of a distribution are:

105,115,125,135,145,155,165,175.

Find the class size and class limits.

5. Find the probability that a number selected at random from the numbers 1,2,3ãÎ 35 is a prime number.

## SECTION B

(3 marks each)

6.Find the mean and mode for the data:

 xi 50 60 70 80 90 100 110 120 fi 10 18 15 20 8 6 12 11

7. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that AD bisects BC and AD bisects A.

Show that the line segments joining the midpoints of the opposite sides of a quadrilateral bisects each other.

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

9. The sides of a triangular plot are in the ratio of 3: 5: 7 and its perimeter is 300m. Find its area.

## SECTION C

(5 marks each)

10. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required. OR

11.Two parallel sides of a trapezium are 120 cm and 154 cm and other sides are 50 cm and 52 cm. Find the area of trapezium.

12. Construct a triangle ABC in which BC = 7 cm, B = 75o and AB + AC = 13 cm. Write steps of construction. Also justify the construction.

13.Draw the graph of equation 2x + y = 5. Use it to find two more solution of this equation. Verify from graph that x = 3, y = – 1 is a solution of given equation.