Mathematics is the subject where you need more practice to score best marks. The more you solve problems the more you gain confidence and lower down the chances of committing mistake. This is vast subject and so to understand what is to be studied you need to view important questions published on the site of CBSE board. For 2011 following are the cbse important questions for class IX for Mathematic subject:
Surface area and volume
· The curved surface area of a right circular cylinder of height 14 cm is 88cm2. Find the diameter of the base of the cylinder.
· Curved surface area of a right circular cylinder is 4.4m2. If the radius of the base of the cylinder is0.7m, find its height.
· Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.Find
(i) the curved surface area and
(ii) the total surface area of a hemisphere of radius 21 cm.
· The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.
· Find the radius of a sphere whose surface area is 154cm2.
· A matchbox measures 4cm x 2.5cm x 1.5cm. What will be the volume of a packet containing 12 such boxes?
· A cubical water tank is 6m long, 5m wide and 4.5m deep. How many liters of water can it hold?
· The capacity of a cubical tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.3m and 10m.
· The height and the slant height of a cone are 21cm and 28 cm respectively. Find the volume of the cone.
· If the volume of a right circular cone of height 9cm is 48? cm3, find the radius of the base. (Use ?=3.14), 10(a) A triangle ABC with sides 5cm, 12cm and 13cm cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
· Find the volume of a sphere whose surface area is 154cm2.
· How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?
· Find the amount of the water displaced by a solid spherical ball of diameter
· Find the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel wad actually used, if 1/12 th of the steel actually used was wasted in making the tank.
· A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine (in mm3) is needed to fill this capsule?
· A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.
· The diameter of a metallic ball is 4.2cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3?
· A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kilolitres?
· The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28cm, find
(i) height of the cone
(ii) Slant height of the cone.
(iii) Curved surface area of the cone.
· A heap of the wheat is the form of a cone whose diameter is 10.5m and height is 3m. Find its volume. The heap is to be covered by congas to protect it from rain. Find the area of the canvas required.
· The circumference of the base of a cylindrical vessel is 132 cm and height is 25 cm. How many liters of water can it hold?
· A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.\
· A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?
· A hemispherical bowl is made of steel, 0.25cm thick. The inner radius of the bowl is 5cm. Find the ratio of their surface areas.
· A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50per m2.
· The floor of a rectangular hall has a perimeter 250m If the cost of painting the four walls at the rate of Rs 10per m2 is Rs 15000, find the height of the hall.
· Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the titles is Rs 360 per dozen.
· A plastics box 1.5 m long wide and 65 cm deep is to made. It is opened at the top. Ignoring the thickness of the plastics sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of the sheet for it, if a sheet measuring the box.
· A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm, wide and 25 cm high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all 12 edges?
· Savitri had to make a model of cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25cm with a 2.5 cm radius? (Use ?=22/7)
· A metal pipe is 77 cm long. The inner diameter of a cross section is 4cm, the outer diameter being 4.4 cm. Find its
(i) inner curved surface area.
(ii) Outer curved surface area.
(iii) Total surface area.
· In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
· The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding.
· A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6m, find the cost of painting it, given the cost of painting is Rs 5 per 100cm2.
· A village, having a population of 4000, requires 150liters of water per head per day. It has measuring 20m x 15 x 6m. For how many days will the water of this tank last?
· It cost Rs. 2200 to paint the inner curved surface of a cylinder of a cylinder vessel 10 deep. If the cost of painting is at the rate of Rs 20per m2, find
(i) inner curved surface area of the vessel.
(ii) Radius of the base,
(iii) Capacity of the vessel.
· The value of ? up to 50 decimal places is given below: 3.14159265658979323846264338327950288419716939937510 (i) make the frequency distribution of the digits from o to 9 after the decimal point. (ii) What are the most and the least frequency occurring digits?
· A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2-2.5.
· The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:
|Length in mm||Number of leaves|
(i) Draw a histogram to represent the given data.
(ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum numbers of leaves are 153mm long? Why?
· A random survey of the number of children of various age groups playing in a park was found as follows:
|Age (in years)||Numbers of children|
Draw a histogram to represent the data above
· The height (in cm) of 9 students of a class are as follows:155 160 145 149 150 147 152 144 148; Find the median of this data.
· The points scored by a Kabaddi team in a series of matches are as follows:17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28 Find the median of the points scored by the team.
· Find the mode of the following marks (out of 10) obtained by 20.4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9.
· The following number of goals were scored by a team in a series of 10 matches 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median, mode of those scores.
· In a mathematics test given to 15 students, the following marks (out of 100) are: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, and 60 Find the mean, median, mode of those scores.
· The following observations have been arraigned 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
· Find the mean salary of 60 workers of a factory from the following table:
|Salary (in Rs)||Number of workers|
· Find the missing (?) frequencies in the following frequency distribution if it is known that the mean of the distribution is 1.46.
|Number of accidents (x)||0||1||2||3||4||5||Total|
Linear equation in two variables
· Find four different solutions of the equation x+2y=6.
· Find two solutions for each of the following equations:
(i) 4x + 3y = 12
(ii) 2x + 5y = 0
(iii) 3y + 4=0
· Write four solutions for each of the following equations:
(i) 2x + y = 7
(ii) ?x + y = 9
(iii) x = 4y.
· Given the point (1, 2), find the equation of the line on which it lies. How many such equations are there?
· Draw the graph of the equation
(i) x + y = 7
(ii) 2y + 3 = 9
(iii) y – x = 2
(iv) 3x – 2y = 4
(v) x + y – 3 = 0
· Draw the graph of each of the following linear equations in two variables:
(i) x + y = 4
(ii) x – y = 2
(iii) y = 3x
(iv) 3 = 2x + y
(v) x – 2 = 0
(vi) x + 5 = 0
(vii) 2x + 4 = 3x + 1.
· If the point (3, 4) lies on the graph of the equation 3y=ax+7, find the value of ‘a’.
· Solve the equations 2x + 1 = x – 3, and represent the solution(s) on
(i) the number line,
(ii) the Cartesian plane.
· Draw a graph of the line x – 2y = 3. From the graph, find the coordinates of the point when
(i) x = – 5
(ii) y = 0.
· Draw the graph of y = x and y = – x in the same graph. Also, find the coordinates of the point where the two lines intersect.
· Prove that 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.
· Show that each angle of a rectangle is a right angle.
· Show that the diagonal of a rhombus are perpendicular to each other.
· ABC is an isosceles triangle in which AB=AC. AD bisects exterior angle PAC and CD||AB. Show that
(i) angle DAC=angle BCA and
(ii) ABCD is a parallelogram (||gm)
· Show that the bisectors of the angles of a parallelogram form a rectangle.
· 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
· If the diagonal of a parallelogram are equal, then show that it is a rectangle.
· Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
· Show that the diagonals of a square are equal and bisect each other at right angles.
· Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
· In a parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ. Show that, AP=CQ, AQ=CP, APCQ is a parallelogram.
· In ? ABC and ? 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
(vi) ? ABC ? DEF.
· 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
(iii) PQRS is a parallelogram.
· 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.
· 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.
· Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
· 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.