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2012 Class IX Mathematics Sample Paper, Exercises of Mathematics

Mathematics

This is a sample mathematics paper for class ix, consisting of multiple choice questions, short answer type questions, and long answer type questions. The paper covers various topics such as equations, geometry, statistics, and probability.

Typology: Exercises

2012/2013

Uploaded on 04/30/2013

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Sample Paper – 2012
Class – IX
Subject – Mathematics
Time Allowed - 3hours M.M - 90
marks
►GENERAL INSTRUCTIONS
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A,B,C and D.
(iii) SECTION A are multiple choice questions carrying one mark each.
(iv) SECTION B are very short answer type questions carrying two marks each.
(v) SECTION C are short answer type questions carrying three marks each.
(vi) SECTION D are long answer type questions carrying four marks each.
(vii) Use of calculators and cell-phones are not permitted in the Examination Hall.
SECTION – A
Multiple choice questions Q1 to Q8, each carry 1 mark
► Write the correct answer in each of the following:
1. What is the value of m for which (−4, −1) a solution of the equation, −x + my = 1?
A. 5B. 3
C. −3D. −5
2. Use the following information to answer the next question.
x : 3 4 5 6 7 8
y : 2 6 10 14 18 22
The rule followed in the given relationship table is
A. 2x − 10 B. 3x + 10
C. 4x − 10 D. 5x + 10
3. If a cone and a cylinder of same radii have the same volume, then what is the ratio of
the heights of the cone and the cylinder?
A. 1 : 1 B. 1 : 2
C. 2 : 1 D. 3 : 1
4. A survey is conducted to know the number of mobile phones used in each family of a
certain locality of 1000 families. The given data shows the results of the survey.
Number of mobile phones: 5 4 3 2 1
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Sample Paper – 2012 Class – IX Subject – Mathematics Time Allowed - 3hours M.M - 90 marks ► GENERAL INSTRUCTIONS (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A,B,C and D. (iii) SECTION A are multiple choice questions carrying one mark each. (iv) SECTION B are very short answer type questions carrying two marks each. (v) SECTION C are short answer type questions carrying three marks each. (vi) SECTION D are long answer type questions carrying four marks each. (vii) Use of calculators and cell-phones are not permitted in the Examination Hall. SECTION – A Multiple choice questions Q1 to Q8, each carry 1 mark ► Write the correct answer in each of the following:

  1. What is the value of m for which (−4, −1) a solution of the equation, −x + my = 1? A. 5 B. 3

C. − 3 D. − 5

  1. Use the following information to answer the next question. x : 3 4 5 6 7 8 y : 2 6 10 14 18 22 The rule followed in the given relationship table is A. 2x − 10 B. 3x + 10

C. 4x − 10 D. 5x + 10

  1. (^) If a cone and a cylinder of same radii have the same volume, then what is the ratio of the heights of the cone and the cylinder?

A. 1 : 1 B. 1 : 2

C. 2 : 1 D. 3 : 1

  1. A survey is conducted to know the number of mobile phones used in each family of a certain locality of 1000 families. The given data shows the results of the survey. Number of mobile phones: 5 4 3 2 1

Number of families: 500 250 150 70 30 What is the probability that a randomly chosen family has 4 mobile phones? A. 1/2 B. 1/ C. 3/20 D. 7/

  1. (^) The given figure shows a solid whose bottom part is a cylinder and top part is a hemisphere

What is the ratio of the curved surface areas of the bottom part and the top part? A. r : h B. h : r C. h : 2r D. 2h : r

  1. The daily wages (in Rs) of six truck drivers are given as: 1,000, 500, 700, 300, 800, 400. What is the median of the given data? A. 600 B. 616. C. 800 D. 850.
  2. The radius of the given circle with centre O is 5 cm. If OP = 3 cm, then what is the length of chord XY?

A. 4 cm B. 6 cm C. 8 cm D. 12 cm

  1. The given figure shows a trapezium ABCD in which AB || CD. O is the point of intersection of diagonals AC and BD.

Which of the following relations is always true? A. Area (ΔACD) = Area (ΔDBC) B. Area (ΔDOC) = Area (ΔAOB) C. Area (ΔDOC) = Area (ΔBOC) D. Area (ΔADC) = Area (ΔABC SECTION - B Very Short Answer type questions Q9 to Q14, each carry 2 Marks

  1. In the given figure, AE = EB = AF = 2 cm and BCDE is a parallelogram. What is the length of FC?
  2. What is the measure of ∠ACD in the given figure?
  3. In the given figure, ABCD is parallelogram, AE∥DC and CF∥AD. If AB = 16 cm, AE= 8 cm and CF = 10 cm, find AD.

Height (in cm) Grade 120 − 130 130 − 140 140 − 150 150 − 160 160 − 170 6 22 25 15 27 11 7 12 33 24 22 9 8 15 34 21 17 13 9 21 25 13 29 12 10 9 17 42 15 17

What is the probability that the height of a randomly chosen student is less than 150 cm?

  1. 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

Number of surnames 1 − 4 4 − 6 6 − 8 8 − 12 12 − 20

(i) Draw a histogram to depict the given information. (ii) Write the class interval in which the maximum number of surname lie.

  1. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
  2. A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup. (use π=22/7) SECTION - D Long Answer type questions Q25 to Q34, each carry 4 Marks
  3. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
  4. Construct a triangle XYZ in which ∠Y = 30^0 , ∠Z = 90^0 and XY + YZ +ZX = 11 cm. Write also the steps of construction.
  1. The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see the following figure). Show that ar (ABCD) = ar (PBQR).
  2. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
  3. Two solid spheres made of the same metal have weights 5920g and 740g respectively. Determine the radius of the largest sphere, if the diameter of the smaller one is 5 cm.
  4. 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 the 12 edges?
  5. Draw the graph of the linear equation 3x + 4y = 6. At what points, the graph cuts the x-axis and the y-axis.
  6. The mean of the numbers 21, 30, 16, x, and 9 is 18. The median of the numbers 23, 30, 31,3x, 3x + y, 60, 67, and 69 is 47.5. What is the value of y?
  7. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Number of balls

Team A

Team B 1 − 6 7 − 12 13 − 18 19 − 24 25 − 30 31 − 36 37 − 42 43 − 48 49 − 54 55 − 60

Represent the data of both the teams on the same graph by frequency polygons.