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Right foundation at the right stage is the most important factor in the success of any student in exam and in life the APEX IIT / PMT foundation program is aimed at students studying in class IX, who aspire to prepare for engineering / medical entrance in future. The program keeps the school curriculum as base and further upgrades the students’ knowledge to meet the requirements of competitive exams. The program has been design in a way so as to develop orientation of the students as well as to motivate him to excel in competitive exams.

Four Year Classroom Program is the ideal program for students who wish to start early in their quest for a seat at the IITs. This program helps the student not only to excel in IIT-JEE but also in Olympiads & KVPY by building a strong foundation, enhance their IQ & analytical ability and develop parallel thinking processes from a very early stage in their academic career. Students joining this program will have more time to clear their fundamentals and practice extensively for IIT-JEE, their ultimate goal!

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- 1. APEX INSTITUTE IIT-JEE AIPMT NTSE OLYMPIAD SA-2 To know more about our courses call 999 0495 952, 991 0817 866 Summative Assessment-II (Summative Assesment-2) (Three Mock Test Papers) Sample Paper (for Class 9th Students) “NO GOAL IS TOO HIGH IF WE CLIMB IT WITH CARE, CONFIDENCE & COMMITMENT” APEX INSTITUTE IIT-JEE AIPMT NTSE OLYMPIAD
- 2. MODEL PAPER CLASS-IX -2014 Class – IX Subject – MATHEMATICS Sample Paper-1 Time: 3 hours Maximum Marks: 80 General Instruction: 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into four sections A, B, C and D. Section- A comprises of10 questions of 1mark each, Section- B comprises of 8 questions of 2 marks each, Section -C comprises of 10 questions of 3 marks each and Section- D comprises of 6 questions of 4 marks each. 3. Question numbers 1 to 10 in Section- A are multiple choice questions where you are to select one correct option out of the given hour. 4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 4 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such question. 5. Use of calculator is not permitted. 6. An additional 15 minutes time has been allotted to read this question paper only. SECTION –A Question number 1 to 10 carry 1 mark each. 1. For what value of k, x=2 and y=-1 is a solution of x+3y-k=0: (A) -1 (B) 2 (C) -2 (D) 3 2.The mean of prime numbers between 20 and 30 is: (A) 21 (B) 26 (C) 25 (D) 27 3. If the diagonals AC and BD of a quadrilateral ABCD bisect each other, then ABCD is a: (A) parallelogram (B) rectangle (C) rhombus (D) trapezium 4. The height of a right circular cylinder with lateral surface area 792 sq cm is 21. The diameter of the base is: (A) 3cm (B) 6cm (C) 12cm (D) 24cm 5. The diagonals of a parallelogram PQRS intersect at O. If QOR= 900 and 0 0 0 0 (A) 90 (B) 40 (C) 70 (D) 50 6. Which of the following is a linear equation in one variable: (A) 2x+3y=0 (B) x2 =5x+3 (C) 5x=y2+3 (D) x+5=6 QSR=500 , then ORS is 7. D and E are the points on the sides AB and AC respectively of triangle ABC such that DE||BC. If area of DBC =15cm2 then area EBC is: 2 2 2 (A) 30cm (B) 7.5cm (C) 15cm (D) 20cm2 8. AD is a diameter of a circle and AB is chord. If AD= 34 cm and AB =30 cm, the distance of AB from the centre of the circle is: (A) 17cm (B) 15cm (C) 4cm (D)8cm 9. The median of a triangle divide it into two Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 3. MODEL PAPER CLASS-IX -2014 (A) Triangles of equal area (B) Right triangles (C) Equilateral triangles (D) Isosceles triangles. 10. Three angles of a quadrilateral are 700, 1200 and 650. Then fourth angle of the quadrilateral is: (A) 950 (B) 750 (C) 1050 (D) 900 SECTION- B Question numbers 11 to 18 carry 2 marks each. 11. A river 3m deep and 40 m wide is flowing at the rate of 2km/hour. How much water will fall into the sea in one minute? 12. Two circles intersect at two points A and B. AD and AC are diameters to the two circles. Prove that B Lies on the line segments DC. 13. Find the coordinates of the points where the line 2x-y=3 meets both the axis. 14. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Assume π = 22/7. 15. Following table shows the marks obtained by 30 students in a class test: Marks Obtained 70 58 60 52 65 75 68 Number of Students 3 5 4 7 6 2 3 Find the probability that a student secures (a) 60 marks (b) Less than 60 marks. 16. Show that diagonals of a square are equal and bisect each other at right angles. 17. Curved surface area of a cone of radius 4cm is 20π cm2 . Find total surface area of the same cone in terms of π. 18. In A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. SECTION –C Question numbers 19 to 28 carry 3 marks each. 19. The radius of a spherical balloon increases from 7 cm to 14cm as air is pumped into it. Find the ratio of surface areas of the balloon in two cases. 20. The median of the following observations arranged in arranged in ascending order is 27. Find x. 13, 15, 17, 21, x+2, x+4, 32, 37, 41, and 48. 21. Obtain the mean of the following data: Variable (xi) 4 6 8 10 12 Frequency (fi) 4 8 14 11 3 Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 4. MODEL PAPER CLASS-IX -2014 22. XY is a line parallel to side BC of a triangle ABC. If BE||AC and CF||AB meet XY at E and F respectively. Show that area ABE=area ACF. 23. The food charges in a hostel are as follows: For the first day, the charges are Rs.100 and for the subsequent days it is Rs 50 per day. Taking the number of days as x and total charges as Rs y, write a linear equation for this information and draw its graph. 24. Two parallel liners l and m are intersected by a transversal p. Show that the quadrilateral formed by the bisectors of interior angles as a rectangle. 25. Sum of the digits of a two digit number is 14. If we add 18 to the original number, the digits interchange their places. Write two equations for these two statements. 26. Construct a triangle PQR with base PQ=8.4cm, P=450 and PR-OR=2.8cm 27. The radius and height of a cone are in the ratio 4:3. The area of its base 154cm2. find its curved surface area. 28. The following table gives the distribution of students of two sections according to the marks obtained by them. Section A Section B Marks Frequency Marks Frequency 0-10 2 0-10 5 10-20 12 10-20 11 20-30 18 20-30 15 30-40 13 30-40 12 40-50 5 40-50 7 Represent the marks of the students of both the sections on the same graph by two frequency polygons. SECTION- D Question numbers 29 to 34 carry 4 marks each. 29. The two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection; prove that the chords are equal. Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 5. MODEL PAPER CLASS-IX -2014 30. The distribution of weight (in kgs) of 100people is given below. Weight in kg Frequency 40-50 13 45-50 25 50-55 28 55-60 15 60-65 12 65-70 5 70-75 2 Construct a histogram for the above distribution. 31. The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10m, how much concrete mixture would be required to build 14 such pillars? 32. Prove that parallelograms on the same base and between the same parallels are equal in area. 33. Draw the graphs of each of the equation-2y-3=0 and 4x+3y-1=0 on the same graph. 34. 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. Show that area ABCD=area PBQR. Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 6. MODEL PAPER CLASS-IX -2014 Class – IX Subject – MATHEMATICS Sample Paper-2 Max. Marks : 90 Allotted Time : 3 Hrs SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. In the given figure, PQRS is a rectangle. If ∠RPQ = 30°, then the value of (x + y) is : (a) 90° (b) 120° (c) 150° (d) 180° 2. In the figure, if area of parallelogram ABCD is 30 cm2, then ar (ADE) + ar (BCE) is equal to : (a) 20 cm2 (b) 30 cm2 (c) 15 cm2 (d) 25 cm2 3. In the figure, chord AB is greater than chord CD. OL and OM are the perpendiculars from the centre O on these two chords as shown in the figure. The correct relation between OL and OM is : (a) OL = OM (b) OL < OM (c) OL > OM (d) none of these 4. Ratio of the volume of a cone and a cylinder of same radius of base and same height is : (a) 1 : 1 (b) 1 : 2 (c) 1 : 3 (d) 1 : 4 5. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are written in ascending order. If median of data is 63, then x is : (a) 62 (b) 63 (c) 124 (d) 126 6. In the given figure, ABCD is a rhombus. If ∠ OAB = 35°, then the value of x is (a) 25° (b) 35° (c) 55° (d) 70° 7. If the slant height of a cone is 13 cm and the base radius is 5 cm, then the height of cone is : (a) 12 cm (b) 8 cm (c) 10 cm (d) 18 cm 8. If P(E) denotes the probability of an event E, then : (a) P(E) < 0 (b) P(E) >1 (c) 0 < P(E) < 1 (d) –1 < P(E) < 1 Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/ :
- 7. Our Result reflects our excellence and credibility CBSE Class 12th Result 2013 IIT-Main 2013 521 93.6% 93.6% P:93,C: 90,M:95 P:91,C: 98,B:90 Prerna Kashyap Amity International Rank 96% P:95,C: 96,M:95 Anagha Tripathi DAV Noida 91% Prachi Sarawat DAV Noida 90% 88.8% P:91,C: 98,M:86 P:95,C: 96,M:95 P:90,C:93 ,M:95 Prerna Kashyap Student of two year classroom Program for IIT-JEE Sneha K. St. Thomas 96% in CBSE 86% P:95,C: 96,M:95 Sanchit D.P.S. Indirapuram 85.2% Shilpi Garg I.P.S. Indirapuram 83% 81% P:80,C:90 P:83,C: 85,M:83 P:80,C: 82, P:87,C: 80,M:95 Shubham Shakya Danish Rafi St. Thomas Mridul G.P.S. Delhi Paras Ghai Ryan International Classroom Teaching D. P. on P.& a lat ss es ign tp m att en ern t Re vis ion &A ITS of pro ial rn ater tte Pa dy m stu ay nd t Su tes lar se gu ha Re t & P tes Doubt clearing& intensive care session Vanasthali Public school FREE DEMO CLASSES Before joining any institute, attend FREE Demo classes and you still find better classes,go & join Congratulations !!! All our students selected in IIT-Mains 2013 Akshay Agarwal Prerna Kashyap Saurabh Bisht Sanchit Adarsh Rishabh Mehta Saurabh Singh Anirudh Kalia Shubham Shakya Cambridge Indirapuram Amity International D.P.S. Indirapuram D.P.S. Indirapuram I.P.S. Indirapuram Summerville school Father Agnel Noida Indus Valley Noida Vanasthali Public school Ghaziabad APEX INSTITUTE Indirapuram 62, Nitikhand-III, Near Jaipuriya Sunrise. Vaishali 1030-31,Sec-3 Near Mahagun Metro mall. Raj nagar 27-C R.D.C. Raj nagar, near Bikaner sweet. IIT-JEE AIPMT NTSE OLYMPIAD To know more about our courses call 999 0495 952, 991 0817 866 www.apexiit.co.in/
- 8. MODEL PAPER CLASS-IX -2014 SECTION B (Question numbers 9 to 14 carry 2 marks each.) 9. The cost of 6 eggs is the same as the cost of one bread. Express this statement as a linear equation in two variables. (Take the cost of one egg to be Rs x and that of a bread to be Rs y). 10. In the figure, ABCD is a quadrilateral and BD is one of its diagonals. Show that ABCD is a parallelogram and find its area. 11. In the figure, ABCD is a rectangle. P and Q are the mid-points of AD and DC respectively. Find the length of PQ. 12. AOB is a diameter of a circle and C is a point on the circle. Check whether AC2 + BC2 = AB2 is true or not. 13. If the edge of a cube is doubled, what is the ratio of the volume of the first cube to that of the second cube? 14. A die is thrown 225 times and the results were as follows : Find the probability of getting a prime number. SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. Draw the graph of the equation 2y . x = 7 and determine from the graph whether x = 3, y = 2 is its solution or not. 16. Determine the point on the graph of the linear equation 2x + 5y = 19 whose ordinate is 1.5 times its abscissa. 17. ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are the mid-points of the non-parallel sides. Show that the ratio of ar(ABFE) and ar(EFCD) is (3a + b) : (a + 3b). 18. Construct a triangle whose sides are 4.2 cm, 3.9 cm and 6.1 cm. Bisect its greatest angle and measure each part. 19. If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ≡ arc PYB. 20. The total surface area of a solid cylinder is 462 cm2 and its curved surface area is one third of its total surface area. Find the radius of the cylinder. 21. A hemispherical vessel full of water is emptied in a cone. The radii of the vessel and the cone are 12 cm and 8 cm respectively. Find the height of the water in the cone. Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 9. MODEL PAPER CLASS-IX -2014 22. Prepare a continuous grouped frequency distribution from the following data : Also find the size of class intervals. 23. Show that if diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. 24. A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 and that of boys is 71. Find the mean score of the whole class. SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. Draw the graph of the linear equation 2x + 3y = 12. At what points, the graph of the equation cuts the xaxis and the y-axis? 26. E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram. 27. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium. 28. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 29. The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone. 30. Draw a histogram for the following data : 31. Show that the diagonals of a rhombus are perpendicular to each other. Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 10. MODEL PAPER CLASS-IX -2014 32. Show that a diagonal of a parallelogram divides it into two congruent triangles and hence prove that the opposite sides of a parallelogram are equal. 33. The parking charges of a car in a parking lot is Rs 30 for the first two hours and Rs 10 for subsequent hours. Taking total parking time to be x hours and total charges as Rs y, write a linear equation in two variables to express the above statement. Draw a graph for the linear equation and read the charges for five hours 34. Metal spheres, each of radius 2 cm are packed into a rectangular box of dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed in the box, it is filled with preservative liquid. Find the volume of this liquid to the nearest integer. [use π = 3.14] Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 11. MODEL PAPER CLASS-IX -2014 Class – IX Subject – MATHEMATICS Sample Paper-3 Max. Marks : 90 Allotted Time : 3 Hrs SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. Diagonals of a parallelogram ABCD intersect at O. If ∠ BOC = 90° and ∠ BDC = 50°, then ∠ OAB is : (a) 90° (b) 50° (c) 40° (d) 10° 2. In the figure, the area of parallelogram ABCD is : (a) AB × BM (b) BC × BN (c) DC × DL (d) AD × DL 3. In the figure, AB and CD arc two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively, if ∠ POQ = 150°, then ∠ APQ is : (a) 30° (b) 75° (c) 15° (d) 60° 4. The class mark of the class 90-120 is : (a) 90 (b) 105 (c) 115 (d) 120 5. The total surface area of a cube 96 cm2. The volume of the cube is : (a) 8 cm3 (b) 512 cm3 (c) 64 cm3 (d) 27 cm3 6. In the figure, if ∠ ABC = 20°, then ∠ AOC is equal to : (a) 20° (b) 40° (c) 60° (d) 10° 7. Base area of a cylinder is 154 sq cm. Its height is 5 cm. Then its volume is : (a) 308 cubic cm (b) 770 cubic cm (c) 525 cubic cm (d) 600 cubic cm 8. In a class, there are x girls and y boys. A student is selected at random, then the probability of selecting a boy is : (a) (b) (c) (d) SECTION B (Question numbers 9 to 14 carry 2 marks each.) 9. Write each of the following equations as equations in two variables. Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/
- 12. MODEL PAPER CLASS-IX -2014 (i) x = 17 (ii) y = –5 10. Show that each angle of a rectangle is a right angle. 11. The lengths of the diagonals of a rhombus are 24 cm and 18 cm. Find the length of each side of the rhombus. 12. Calculate the length of a chord which is at a distance 5 cm from the centre of a circle whose radius is 13 cm. 13. The rectangular sheet of paper 22 cm × 15 cm is rolled along its length to form a hollow cylinder. Find the radius of the cylinder thus formed. 14. In a sample study of 420 people, it was found that 240 people were government employees. If a person is selected at random, find the probability that the person is not a government employee. SECTION C (Question numbers 15 to 24 carry 3 marks each.) 15. Draw the graph of the equation 5x – 3y = 1. Find four solutions of the equation. Using the graph check whether x = 2 and y = 3 is a solution of the equation. 16. In a parallelogram, AP and CQ are perpendiculars from A and C on its diagonal BD. Prove that AP = CQ. 17. In the figure, PSDA is a parallelogram, points Q and R are taken on PS such that PQ = QR = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD). 18. Construct a ∆ XYZ in which ∠ Y = 30°, ∠ Z = 90° and XY + YZ + ZX = 11 cm. 19. Find the points where the graph of the equation 3x + 4y = 12 cuts the x-axis and the y-axis. 20. A sphere of radius r has been cut into two hemispheres. Find the ratio of the surface area of the original sphere to the total surface area of the two hemispheres. 21. The dimensions of a cuboid are in the ratio 3 : 2 : 1. If the lateral surface area of the cuboid is 360 cm2, find its total surface area. 22. Find the median of 40, 42, 120, 99, 61, 92, 71, 58, and 58. If 56 is replaced by 85 then find the new Median. 23. In a one day cricket match, a batsman played 40 balls. The runs scored are as follows : Find the probability that the batsman will score (i) 6 runs (ii) 0 or 4 or 6 runs. 24. Prove that equal chords of a circle subtend equal angles at the centre. SECTION D (Question numbers 25 to 34 carry 4 marks each.) 25. The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/ .
- 13. MODEL PAPER CLASS-IX -2014 (i) If the temperature is 86°F, what is the temperature in Celsius ? (ii) If the temperature is 35°C, what is the temperature in Fahrenheit ? (iii) If the temperature is 0°F, what is the temperature in Celsius ? (iv) What is the numerical value of the temperature which is same in both the scales ? 26. ABC is an isosceles triangle in which AB = AC. A circle passing through B and C intersects AB and AC at D and E respectively. Prove that BC || DE. 27. In the figure, AP || BQ || CR. Prove that ar(AQC) = ar(PBR) 28. Show that the diagonals of a rhombus are perpendicular to each other. 29. A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface area of the solid thus generated. 30. Draw a frequency polygon for the following distribution. 31. ABCD is a parallelogram. On diagonal BD are points P and Q such that DP = BQ. Show that APCQ is a parallelogram. 32. Circumference of the base of a cylinder, open at the top, is 132 cm. The sum of radius and height is 41 cm. Find the cost of polishing the outer surface area of cylinder at the rate Rs 10 per square dm (decimetre). 33. Construct a histogram for the following data : 34. A water tank is getting filled up by water flowing at the rate of 15 cm3/sec. If the volume of water filled in y seconds is x cm3, write a linear equation in two variables to represent this situation. Draw a graph for the equation formed and hence find the volume of water filled in 9 seconds. Head office: 62, Nitikhand-III, Indirapuram, Ghaziabad. Call us +91-9910817866 +91-9990495952 +91-9310122993| http://www.apexiit.co.in/

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