Class 9 Cbse Maths Sample Paper Model 1Sunaina Rawat
This document contains a sample test paper for mathematics for class 9. It has 37 multiple choice questions divided into 4 sections - A, B, C and D. Section A contains 10 one-mark questions. Section B has 9 two-mark questions. Section C contains 10 three-mark questions. Section D has 8 four-mark questions. The paper tests concepts related to algebra, geometry, trigonometry, statistics and probability. Students are instructed to answer all questions within the given time of 3 hours.
Class 9 Cbse Maths Sample Paper Model 1Sunaina Rawat
This document contains a sample test paper for mathematics for class 9. It has 37 multiple choice questions divided into 4 sections - A, B, C and D. Section A contains 10 one-mark questions. Section B has 9 two-mark questions. Section C contains 10 three-mark questions. Section D has 8 four-mark questions. The paper tests concepts related to algebra, geometry, trigonometry, statistics and probability. Students are instructed to answer all questions within the given time of 3 hours.
Prova Canguru da Matemática - 6º ano - 2016Célio Sousa
1) O documento apresenta 24 problemas matemáticos de múltipla escolha para estudantes do nível E. 2) Os problemas variam de 3 a 5 pontos e envolvem tópicos como soma de dados, conversão de semanas para dias, reconhecimento de padrões numéricos e geométricos. 3) As respostas corretas para cada problema são identificadas por letras entre parênteses.
Lista 02 exercícios de função do 1º grau (gabarito)Manoel Silva
1) O custo total de produzir x peças é dado pela função C(x) = 0,5x + 8. O custo de produzir 100 peças é R$ 58,00.
2) As funções que representam o custo total de cada plano de saúde em função do número x de consultas são: Plano A = 50x + 100 e Plano B = 40x + 180.
3) A lista apresenta exercícios de funções afins do 1o grau, incluindo construção de gráficos e determinação de equações a partir de pontos dados.
1) The document is about a full length MCAT paper with 220 multiple choice questions covering physics and chemistry.
2) Sample physics questions include momentum, dimensions, torque, terminal velocity, strain, and waves/oscillations.
3) Sample chemistry questions cover topics like gases, thermodynamics, equilibrium, kinetics, periodic trends, and organic/inorganic reactions.
Cbse class ix sample papers for Summative assessmentAPEX INSTITUTE
This document provides an unsolved model test paper for mathematics for 9th standard students in India. It consists of 4 sections - Section A with 8 multiple choice questions carrying 1 mark each, Section B with 6 questions carrying 2 marks each, Section C with 12 questions carrying 3 marks each, and Section D with 8 questions carrying 4 marks each. The test covers topics in mathematics like linear equations, coordinate geometry, trigonometry, mensuration, statistics, and probability. The document provides the instructions, questions and some supporting diagrams for the test but does not include the answers. The total marks for the test are 90.
AULA 11 - EQUAÇÃO DO 2° GRAU - RECONHECER UMA EQUÇÃO DO 2° GRAU.pptxFernandaMarcelinoCor
O documento apresenta uma aula sobre equações do 2° grau. O objetivo é compreender os processos de fatoração de expressões algébricas com base em produtos notáveis para resolver problemas representados por equações polinomiais do 2° grau. O conteúdo aborda o reconhecimento de uma equação do 2° grau, apresentando exemplos de aplicações no cotidiano.
mathematics-question-bank-for-summative-assesmentAPEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
Prova Canguru da Matemática - 6º ano - 2016Célio Sousa
1) O documento apresenta 24 problemas matemáticos de múltipla escolha para estudantes do nível E. 2) Os problemas variam de 3 a 5 pontos e envolvem tópicos como soma de dados, conversão de semanas para dias, reconhecimento de padrões numéricos e geométricos. 3) As respostas corretas para cada problema são identificadas por letras entre parênteses.
Lista 02 exercícios de função do 1º grau (gabarito)Manoel Silva
1) O custo total de produzir x peças é dado pela função C(x) = 0,5x + 8. O custo de produzir 100 peças é R$ 58,00.
2) As funções que representam o custo total de cada plano de saúde em função do número x de consultas são: Plano A = 50x + 100 e Plano B = 40x + 180.
3) A lista apresenta exercícios de funções afins do 1o grau, incluindo construção de gráficos e determinação de equações a partir de pontos dados.
1) The document is about a full length MCAT paper with 220 multiple choice questions covering physics and chemistry.
2) Sample physics questions include momentum, dimensions, torque, terminal velocity, strain, and waves/oscillations.
3) Sample chemistry questions cover topics like gases, thermodynamics, equilibrium, kinetics, periodic trends, and organic/inorganic reactions.
Cbse class ix sample papers for Summative assessmentAPEX INSTITUTE
This document provides an unsolved model test paper for mathematics for 9th standard students in India. It consists of 4 sections - Section A with 8 multiple choice questions carrying 1 mark each, Section B with 6 questions carrying 2 marks each, Section C with 12 questions carrying 3 marks each, and Section D with 8 questions carrying 4 marks each. The test covers topics in mathematics like linear equations, coordinate geometry, trigonometry, mensuration, statistics, and probability. The document provides the instructions, questions and some supporting diagrams for the test but does not include the answers. The total marks for the test are 90.
AULA 11 - EQUAÇÃO DO 2° GRAU - RECONHECER UMA EQUÇÃO DO 2° GRAU.pptxFernandaMarcelinoCor
O documento apresenta uma aula sobre equações do 2° grau. O objetivo é compreender os processos de fatoração de expressões algébricas com base em produtos notáveis para resolver problemas representados por equações polinomiais do 2° grau. O conteúdo aborda o reconhecimento de uma equação do 2° grau, apresentando exemplos de aplicações no cotidiano.
mathematics-question-bank-for-summative-assesmentAPEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
The document discusses the benefits of meditation for reducing stress and anxiety. Regular meditation practice can help calm the mind and body by lowering heart rate and blood pressure. Studies have shown that meditating for just 10-20 minutes per day can have significant positive impacts on both mental and physical health.
This document contains the details of a 9th class mathematics exam, including instructions, questions, and solutions. It provides 34 multiple choice and short/long answer questions on topics like coordinate geometry, trigonometry, probability, statistics, and mensuration. The questions range from 1-5 marks each. Detailed step-by-step solutions are provided for some questions.
The document provides information about scale drawings and building plans used in the construction of homes. It discusses scale drawings and scale factors, explaining how to convert between plan measurements and actual field measurements. It then describes the different types of plans used in construction, including survey plans, site plans, floor plans, and elevations. Survey plans show the boundaries of a property. Site plans show where a structure will be situated on a lot. Floor plans provide dimensions and details of rooms, doors, windows, and wall thicknesses.
The document discusses the importance of summarization techniques for extracting key information from lengthy documents. Automatic summarization systems aim to generate concise summaries while retaining the most important concepts and facts from the original text. However, accurately summarizing documents continues to be a challenging task that sees ongoing research and development of new approaches.
This document provides guidelines for creating effective assessment tests for students. It outlines objectives such as understanding teaching effectiveness, assessing student understanding, and identifying weaknesses. It describes preparatory activities for students like completing the syllabus and revising. Test scheduling and formatting are also addressed, emphasizing clear organization, appropriate length and difficulty, and child-friendly language. Quality control measures include validation by parallel teachers and subject conveners. Post-test analysis provides feedback to improve instruction and help students.
This document provides guidelines for developing a blueprint for the 1st Professional Examination of the MD Program at Universiti Putra Malaysia. It defines what a blueprint is and its purposes, which include providing an overview of the exam format and content areas. The document outlines the structural components of a blueprint, which include tables showing exam question types and weightings, topics and learning objectives, and the number and distribution of questions. It emphasizes ensuring content validity and coverage of learning objectives. Developing a blueprint can guide students' learning approaches and influence how assessment defines the curriculum.
A blueprint provides a detailed guide for developing an assessment. It outlines the key topics to be covered, learning objectives to be assessed, and the number and type of questions to include. The document presented discusses how to create a blueprint by analyzing content, determining learning objectives based on Bloom's taxonomy, allocating questions to each topic based on objectives, and specifying question types and their weightings. Blueprints benefit students, teachers and administrators by ensuring assessments comprehensively and validly measure the intended curriculum.
The document contains 8 math word problems involving the calculation of surface areas and volumes of various shapes. The problems require determining the surface area or cost of materials needed based on given dimensions of boxes, rooms, halls, and other objects. Formulas for lateral surface area and total surface area of cubes, cuboids, and other rectangular prisms are applied. The document provides the questions, formulas used, working steps, and answers for each problem.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help regulate emotions and stress levels.
This document provides instructions for a summative assessment math exam for Class 10 CBSE. It states that the exam is 3 hours long and consists of 34 questions divided into 4 sections (A, B, C, D). Section A has 8 multiple choice 1-mark questions. Section B has 6 2-mark questions. Section C has 10 3-mark questions. Section D has 10 4-mark questions. Calculators are not permitted and an extra 15 minutes is provided to read the paper only. The document then provides the first few questions in Section A as examples.
The document provides instructions for a summative assessment math exam for Class 10 CBSE. It states that the exam will be 3 hours long and consist of 34 questions divided into 4 sections (A-D). Section A has 9 multiple choice questions worth 1 mark each. Section B has 6 questions worth 2 marks each. Section C has 10 questions worth 3 marks each. Section D has 10 questions worth 4 marks each. Calculators are not permitted and an extra 15 minutes is provided to read the paper only.
This document contains a solved paper for Class 9 mathematics with 34 multiple choice and short answer questions. It provides instructions for the exam, including the duration, maximum marks, and types of questions. The questions cover topics like geometry, algebra, data handling, and trigonometry. Sample questions, solutions and explanations are given for questions 1-10. The remaining questions require constructing tables, graphs, and geometric proofs.
The document is a sample question paper for a term 2 exam. It provides instructions and questions in four sections - Section A has 8 multiple choice questions worth 1 mark each, Section B has 6 questions worth 2 marks each, Section C has 10 questions worth 3 marks each, and Section D has 10 questions worth 4 marks each. The paper covers topics in mathematics including geometry, trigonometry, probability, graphs, and algebraic equations. Students are instructed that calculators are not permitted and that some questions offer internal choice between parts.
This document contains a quantitative aptitude practice test with 53 multiple choice questions. The questions cover topics such as geometry, algebra, arithmetic, number theory, and word problems. For each question there are 4 possible answer choices labeled a, b, c, or d. The test is 90 minutes long with 3 marks awarded for each correct answer and 1 mark deducted for each incorrect answer.
This document provides a sample question paper for a mathematics summative assessment for Class X. It consists of 31 questions divided into 4 sections (A, B, C, D) with varying mark values. Section A has 4 single mark questions, Section B has 6 two-mark questions, Section C has 10 three-mark questions, and Section D has 11 four-mark questions. The questions cover a range of mathematics topics including algebra, arithmetic, geometry and calculus. A marking scheme is also provided with answers and working for all questions. The paper is designed to comprehensively assess students' mathematical skills and knowledge.
This document provides instructions for a mathematics exam for Class X. It has the following key details:
- The exam has 4 sections (A, B, C, D) with a total of 40 questions. All questions are compulsory.
- Section A has 20 one-mark multiple choice questions. Section B has 6 two-mark questions. Section C has 8 three-mark questions. Section D has 6 four-mark questions.
- There is no overall choice but some questions provide an internal choice between alternatives. Students must attempt only one of the choices for those questions.
- Calculators are not permitted. The instructions provide details about the number and type of questions in each section and remind students
This document contains a mock test for the CBSE Class 9 math final exam. It has 34 multiple choice and constructed response questions across 4 sections (A, B, C, D) testing topics like lines and angles, probability, data representation, surface area, and geometric proofs. The test has a total of 90 marks and is to be completed within 3 hours.
The document contains a solved math exam paper for class 9 with 34 questions. It provides instructions that all questions are compulsory and carry varying marks. The questions cover a range of math topics like geometry, algebra, data representation and interpretation. Sample questions include finding the angle measures in geometric shapes, solving linear equations, constructing frequency distribution tables from data sets, calculating volumes of geometric solids, and properties of parallelograms, circles and triangles. The document also provides solutions for some of the questions as examples.
Summative assessment -I guess papers for class-ixAPEX INSTITUTE
Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject, tricks of tackling the questions and above all enthusing students with self confidence, ambition and a 'never say give up' spirit. As secrets of success these are no substitutes for hard work and patience.
This document contains a math exam for class 9 with 34 questions ranging from 1 to 4 marks each. It provides instructions for the exam, lists the questions with answer options for multiple choice questions and space for working for multi-step problems. The questions cover a variety of math topics including geometry, algebra, statistics, and trigonometry. An objective is also provided wishing students good luck on the exam.
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!
This document contains notes on additional mathematics including topics on progression, linear laws, integration, and vectors. Some key points:
- It discusses arithmetic and geometric progressions, defining the terms and formulas for finding terms and sums. Examples are worked through finding terms, sums, and differences between sums.
- Linear laws are explained including lines of best fit, converting between linear and non-linear forms using logarithms, and working through examples of finding equations from graphs.
- Integration techniques are outlined including formulas for integrals of powers, areas under and between curves, volumes of revolution, and the basic rules of integration. Worked examples find areas and volumes.
- Vectors are introduced including addition using the triangle
This document contains a mathematics exam for 9th grade with 34 questions. It provides instructions for the exam, listing the number and type of questions. It then lists the 34 questions, ranging from objective questions to word problems. The questions cover topics in mathematics including geometry, algebra, statistics, and probability. The document is signed off with "ALL THE BEST" and includes contact information for Jayant Sharma.
enjoy the formulas and use it with convidence and make your PT3 AND SPM more easier..togrther we achieve the better:)
good luck guys and girls...simple and short ans also sweet formulas..
This document contains notes and formulas for mathematics from Form 1 to Form 5. It covers topics such as solid geometry, circle theorems, polygons, factorisation, indices, linear equations, trigonometry, statistics, and lines and planes. For each topic, key formulas and properties are listed. For example, under solid geometry it defines the formulas for calculating the areas and volumes of shapes like cubes, cuboids, cylinders, cones and spheres. Under statistics it explains how to calculate measures like the mean, mode, median, and introduces different types of graphs like histograms and frequency polygons.
This document contains notes and formulas for mathematics from Form 1 to Form 5. It covers topics such as solid geometry, circle theorems, polygons, factorisation, indices, linear equations, trigonometry, statistics, and lines and planes. For each topic, key formulas and properties are listed. For example, under solid geometry it defines the formulas for calculating the areas and volumes of shapes like cubes, cuboids, cylinders, cones and spheres. Under statistics it explains how to calculate measures like the mean, mode, median, and introduces different types of graphs like histograms and frequency polygons.
This document provides notes and formulas for mathematics topics covered in Form 1 through Form 4 in Malaysian secondary schools. It includes formulas and explanations for topics like solid geometry, circle theorems, polygons, factorisation, expansion of algebraic expressions, indices, algebraic fractions, linear equations, simultaneous equations, quadratic expressions, sets, statistics, trigonometry, angles of elevation and depression, and lines and planes. The document is intended to serve as a single reference for key mathematics concepts and formulas for secondary school students.
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Class 9 Cbse Maths Sample Paper Term 2
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BLUE PRINT : SA-II (IX) : MATHEMATICS.
UNIT/TOPIC 1 2 3 4 Total
Algebra
(Linear Equations in Two
Variables)
2(2) 6(2) 8(2) 16(6)
Geometry
(Quadrilaterals, Area,
Circles, Constructions)
2(2) 4(2) 12(4) 20(5) 38(13)
Mensuration
(Surface Areas and
Volumes)
2(2) 2(1) 6(2) 8(2) 18(7)
Statistics and Probability 2(2) 6(3) 6(2) 4(1) 18(8)
Total 8(8) 12(6) 30(10) 40(10) 90(34)
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SAMPLE QUESTION PAPER SA-II
CLASS IX
(SECTION-A)
TIME 3 HRS. M.M.:90
Question numbers 1 to 8 carry 1mark each. For each question, four alternative choices have
been provided of which only one is correct. You have to select the correct choice.
1. Equation of x-axis is
(A) x = 0 (B) x = y (C) y = 0 (D) x + y = 0
2. The median of a triangle divides it into two
(A) triangles of equal area (B) equilateral triangles
(C) right triangles (D) isosceles triangles
3. In Fig.1, AOB is a diameter of the circle and AC = BC, then CAB is equal to
(A) 30o
(B) 45o
(C) 90o
(D) 60o
Fig. 1
4. Linear equation of the type y = mx, m o has
(A) infinitely many solutions (B) a unique solution
(C) only solution x = 0, y = 0 (D) solution m = 0.
5. In a frequency distribution, the mid-value of a class is 20 and the width of the class is 8.
then the lower limit of the class is
(A) 12 (B) 24 (C) 28 (D) 16
6. If the volume of a sphere is numerically equal to its surface area, then radius of the
sphere is
(A) 1 unit (B) 3 units (C) 2 units (D) 6 units
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7. Which of the following cannot be empirical probability of an event?
(A) 4/5 (B) 1 (C) 0 (D) 5/4
8. The total surface area of a cone of radius 2r and slant height ℓ/2 is
(A) 2 ℓ (B) ℓ (C) 4 ℓ (D) 2
SECTION-B
Question numbers 9 to 14 carry 2 marks each.
9. D and E are points on sides AB and AC respectively of ABC such that ar (DBC) = ar (EBC).
Prove that DE BC.
10. An edge of a cube is increased by 10%. Find the percentage by which the surface area of
the cube has increased.
11. Find the mode of the following data:
5, 7, 6, 5, 9, 8, 6, 7, 11, 10, 5, 7, 6, 8, 6, 9, 10.
12. In a cricket match, a batsman hits a boundary 4 times out of 30 balls, he plays. Find the
probability that he did not hit a boundary.
13. Prove that equal chords of a circle subtend equal angles at the centre.
OR
In Fig.2 , DAB = 70o
, DBA = 35o
.
Find the measure of ACB.
Fig. 2
14. If the arithmetic mean of 25, 30, 32, x, 43 is 34, then find the value of x.
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SECTION-C
Question numbers 15 to 24 carry 3 marks each.
15. Find three different solutions for the equation
3x – 8y = 27
16. Prove that a diagonal of a parallelogram divides it into two congruent triangles.
17. Draw a line segment AB = 5cm. From the point A, draw a line segment AD = 6cm making
DAB = 60o
. Draw the perpendicular bisector of AD. Does it pass through B? (Use ruler
and compass only).
18. 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 7mm and the diameter of the graphite is 1mm. If
the length of the pencil is 14cm, find the volume of the wood. (use = 22/7)
OR
A heap of wheat is in the form of a cone, the diameter of whose base is 14m and height is
3m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the
area of the canvas required.
19. Find mean of the following data:
Marks: 10 11 12 13 14 15
Number of students: 6 3 4 5 7 5
OR
The points scored by a basket-ball team in a series of matches are as follows:
17, 2, 7, 27, 25, 5, 14, 18 , 10, 24, 10, 8, 7, 10
Find mean, median and mode for the data.
20. Give the geometrical representation of x = -3 as an equation
(i) in one variable (ii) in two variables.
OR
Solve the equation 2x+1 = x–3 and represent the solution(s) (i) on the number line
(ii) in the Cartesian plane.
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21. The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into
it. Find the ratio of surface areas of the balloon in the two cases.
22. In Fig.3, ABCD is a parallelogram and E is the mid point of AD.DL BE meets AB produced
at F. Prove that B is the midpoint of AF and EB =LF.
Fig. 3
23. In Fig.4, ABCD is a trapezium in which AB DC. O is the mid point of BC. Through the point
O, a line PQ AD has been drawn which intersects AB at Q and DC produced at P. Prove
that ar (ABCD) = ar (AQPD).
Fig. 4
24. A die is thrown 400 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as
given in the following table.
Outcome: 1 2 3 4 5 6
Frequency: 72 65 70 71 63 59
Find the probability of
(i) getting a number less than 3.
(ii) getting an outcome 6.
(iii) getting a number more than 4.
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SECTION-D
Question numbers 25 to 34 carry 4 marks each.
25. Show that the line segments joining the mid points of the opposite sides of a quadrilateral
bisect each other.
26. Construct a triangle ABC in which BC = 8cm, B = 30o
and AB – AC = 3.5cm
OR
Construct a triangle PQR in which R = 45o
, Q = 60o
and PQ + QR + RP = 11cm.
27. Draw the graph of linear equation x + 2y = 8. From the graph, check whether (-1, -2) is a
solution of this equation.
28. A storage tank is in the form of a cube. When it is full of water, the volume of the water is
15.625m3
. If the present depth of the water is 1.3m, find the volume of water already
used from the tank.
29. In Fig.5, PQ is the diameter of the circle with centre O. If PQR = 65o
, RPS = 40o
and
PQM = 50o
, find QPR, PRS and QPM.
Fig. 5
30. 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.
OR
Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that
ar (APB) x ar (CPD) = ar (APD) x ar (BPC)
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31. The following table shows the amount received on a certain sum of money invested at
simple interest for different periods of time:
Time (in years) 2 5 10 15 20
Amount (in Rs.) 240 300 400 500 600
Plot these points on Cartesian plane, taking Time along x-axis and Amount along y-axis.
Join the points. From the graph, write down the amount after 12 years.
32. If two equal chords of a circle intersect within the circle, prove that the line joining the
point of intersection to the centre makes equal angles with the chords.
33. The circumference of the base of a cone is cm and its slant height is 13cm. Find the
volume of the cone. (Use
22
7
)
34. Construct a histogram and frequency polygon for the following frequency distribution:
Weight (in kg): 40-45 45-50 50-55 55-60 60-65 65-70
Number of persons: 15 25 28 15 12 5
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MARKING SCHEME (SA – II)
CLASS IX
SECTION-A
1. (C) 2. (A)
3. (B) 4. (A)
5. (D) 6. (B)
7. (D) 8. (C) 1mark each
SECTION-B
9. Figure, construction. ½
ar (DBC) = ar (EBC)
BC x DG = x BC x EF ½
DG = EF ½
DE BC ½
10. Let the edge of the cube be x units
Increased edge = units ½
Original Surface Area = 6x2
½
New Surface Area = 6 x x2
, Increase in area = 6 x x2
-6x2
½
Surface Area increased by 21% = x2
½
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11. Arranging the data (17 terms) in ascending order.
5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11 1
6 is repeated maximum number of times i.e. 4
mode = 6 1
12. Prob. (he hits a boundary) = 4/30 1
Prob. (he does not hit a boundary) = 1 – = or 1
13. Fig. ½
OA = O’ A’ (Radii of congruent circles)
OB = O’ B’
AOB = A’ O’ B’ (given)
OAB O’ A’ B’ (SAS) 1
AB = A’ B’ (CPCT) ½
OR
ADB = 180o
– (70 + 35)o
= 75o
1
ACB = 75o
(angles in the same segment) ½ + ½
14. = 34 1
= 40 1
SECTION-C
15. 3x – 8y = 27: Some of the solution are (9,0), (1,-3), (-7, -6).
For each correct solution one mark
[These may be different also]
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16. Given, To prove, Figure 1
Correct Proof of the theorem 2
17. For constructing BAD = 60o
correctly 2
For drawing perpendicular bisector of AD ½
No, it does not pass through the point B. ½
18. Inner radius of the cylinder = 0.5mm (r1)
Outer radius of the cylinder = 3.5mm . (r2) ½
Volume of the wood = (r2
2 - r1
2
) h ½
= (12.25 - .25) x 140 1
= 5280mm3
. 1
OR
Volume of the wheat = r2
h
= x x 7 x 7 x 3
= 154 m3
r = 7m, h = 3m ℓ = √ √58 m. 1½
Area of the canvas required = rℓ
= x 7 x √58
= 22 √58 m2
1
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19. Marks (x) Number of students (f) f x x
10 6 60
11 3 33
12 4 48
13 5 65
14 7 98
15 5 75
∑ 30 ∑ =379 2
Mean ( )x =
∑
∑
= ½
= 12.63 ½
OR
Arranging the data in ascending order
2, 5, 7, 7, 8, 10, 10, 10, 14, 17, 18, 24, 25, 27
n = 14, median =
= = 10 1
Mode = 10 ½
Mean = 1
= 13.14 ½
20. (i) In one variable: x =-3, is represented on number line.
1
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(ii) in two variables: Equation is x + o.y = -3 ½
1
AB is the required line parallel to y-axis. ½
OR
2x + 1 = x – 3
2x – x = -3 -1 1
(i) 1
(ii) 1
21. initial radius (r1) = 7cm
Present radius (r2) = 14cm
Initial surface area (S1) = 4 x 7 x 7cm2
Present surface area (S2) = 4 x 14 x 14cm2
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S
S
= or 4:1 1
22. DL BE and DE BL quad. BEDL is a parallelogram. ½
DE = BL AE = BL
EBA = LFB (corresponding angles)
FBL = BAE (Corresponding angles
∆FLB ∆BEA 1½
FB = BA or B is the mid point of FA. ½
and, EB = LF (cpct) ½
23. OB = OC (given)
1 = 2 (Vert. opp. angles)
3 = 4 (Alt. int. angles)
ΔOQB ΔOPC (ASA) 1½
ar (OQB) = ar (OPC) ½
Now ar (ABCD) = ar (AQOCD) + ar (OQB)
= Ar (AQOCD) + ar (OPC)
= Ar (AQPD) 1
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24. (i) Prob. (getting a number less than 3) = = 1
(ii) Prob. (getting an outcome 6) = 1
(iii) Prob. (getting a number more than 4) = = 1
SECTION-D
25. Let ABCD be a quadrilateral. P, Q, R, S are mid points of AB, BC, CD and DA respectively.
Join PQ, QR, RS and SP.
Join AC 1
In ∆DAC, SR AC & SR = AC (Mid point theorem) 2
In ∆BAC, PQ AC & PQ = AC
PQRS is a parallelogram ½
PR and SQ are diagonals of PQRS, therefore PR & SQ bisect each other. ½
26. Correct construction of ∆ CBD 2
Correct construction of ∆ABC 2
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Correct graph 2½
(-1, -2) does not lie on the line, therefore not a solution 1
28. Let the edge of the cube be x m.
Volume of water when tank is full = 15.625m3
1
x3
= 15.625 m3
x = 2.5m. 1
Volume of water remained in tank = (2.5)2
x 1.3 m3
= 8.125m3
1
Volume of water already used = (15.625 – 8.125) m3
= 7.500m3
1
29. QRP = 90o
(angle in a semi circle)
QPR = 90o
– 65o
= 25o
1
PQRS is a cyclic quadrilateral
PSR = (180-65)° = 115o
1
PRS = 180°- (115 + 40)° = 25o
1
M = 90o
QPM = 90°-50°=40o
1
30. Draw perpendicular DE ad CF on AB from D and C respectively ½
ar (AOD) = ar (BOC)
ar (AOD) + ar (AOB) = ar (BOC) + ar (AOB) ½
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ar (DAB = ar (CAB) ½
AB x DE = AB x CF 1
DE = CF ½
AB DC ½
ABCD is a trapezium. ½
OR
Draw perpendiculars CN and AM on BD from C and A respectively 1
ar (APB) x ar (CPD)
= (PB x AM) x (PD x CN) 1
= (PB X CN) x (PD x AM) 1
= ar (BPC) x ar (APD) 1
31. Plotting the points correctly x 5 = 2½
Joining the points ½
Amount after 12 years = Rs. 440 1
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32. AB = CD
Draw OP AB, OQ CD. 1
OP = OQ (equal chords are equidistant from centre)
OM = OM
OPM = OQM (90o
each)
OPM OQM (RHS) 2
1 = 2 (cpct)
Or OMP = OMQ 1
33. Let the radius of the cone be r, slant height be ℓ, height be h.
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2 r = cm 1
r = 5cm
ℓ = 13cm 1
h = √13 5 = 12cm 1
Volume of the cone = r2
h
= x x 5 x 5 x 12 1
= cm3
34. Correctly drawn Histogram 3
Frequency polygon 1