CLASS 10

ICSE

Strictly based on the latest ICSE Curriculum

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MATHEMATICS

QUESTION BANKCHAPTERWISE & TOPICWISE

Includes :l Solved Board Question Paper of 2018 Exam

l Handwritten Toppers' Answers Sheet

l Previous Years Solved Papers upto 2018

l Topics and Concepts found Confusing & Difcult by Students

l Suggestions for Students

l Board's Examiners' Comments

l Answering Tips

For2019Exam

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CONTENTS

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1. Value Added Tax (VAT) 1 - 5

2. Banking 6 - 9

3. Shares & Dividends 10 - 18

4. Linear Inequations 19 - 24

5. Quadratic Equations 25 - 53

Topic 1. Solution of Quadratic

Equations

Topic 2. Discriminant and Nature

of Roots

Topic 3. Word Problems

6. Ratio and Proportion 54 - 61

RatioTopic 1.

ProportionsTopic 2.

7. Factorisation 62 - 66

8. Matrices 67 - 78

9. Arithmetic Progression 79 - 95

Topic 1. thTo find n Term of

the Arithmetic Progression

Topic 2. Sum of an Arithmetic

Progression

10. Geometric Progression 96 - 106

Topic 1. th To find n term of the

Geometric Progression

Topic 2. nSum of a Geometric

Progression

11. Reflection 107 – 114

12. Section And Mid-Point

Formula 115 - 129

13. Equation of Straight Lines 130 - 146

Topic 1. Equation of Straight Lines

Topic 2. Parallel and

Perpendicular lines

14. Similarity 147 - 162

15. Locus 163 - 167

16. Circles 168 - 176

17. Tangents and its Properties 177 - 199

18. Constructions 200 - 204

19. Mensuration 205 - 230

Topic 1. Surface areas and Volumes

Topic 2. Problem Involving Converting

One Type of Metallic

Solid into Another

20. Trigonometric Identities 231 - 245

21. Heights and Distances 246 - 272

22. Statistics 273 - 320

23. Probability 321 - 327

qq

l Latest Syllabus issued by CISCE for Academic Year 2018 –19 8 - 11

l ICSE Solved Paper – 2018 13 - 28

l ICSE Specimen Paper – 2018 (Issued by Board) 29 - 43

l ICSE Solved Paper 2017, with Marking Scheme (Qualitative Analysis) – ,

Issued by CISCE Board 44 - 57

l Handwritten T oppers' Answer Sheet – 2017 58 - 71

Born : 10 September, 1920Mathematician and statistician

C.R. RaoC.R. Rao

( 4 )

He received an M.Sc. in mathematics from Andhra University and

an M.A. in statistics from Calcutta University in 1943. He was

among the first few people in the world to hold a master's degree in

Statistics.

He is an Indian-born, naturalized American, Mathematician and statistician. His is currently professor

emeritus at Penn State University and Research Professor at the University at Buffalo. Rao has been

honoured be numerous colloquia, honorary degrees, and festschrifts and was awarded the US National

Medal of Science in 2002. The American Statistical Association has described him as "A living legend

whose work has influenced not just statictics, but has had far reaching implications for fields as varied

as economics, genetics, anthropology, geology, national planning, demography, biometry and

medicine". The Times of India listed Rao as one of the top 10 Indian scientists of all time.

( 5 )

PREFACEThe Indian Certificate of Secondary Education Examination conducts examination, in accordance with

the recommendations of the New Education Policy 1986, through the medium of English.

The Council for the Indian School Certificate Examinations is committed to serving the nation's

children, through high quality educational endeavours, with a commitment to excellence.

Excellence is a continuous process and not an accident! - A.P. J. ABDUL KALAAM

With an increasing number of new technologies and an expanding global population, being an

autodidact, or self-teacher, has become increasingly crucial to achieve excellence. In order to aid the

students in this task, Oswaal Books has designed this book which will surely cater to their needs.

The unique character of this book is that it ensures an in-depth; and not merely superficial learning of

ICSE topics. The remarkable feature is the inclusion of Answering Tips and Examiner's Comments at the

end of every question, which will empower the students to comprehend their mistakes and rectify

them.

Questions incorporated in this book follow the syllabus, pattern and marking guidelines of the Council

to guide the candidates to answer with precision. This will help students to get familiar with the

examination techniques.

This book would not have taken shape without the support of our authors and editors. We would like to

extend our heartfelt gratitude to them. There is always a scope of improvement and any constructive

suggestion will be heartily considered. Together we can make this book stand in the category as 'One of

the Best'. Wish you Happy Learning!

-Team Oswaal

Topics/Concepts found Difficult or Confusing

( 6 )

Examination Paper 2017l Value Added Tax (VAT). l Shares and Dividend. l Use of Remainder and Factor Theorem. l Inequation solving and representing solution. l Geometry: Constructions and solving problems using properties of circle and

similar triangles.l Application of Circle Theorems. l Finding out minimum balance in a month of a Savings Bank account. l Coordinate geometry: Section formula. l Trigonometry, complementary angles and Heights and Distances. l Properties of Ratio and Proportion. l Approximation to given significant figures or to nearest whole number. l Statistics: finding mean by using step-deviation Method.l Representing solutions on number line. l Probability. l Problems based on graph. Choosing correct axis and scale.

Examination Paper 2016l VAT. l Shares and Dividend l Geometry solving problems using properties of circle and similar triangles l Geometry Constructions l Coordinate geometry: Section formula l Trigonometry, complementary angles and Heights and Distances. l Properties of Ratio and Proportion. l Approximation: to given significant figures or to nearest whole number.

Examination Paper 2015l Value Added Tax (VAT) l Compound Interest inverse problems. l Trigonometry l Similarity l Rounding off final result e.g. significant figures. l Theorems on properties of circle. l Properties of proportion. l Constructing a circle about a constructed Hexagon. l Calculation of mean l Coordinate geometry, Section formula and identifying points on x or y axis. l Quadratic equation problem l Inequation: writing solution and representation on number line

Examination Paper 2014l Value Added Tax (VAT)l Compound Interest inverse problems.l Trigonometryl Similarityl Rounding off final result e.g. significant figures.l Theorems on properties of circle.l Properties of proportion.l Construction of incircle.l Short cut method of calculation of meanl Coordinate geometry, Section formula and identifying points on x or y axis. Conditions of collinear.l Quadratic equation problem.

( 7 )

Suggestions for the Students

ð Reading time must be utilised to make the right choice of question and to be thorough with the given data.

ð Round off the answers where asked.

ð Choose the correct scale while drawing graphs and special care must be taken while marking the axes and plotting points.

ð Use mathematical tables to find square roots.

ð Show all steps of working including rough work on the same answer page.

ð While solving geometry problems reasons must be given.

ð Show clearly all traces of constructions.

ð To avoid calculation errors, all calculations must be rechecked.

ð Make wise choices from the options available in the question paper and manage time wisely.

ð Study the entire syllabus thoroughly and revise from time to time. Concepts of Class IX must be revised and integrated with the Class X syllabus.

ð Develop logical and reasoning skills to have a clear understanding.

ð Revise all topics and formulae involved and make a chapter wise or topic-wise list of these.

ð Be methodical and neat in working.

ð More practice is necessary in rounding off of numbers.

ð Must choose the correct scale while drawing graphs and special care must be taken while marking the axes and plotting points.

ð Logarithm tables may be used to find square roots.

ð All steps of working including rough works must be clearly shown on same answer page.

ð All traces of constructions must be clearly shown.

ð Reading time must be utilized to make the right choice of questions and make oneself familiar with all given data.

ð More practice must be done on rounding off of digits.

ð Use graph paper for questions based on graphs.

ð Use of log table to find square root of numbers.

ð Avoid skipping steps. All necessary steps must be clearly shown.

ð Working for matrix multiplication is essential.

ð Rounding off of decimals.

ð Adopt methods where lesser calculation is necessary to get final result.

ð Necessary sample space must be written for probability problems.

ð Steps of working is necessary in conversion of trigonometric ratios of complementary angles.

ð Reasons must be provided for all geometry problems.

(8)

LATEST SYLLABUS

MathematicsCLASS 10

There will be one paper of two and a half hours duration carrying 80 marks and Internal Assessment of 20 marks.The paper will be divided into two sections, Section I (40 marks), Section II (40 marks).Section I: Will consist of compulsory short answer questions.Section II: Candidates will be required to answer four out of seven questions.1. Commercial Mathematics (i) Value Added Tax Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases. (ii) Banking Recurring Deposit Accounts : computation of interest and maturity value using the formula:

I =

P

n n r( )+×

×1

2 12 100

MV = P x n + I (iii) Shares and Dividends (a) Face/Nominal value, Market Value, Dividend, Rate of Dividend, Premium. (b) Formulae l Income = number of shares × rate of dividend × FV. l Return = (Income/Investment) × 100. Note : Brokerage and fractional shares not included.2. Algebra (i) Linear Inequations Linear Inequations in one unknown for x Î N, W, Z, R. Solving l Algebraically and writing the solution in set notation form. l Representation of solution on the number line. (ii) Quadratic Equations in one variable (a) Nature of roots l Two distinct real roots if b2 – 4ac > 0 l Two equal real roots if b2 – 4ac = 0 l No real roots if b2 – 4ac < 0 (b) Solving Quadratic equations by: l Factorisation l Using Formula. (c) Solving simple quadratic equation problems. (iii) Ratio and Proportion (a) Proportion, Continued proportion, mean proportion. (b) Componendo, dividendo, alternendo, invertendo properties and their combinations. (c) Direct simple applications on proportions only.

(iv) Factorisation of polynomials: (a) Factor Theorem. (b) Remainder Theorem. (c) Factorising a polynomial completely after obtaining one factor by factor theorem. Note : f (x) not to exceed degree 3. (v) Matrices (a) Order of a matrix. Row and column matrices. (b) Compatibility for addition and multiplication. (c) Null and Identity matrices. (d) Addition and subtraction of 2×2 matrices. (e) Multiplication of a 2×2 matrix by l a non-zero rational number l a matrix. (vi) Arithmetic and Geometric Progression l Finding their General term. l Finding Sum of their first ‘n’ terms. l Simple Applications. (vii) Co-ordinate Geometry (a) Reflection (i) Reflection of a point in a line : x=0, y =0, x= a, y=a, the origin. (ii) Reflection of a point in the origin. (iii) Invariant points. (b) Co-ordinates expressed as (x,y), Section formula, Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines. (i) Section and Mid-point formula (Internal section only, co-ordinates of the centroid of a triangle included). (ii) Equation of a line: l Slope –intercept form y = mx + c l Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as slope/

gradient tanq where q is the angle the line makes with the positive direction of the x axis.

Geometric understanding of ‘c’ as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.

l Conditions for two lines to be parallel or perpendicular.

Simple applications of all the above.3. Geometry (a) Similarity Similarity, conditions of similar triangles.

(9)

(i) As a size transformation. (ii) Comparison with congruency, keyword being proportionality. (iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). (iv) Applications of Basic Proportionality Theorem. (v) Areas of similar triangles are proportional to the squares of corresponding sides. (vi) Direct applications based on the above including applications to maps and models. (b) Loci Loci : Definition, meaning, Theorems and constructions based on Loci. (i) The locus of a point at a fixed distance from a fixed point is a circle with the fixed point as centre and fixed distance as radius. (ii) The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines. (iii) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points. Proofs not required (c) Circles (i) Angle Properties l The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle. l Angles in the same segment of a circle are equal (without proof). l Angle in a semi-circle is a right angle. (ii) Cyclic Properties: l Opposite angles of a cyclic quadrilateral are supplementary. l The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof). (iii) Tangent and Secant Properties: l The tangent at any point of a circle and the radius through the point are perpendicular to each other. l If two circles touch, the point of contact lies on the straight line joining their centers. l From any point outside a circle two tangents

can be drawn and they are equal in length. l If two chords intersect internally orexter-

nally then the product of the lengths of the segments are equal.

l If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.

l If a line touches a circle and from the point of contact, a chord is drawn, the angles between

the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

Note : Proofs of the theorems given above are to be taught unless specified otherwise. (iv) Constructions (a) Construction of tangents to a circle from an external point. (b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.4. Mensuration Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right

circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

Note : Problems on Frustum are not included.5. Trigonometry (a) Using Identities to solve/prove simple algebraic trigonometric expressions sin2 A + cos2 A = 1 1 + tan2 A = sec2A 1+cot2A = cosec2A; 0 £ A £ 90° (b) Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables. Note: Cases involving more than two right angled triangles excluded.6. Statistics Statistics – basic concepts, Mean, Median, Mode. Histograms and Ogive. (a) Computation of: l Measures of Central Tendency: Mean, median,

mode for raw and arrayed data. Mean*, median class and modal class for grouped data. (both continuous and discontinuous).

* Mean by all 3 methods included:

Direct :

åå

fxf

Short-cut :

A

fdf

+åå

where d = x – A

Step-deviation:

A

ftf

+ ×åå

i where t =

x Ai−

(b) Graphical Representation. Histograms and Less than ogive. l Finding the mode from the histogram, the upper quartile, lower Quartile and median etc. from the ogive. l Calculation of inter Quartile range.

...contd.

(10)

7. Probability l Random experiments l Sample space l Events l Definition of probability l Simple problems on single events Note: SI units, signs, symbols and abbreviations (1) Agreed conventions (a) Units may be written in full or using the

agreed symbols, but no other abbreviation may be used.

(b) The letter's is never added to symbols to indicate the plural form.

(c) A full stop is not written after symbols for units unless it occurs at the end of a sentence.

(d) When unit symbols are combined as a quotient, e.g. metre per second, it is recommended that they be written as m/s, or as m s-1.

(e) Three decimal signs are in common international use: the full point, the mid-point and the comma. Since the full point is sometimes used for multiplication and the comma for spacing digits in large numbers, it is recommended that the mid-point be used for decimals.

(2) Names and symbols

In general Implies that Þ | is logically equivalent to ÛIdentically equal to º is approximately equal to >>

In set language

/Belongs to Î does not belong to ÏIs equivalent to « | is not equivalent to «union È intersection Çuniversal set x |is contained in Ìnatural (counting) N the empty set Ænumbers |whole numbers Wintegers Z real numbers R

In measuresKilometre km Metre mCentimetre cm Millimetre mmKilogram kg Gram gLitre 1 Centilitre clSquare kilometre km2 Square meter m2

Square centimetre cm2 Hectare haCubic metre m3 Cubic centimetre cm3

Kilometres per hour km/h Metres per second m/s

INTERNAL ASSESSMENTThe minimum number of assignments : Two assignments as prescribed by the teacher.Suggested Assignmentsl Comparative newspaper coverage of different items. l Survey of various types of Bank accounts, rates of interest offered.

l Planning a home budget.l Conduct a survey in your locality to study the mode of conveyance / Price of various essential commodities/ favourite sports. Represent the data using a bar graph / histogram and estimate the mode.l To use a newspaper to study and report on shares and dividends.l Set up a dropper with ink in it vertical at a height say 20 cm above a horizontally placed sheet of plain paper. Release one ink drop; observe the pattern, if any, on the paper. Vary the vertical distance and repeat. Discover any pattern of relationship between the vertical height and the ink drop observed.l You are provided (or you construct a model as

shown) - three vertical sticks (size of a pencil) stuck to a horizontal board. You should also have discs of varying sizes with holes (like a doughnut). Start with one disc; place it on (in) stick A. Transfer it to another stick (B or C); this is one move (m). Now try with two discs placed in A such that the large disc is below and the smaller disc is above (number of discs = n=2 now). Now transfer them one at a time in B or C to obtain similar situation (larger disc below). How many moves? Try with more discs (n = 1, 2, 3, etc.) and generalise.

A B C

l The board has some holes to hold marbles, red on one side and blue on the other. Start with one pair. Interchange the positions by making one move at a time. A marble can jump over another to fill the hole behind. The move (m) equal 3. Try with 2 (n=2) and more. Find the relationship between n and m.

Red Blue

l Take a square sheet of paper of side 10 cm. Four small squares are to be cut from the corners of the square sheet and then the paper folded at the cuts to form an open box. What should be the size of the squares cut so that the volume of the open box is maximum?

l Take an open box, four sets of marbles (ensuring that marbles in each set are of the same size) and some water. By placing the marbles and water in the box, attempt to answer the question: do larger marbles or smaller marbles occupy more volume in a given space?

l An eccentric artist says that the best paintings have the same area as their perimeter (numerically). Let us not argue whether such sizes increases the viewer’s

...contd.

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appreciation, but only try and find what sides (in integers only) a rectangle must have if its area and perimeter are to be equal (note: there are only two such rectangles).

l Find by construction the centre of a circle, using only a 60-30 setsquare and a pencil.l Various types of “cryptarithm”.

EVALUATIONThe assignments/project work are to be evaluated by the subject teacher and by an External Examiner. (The External Examiner may be a teacher nominated by the Head of the school, who could be from the faculty, but not

teaching the subject in the section/class. For example, a teacher of Mathematics of Class VIII may be deputed to be an External Examiner for Class X, Mathematics projects.)The Internal Examiner and the External Examiner will assess the assignments independently.Award of marks (20 Marks)Subject Teacher (Internal Examiner) : 10 marksExternal Examiner : 10 marksThe total marks obtained out of 20 are to be sent to the Council by the Head of the school.The Head of the school will be responsible for the entry of marks on the mark sheets provided by the Council.

INTERNAL ASSESSMENT IN MATHEMATICS- GUIDELINES FOR MARKING WITH GRADES

Criteria Preparation Concepts Computation Presentation Understanding Marks

Grade I Exhibits and selects a well-defined problem.Appropriate of techniques.

Admirable use of mathematical concepts and methods and exhibits compe-tency in using extensive range of mathematical techniques.

Careful and accurate work with appropri-ate computa-tion, con-struction and measurement with correct units.

Presents well stated conclusions; mathematical language, sym-bols, conven-tions, tables, diagrams, graphs, etc.

Shows strong personal contribu-tion; demonstrate knowledge and understanding of assignment and can apply the same in different situations.

4 marks for each criterion

Grade II Exhibits and selects routine approach.Fairly good techniques.

Appropriate use of mathematical concepts and methods and shows adequate competency in using limited range of tech-niques.

Commits neg-ligible errors in computation, construction and measure-ment.

Some state-ments of con-clusion; uses appropriate math language,symbols, con-ventions, ta-bles, diagrams, graphs, etc.

Neat with aver-age amount of help; assignment shows learning of mathematics with a limited ability to use it.

3 marks for each criterion

Grade III Exhibits and selects trivial problems.Satisfactory techniques.

Uses appropriate mathematical concepts and shows compe-tency in using limited range of techniques.

Commits a few errors in computation, construction and measure-ment.

Assignment is presentable thought it is disorganized in some places.

Lack of ability to conclude with-out help; shows some learning of mathematics with a limited ability to use it.

2 marks for each criterion

Grade IV Exhibits and selects an insignificant problem.Uses some unsuitable techniques.

Uses inappropri-ate mathematical concepts for the assignment.

Commits many mistakes in computa-tion and meas-urement.

Presentation made is some-what disor-ganized and untidy.

Lack of ability to conclude even with considerable help; assignment contributes to mathematical learning to a cer-tain extent.

1 marks for each criterion

Grade V Exhibits and selects a com-pletely irrel-evant problem.Uses unsuita-ble techniques.

Not able to use mathematical concepts.

Inaccurate computation, construction and measure-ment.

Presentation made is com-pletely disor-ganized untidy and poor.

Assignment does not contribute to mathematical learning and lacks practical applica-bility.

0 marks

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WRITING NOTES

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ICSE Solved Paper, 2018Class-X

Mathematics(Maximum Marks : 80)

(Time allowed : Two hours and a half)

Answers to this Paper must be written on the paper provided separately.

You will not be allowed to write during the first 15 minutes.

This time is to be spent in reading the question paper.

The time given at the head of this Paper is the time allowed for writing the answer

Attempt all questions from Section A and any four questions from Section B.

All working, including rough work, must be clearly shown and must be done on the same

sheet as the rest of the answer.

Omission of essential working will result in loss of marks.

The intended marks for questions or parts of question are given in brackets [ ].

Mathematical tables are provided.

SECTION- A (40 Marks)

Attempt all questions from this Section. 1. (a) Find the value of 'x' and 'y' if : 3

2

79 5

6 74 5

10 722 15

xy −

+

−

=

(b) Sonia had a recurring deposit account in a bank and deposited ` 600 per month for 2½ years. If the rate of interest was 10% p.a., find the maturity value of this account. 3

(c) Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is : 4

(i) a prime number. (ii) a number divisible by 4. (iii) a number that is a multiple of 6. (iv) an odd number. 2. (a) The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the 3 (i) radius of the cylinder

(ii) volume of cylinder. (use )π =

227

(b) If (k – 3), (2k + 1) and (4k + 3) are three consecutive terms of an A.P., find the value of k. 3 (c) PQRS is a cyclic quadrilateral. Given ∠QPS = 73°, ∠PQS = 55° and ∠PSR = 82°, calculate : 4 (i) ∠QRS (ii) ∠RQS (iii) ∠PRQ

14 | OSWAAL ICSE Chapterwise/Topicwise Question Bank, MATHEMATICS, Class-X

3. (a) If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of 'a' and 'b'. 3

(b) Prove that sec cosec22 θ θ+ = tan q + cot q 3

(c) Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data : 3

Runsscored

3000-4000 4000-5000 5000-6000 6000-7000 7000-8000 8000-9000 9000-10000

No. ofbatsmen

4 18 9 6 7 2 4

4. (a) Solve the following inequation, write down the solution set and represent it on the real number line : 3 – 2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ Z (b) If the straight lines 3x – 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, find value of a. 3 (c) Solve x2 + 7x = 7 and give your answer correct to two decimal places. 4

SECTION- B (40 Marks)

Attempt any four questions from this Section 5. (a) The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series. 3 (b) A man invests ` 22,500 in ` 50 shares available at 10% discount. If the dividend paid by the company is 12%,

calculate : 3 (i) The number of shares purchased (ii) The annual dividend received. (iii) The rate of return he gets on his investment. Give your answer correct to the nearest whole number. (c) Use graph paper for this question (Take 2 cm = 1 unit along both x and y axis). 4 ABCD is a quadrilateral whose vertices are A(2, 2), B(2, – 2), C (0 – 1) and D(0, 1) (i) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD. (ii) Write down the coordinates of A' and B'. (iii) Name two points which are invariant under the above reflection. (iv) Name the polygon A'B'CD. 6. (a) Using properties of proportion, solve for x. Given that x is positive : 3

2 4 1

2 4 14

2

2

x x

x x

+ −

− −=

(b) If A = 2 35 7

, B =

0 41 7−

, and C =

1 01 4−

, find AC + B2 – 10C. 3

(c) Prove that (1 + cot q – cosec q)( 1+ tan q + sec q) = 2 4 7. (a) Find the value of k for which the following equation has equal roots. 3

x2 + 4kx + (k2 – k + 2) = 0 (b) One map drawn to a scale of 1 : 50,000, a rectangular plot of land ABCD has the following dimensions.

AB = 6 cm ; BC = 8 cm and all angles are right angles. Find : 3 (i) the actual length of the diagonal distance AC of the plot in km. (ii) the actual area of the plot in sq km. (c) A(2, 5), B(– 1, 2) and C(5, 8) are the vertices of a triangle ABC, 'M' is a point on AB such that AM : MB = 1 : 2.

Find the co-ordinates of 'M'. Hence find the equation of the line passing through the points C and M. 4 8. (a) ` 7500 were divided equally among a certain number of children. Had there been 20 less children, each

would have received ` 100 more. Find the original number of children. 3 (b) If the mean of the following distribution is 24, find the value of 'a'. 3

Marks 0-10 10-20 20-30 30-40 40-50

Number ofstudents

7 a 8 10 5

(c) Using ruler and compass only, construct a DABC such that BC = 5 cm and AB = 6.5 cm and ∠ABC = 120°. 4 (i) Construct a circum-circle of DABC (ii) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.

Oswaal ICSE Question BankChapterwise & Topicwise Class - X

Mathematics For 2019 Exam

Publisher : Oswaal Books ISBN : 9789387504653 Author : Panel Of Experts

Type the URL : http://www.kopykitab.com/product/19176

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