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ICSE Class 10 Maths Solutions

ICSE Mathematics syllabus Class 10 is designed according to the CISCE guidelines. They are systematically arranged and available in an easily downloadable format for the students. The syllabus provided here will help the students in classifying the entire course based on the importance, weightage, and difficulty level. Class 10 Board Examinations plays a vital role in shaping the students’ career and the syllabus of Maths help the students to prepare well for the examinations.

When we talk about educating our children, all we want is the best for them. Every parent wants their children to reach the paramount of success. Therefore, we, at SpeEdLabs, ensure that your children are in the best hands.

Considering all the above facts, SpeEdLabs has come up with a detailed study of each chapter and its subtopics to help students self-analyze their weaknesses and abilities in the best way possible.

In this class, students will learn about different concepts in detail which are Commercial Mathematics, Algebra, Geometry, Mensuration, Trigonometry, Statistics, and Probability.

The duration of the paper is of two and a half hours, carrying 80 marks and an Internal Assessment of 20 marks. The paper is divided into two sections: Section I (40 marks) and Section II (40 marks).

Section I consists of compulsory short answer questions. In Section II, you are required to answer four out of seven questions.

ICSE Class 10 Maths Syllabus

 BIFURCATED SYLLABUS (As per the Reduced Syllabus for ICSE – Class X Year 2022 Examination) SEMESTER 1 SEMESTER 2 (Marks: 40) (Marks: 40) UNIT NO. NAME OF THE UNIT NAME OF THE SUB-UNIT UNIT NO. NAME OF THE UNIT NAME OF THE SUB-UNIT 1 Commercial Mathematics 2 Algebra (vii) Co-ordinate Geometry (Complete Unit) 2 Algebra (i) Linear Inequations 3 Geometry (b) Circles (ii)Quadratic Equations in one variable (iii)Ratio and Proportion (iv)Factorisation of polynomials (v)Matrices (vi)Arithmetic Progression 3 Geometry (a) Similarity 4 Mensuration (Complete Unit) 5 Trigonometry (Complete Unit) 6 Statistics (Complete Unit) 7 Probability (Complete Unit) Students are advised to refer to the concepts and numerical provided on our platform to get sparkling results.
1. Commercial Mathematics

(i) Compound Interest (a) Compound Interest as a repeated Simple Interest Computation with a growing Principal. Use of this is in computing amount over a period of 2 or 3 years. (b) Use of formula A = P (1+ r/100) n. Finding CI from the relation CI = A–P.
•       Interest compounded half-yearly included.
•       Using the formula to find one quantity given different combinations of A, P, r, n, CI and SI; the difference between CI and SI type included.
•       Rate of growth and depreciation.
Note: Paying back in equal instalments, being given rate of interest and instalment amount, not included. (ii) Sales Tax and Value Added Tax Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases. (iii) Banking (a) Savings Bank Accounts. Types Of Accounts. The idea of Savings Bank Account, Computation Of Interest for a series of months. (b) Recurring Deposit Accounts: Computation Of Interest using the formula: SI = P x [n(n+1)/2×12] x r/100 (iv) Shares and Dividends (a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium. (b) Formulae
•       Income = number of shares x rate of dividend x FV
•       Return = (Income / Investment) x 100.
Note: Brokerage and fractional shares not included
1. Algebra

(i) Linear Inequations Linear Inequations in one unknown for x ε N, W, Z, R. Solving
•       Algebraically and writing the solution in set notation form.
•       Representation of solution on the number line.
•       Factorization.
•       Formula.
(b) Nature of roots
•       Two distinct real roots if b2 – 4ac > 0
•       Two equal real roots if b2 – 4ac = 0
•       No real roots if b2 – 4ac < 0
(c) Solving problems. (iii) Reflection (a) Reflection of a point in a line: x=0, y=0, x=a, y=a, the origin. (b) Reflection of a point in the origin. (c) Invariant points. (iv) Ratio and Proportion (a) Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios. (b) Continued proportion, mean proportion (c) Componendo and dividendo, alternendo and invertendo properties. (d) Direct applications. (v) Factorization (a) Factor Theorem. (b) Remainder Theorem. (c) Factorizing a polynomial completely after obtaining one factor by factor theorem. Note: f(x) not to exceed degree 3. (vi) 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
•       a non-zero rational number
•       a matrix
(vii) Co-ordinate Geometry Co-ordinates expressed as (x,y) Distance between two points, section, and Midpoint formula, Concept of a slope, equation of a line, Various forms of straight lines. (a) Distance formula. (b) Section and Mid-point formula (Internal section only, coordinates of the centroid of a triangle included). (c) Equation of a line:
•       Slope-intercept form y = mx + c
•       Two-point form (y-y1) = m(x-x1)
Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ 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. Conditions for two lines to be parallel or perpendicular. Simple applications of all of the above.
1. Geometry

(i) Symmetry (a) Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamond-shaped figure. (b) Being given a figure, to draw its lines of symmetry. Being given part of one of the figures listed above to draw the rest of the figure based on the given lines of symmetry (neat recognizable freehand sketches acceptable). (ii) Similarity Axioms of similarity of triangles. The Basic theorem of proportionality. (a) Areas of similar triangles are proportional to the squares on corresponding sides. (b) Direct applications based on the above including applications to maps and models. (iii) Loci Loci: Definition, meaning, Theorems based on Loci. (a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre. (b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines. (c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points. (iv) Circles (a) Chord Properties:
•       A straight line is drawn from the center of a circle to bisect a chord that is not a diameter is at right angles to the chord.
•       The perpendicular to a chord from the center bisects the chord (without proof).
•       Equal chords are equidistant from the center.
•       Chords equidistant from the center are equal (without proof).
•       There is one and only one circle that passes through three given points, not in a straight line.
(b) Arc and chord properties:
•       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.
•       Angles in the same segment of a circle are equal (without proof).
•       Angle in a semi-circle is a right angle.
•       If two arcs subtend equal angles at the center, they are equal, and its converse.
•       If two chords are equal, they cut off equal arcs, and its converse (without proof).
•       If two chords intersect internally or externally then the product of the lengths of the segments are equal.
(c) Cyclic Properties:
•       Opposite angles of a cyclic quadrilateral are supplementary.
•       The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).
(d) Tangent Properties:
•       The tangent at any point of a circle and the radius through the point are perpendicular to each other.
•       If two circles touch, the point of contact lies on the straight line joining their centers.
•       From any point outside a circle, two tangents can be drawn and they are equal in length.
•       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.
•       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. (v) 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.
1. Mensuration

Area and circumference of circle, Area and volume of solids – cone, sphere. (a) Circle: Area and Circumference. Direct application problems including Inner and Outer areas. (b) Three-dimensional solids – right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems include cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. A Combination of two solids included. Note: Frustum is not included. Areas of sectors of circles other than quarter circle and semicircle are not included.
1. Trigonometry

(a) Using Identities to solve/prove simple algebraic trigonometric expressions
•       sin2A + cos2A = 1
•       1 + tan2A = sec2A
•       1+cot2A = cosec2A; 0 ≤ A ≤ 90°
(b) Trigonometric ratios of complementary angles and direct application:
•       sin A = cos(90 – A), cos A = sin(90 – A)
•       tan A = cot(90 – A), cot A = tan(90 – A)
•       sec A = cosec(90 – A), cosec A = sec(90 – A)
(c) 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.
1. Statistics

Statistics – basic concepts, Histograms and Ogive, Mean, Median, Mode. (a) Graphical Representation. Histograms and ogives.
•       Finding the mode from the histogram, the upper quartile, lower Quartile and median from the ogive.
•       Calculation of inter Quartile range.
(b) Computation of:
•       Measures of Central Tendency: Mean, median, and 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, Short-cut, Step-deviation.
1. Probability

•       Random experiments
•       Sample space
•       Events
•       Definition of probability
•       Simple problems on single events

STUDY MATERIAL FOR ICSE CLASS 10 MATHEMATICS

ICSE exam preparation is not a walk in the park as it requires in-depth understanding and application of every concept in the syllabus, but, with the proper strategy and planning, you can attain great results. Good Study material is the basis of excellent preparation for any exam.

We, at SpeEdLabs, aim to provide quality study material, well-suited according to the updated guidelines of CISCE. We have provided the ICSE Class 10 Maths syllabus for the year 2021-2022. The students can plan their studies and clear their doubts from their teacher in the next class.

While studying, they can refer to this syllabus and keep a track of the topics they have covered till now.

ICSE Class 10 Maths Important Questions

The ICSE course structure is designed in a manner to ensure that students do not go through a lot of pressure, moreover, books are made interactive and interesting for students to enjoy their studies. A lot of fun activities are included in between the chapters to help students learn playfully. It makes the process of conveying knowledge to the students effective and healthy.

ICSE Class 10 Maths Sample Papers

Sample Papers are an essential component of study material. It helps students give an idea about marks distribution, exam pattern, question paper style, important topics, and other important guidelines to keep in mind while attempting the exam.

Previous Years’ Question Papers

Class 10 ICSE previous year question papers are regarded as a worthy learning resource for the students while preparing for their exams. By practicing previous year question papers the students can easily get an idea about the topics important for the examination point of view and the question paper style.

WHY SpeEdLabs?

SpeEdLabs is India’s leading adaptive practice platform and is used by more than 60,000 students, across 200+ cities in India. SpeEdLabs AI offers you online activities, regular classes through video conferencing, and certain testing activities. Our AI system helps track the daily performance of each student and enables them to learn at their own pace.

Students can also connect with mentors 24/7 for doubt clearing, and revise at their own pace, using personalized worksheets. Here’s how we help:
•         An AI-powered individualized improvement plan, based on your strengths and weaknesses.
•         Learning is made easy with interactive and interesting lectures.
•         Personalized attention from subject matter experts with 24/7 doubt-clearing sessions.
•         Customized assessments with the instant evaluation of your tests.
•         Complete study material for ICSE class 10, with relevant question papers and practice papers along with the answer keys, are available.
•         Constant support and feedback to keep you motivated and make you exam-ready.
•         Cross-reference of a single question, globally that helps you study a particular topic/concept from different angles possible.
•         Direct interaction with experts for clarifying your unlimited doubts.

CONCLUSION

We, at SpeEdLabs, provide all the important tools which include chapter-wise solutions, equipping the students with the key to unlocking their problem-solving skills. We aim to create a significant impact on the academic career of students by adopting a suitable learning strategy. SpeEdLabs students not only find solutions to their questions but can also verify if their answers are correct. Helping students to achieve an in-depth understanding of the core topics is our ultimate aim.

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