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ICSE Class IX Mid-term 2024 : English Paper 1 (English Language) : Final exam

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MATHEMATICS (51) CLASS X There will be one written paper of two and a half hours duration carrying 80 marks and Internal Assessment of 20 marks. Certain questions may require the use of Mathematical tables (Logarithmic and Trigonometric tables). 1. Commercial Mathematics (b) Solving Quadratic equations by: Factorisation 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. (iv) Factorisation of polynomials: (i) Goods and Services Tax (GST) Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases. Candidates are also expected to find price paid by the consumer after paying State Goods and Service Tax (SGST) and Central Goods and Service Tax (CGST) - the different rates as in vogue on different types of items will be provided. Problems based on corresponding inverse cases are also included. (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. (ii) Banking Recurring Deposit Accounts: computation of interest and maturity value using the formula: I =P n(n + 1) r 2 12 100 (v) Matrices MV=P n+I (a) Order of a matrix. Row and column matrices. 2. Algebra (i) Linear Inequations (b) Compatibility multiplication. Linear Inequations in one unknown for x N, W, Z, R. Solving: Algebraically and writing the solution in set notation form. Representation of solution on the number line. (ii) Quadratic Equations in one variable addition and (c) Null and Identity matrices. (d) Addition and matrices. subtraction of 2 2 (e) Multiplication of a 2 2 matrix by a non-zero rational number a matrix. (vi) Arithmetic Progression (a) Nature of roots for Two distinct real roots if b2 4ac > 0 Two equal real roots if b2 4ac = 0 No real roots if b2 4ac < 0 1 Finding the General term of an A.P. Finding Sum of first n terms of an A.P. (vii) Co-ordinate Geometry Angles in the same segment of a circle are equal. Angle in a semi-circle is a right angle. (ii) Cyclic Properties: Opposite angles of a cyclic quadrilateral are supplementary. (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: Slope intercept form y = mx + c Two- point form (y-y1) = m(x-x1) Geometric understanding of m as slope/ gradient/ tan where 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. 3. Geometry (iii) Tangent and Secant Properties: The tangent at any point of a circle and the radius through the point are perpendicular to each other. (a) Similarity Similarity, conditions of similar triangles. (i) Comparison with congruency, keyword being proportionality. If two circles touch, the point of contact lies on the straight line joining their centres. From any point outside a circle, two tangents can be drawn, and they are equal in length. If two chords intersect internally or externally then the product of the lengths of the segments are equal. 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 are not required. (ii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). Applications of all Circle Theorems in solving numerical and theoretical problems are included. (iii) Applications of Basic Proportionality Theorem. (b) Circles (iv) Constructions (i) Angle Properties The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. (a) Construction of tangents to a circle from an external point. The angle that an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circle. 2 (b) Circumscribing and inscribing a circle on a triangle and a regular hexagon. Finding the mode from the histogram, the upper quartile, lower Quartile and median etc. from the ogive. Calculation of inter Quartile range. 7. Probability Random experiments, Sample space, Events, definition of probability, Simple problems on single events. 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. SI UNITS, SIGNS, ABBREVIATIONS SYMBOLS AND (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 it should 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. Note: Problems on Frustum are not included. 5. Trigonometry (a) Using Identities to 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 (2) Names and symbols Statistics basic concepts, Mean, Median, Mode. Histograms and Ogive. (a) Computation of: Measures of Central Tendency: Mean*, median class and modal class for grouped data (only continuous data). * Mean by all 3 methods included: fx Direct : f In general Implies that Identically equal to In set language Belongs to is equivalent to union universal set natural (counting) numbers integers fd Short-cut : A+ where d = x A f Step-deviation: A + ft i where t = x A f i In measures Kilometre Centimetre Kilogram Litre square kilometre square centimetre cubic metre kilometres per hour (b) Graphical Representation. Histograms and Less than Ogive. 3 is logically equivalent to is approximately equal to >> does not belong to is not equivalent to intersection is contained in the empty set whole numbers real numbers W R km cm kg L km2 cm2 m3 km/h Metre Millimetre Gram Centilitre Square meter Hectare Cubic centimetre Metres per second m mm g cL m2 ha cm3 m/s INTERNAL ASSESSMENT The minimum number of assignments: assignments as prescribed by the teacher. Two A B C Suggested Assignments Comparative newspaper coverage of different items. Survey of various types of Bank accounts, rates of interest offered. Planning a home budget. 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. To use a newspaper to study and report on shares and dividends. 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 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. 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. 4 Blue 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? 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? An eccentric artist says that the best paintings have the same area as their perimeter (numerically). Let us not argue whether such sizes increase the viewer s 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). Find by construction the centre of a circle, using only a 60-30 setsquare and a pencil. Various types of cryptarithm . EVALUATION Award of Marks (20 Marks) The 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.) Subject Teacher (Internal Examiner) 10 marks External Examiner 10 marks The 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 online entry of marks on the Council s CAREERS portal by the due date. The Internal Examiner and the External Examiner will assess the assignments independently. 5 INTERNAL ASSESSMENT IN MATHEMATICS - GUIDELINES FOR MARKING WITH GRADES Criteria Preparation Concepts Computation Presentation Understanding Marks Grade I Exhibits and selects a welldefined problem. Appropriate use of techniques. Admirable use of mathematical concepts and methods and exhibits competency in using extensive range of mathematical techniques. Careful accurate work appropriate computation, construction measurement correct units. Presents well stated conclusions; uses effective mathematical language, symbols, tables, conventions, diagrams, graphs, etc. Shows strong personal contribution; 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 techniques. Commits negligible errors in computation, and construction measurement. Some statements of conclusions; uses math appropriate language, symbols, conventions, tables, diagrams, graphs, etc. Neat with average 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 competency in using limited range of techniques. Commits a few errors in computation, construction and measurement. Assignment is presentable though it is disorganized in some places. Lack of ability to conclude without 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 inappropriate mathematical concepts for the assignment. Commits many mistakes in computation, construction and measurement. Presentation made is somewhat disorganized and untidy. Lack of ability to conclude even with considerable help; assignment contributes to mathematical learning to a certain extent. 1 mark for each criterion Grade V Exhibits and selects a completely irrelevant problem. Uses unsuitable techniques. Not able to use mathematical concepts. Inaccurate computation, and construction measurement. Presentation made is completely disorganized, untidy and poor. Assignment does not contribute to mathematical learning and lacks practical applicability. 0 mark and with and with 6

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