L1 Lesson 1.1 Euclid's division algorithm based on Euclid's division lemma Lesson 1.2 Fundamental Theorem of Arithmetic Lesson 1.3 Revisiting irrational numbers: proof of results: irrationality of √2, √3, √5 and their representation on number line Lesson 1.4 Revisiting Rational Numbers (in terms of terminating/non terminating recurring decimals) and other Decimal Expressions Lesson 1.5 Challenging Questions integrating the above concepts Chapter : 2.Polynomials L2 Lesson 2.1 The degrees of Linear polynomials Lesson 2.2 The degrees of Quadratic polynomials Lesson 2.3 The degrees of Cubic polynomials Lesson 2.4 Zeroes of a quadratic polynomial Lesson 2.5 Zeroes of a cubic polynomial Lesson 2.6 Geometrical meaning of the zeroes of a polynomial Lesson 2.7 Relationship between zeroes and coefficients of a polynomial Lesson 2.8 Statement and simple problems on division algorithm for polynomials with real coefficients Lesson 2.9 Challenging Questions integrating the above concepts Chapter : 4.Quadratic Equations L4 Lesson 4.1 Standard form of a quadratic equation ax 2 +bx+c=0, (a ≠ 0) Lesson 4.2 Solution of the quadratic equation (only real roots) by: Factorization Lesson 4.3 Solution of the quadratic equation (only real roots) by: Completing the squares Lesson 4.4 Solution of the quadratic equation (only real roots) by: Using quadratic formula Chapter : 3.Pair of Linear Equations in Two Variables L3 Lesson 3.1 Pair of Linear Equations in two variables (Each solution (x, y) of a Linear Equation in two variables ax + by + c = 0 corresponds to a point on the line representing the equation and vice versa) Lesson 3.2 Graphical Method of solution of a pair of Linear Equations (Consistent and inconsistent solutions depending on whether the lines are intersecting, coincident or parallel) Lesson 3.3 Geometric representation of different possibilities of solutions/inconsistencies Lesson 3.4 Discriminant and nature of roots - Two distinct real roots Lesson 4.6 Discriminant and nature of roots - Two equal real roots Algebraic Method of solving a pair of Linear Equations with Substitution Method Lesson 3.5 Algebraic Method of solving a pair of Linear Equations with Cross – Multiplication Method Lesson 3.6 Lesson 3.7 Algebraic Method of solving a pair of Linear Equations with Verification for all the above three Equations reducible to a pair of Linear Equations in two variables Lesson 3.8 Lesson 3.9 Equations reducible to a pair of Linear Equations in two variables Word problems on all the above Chapter : 5.Arithmetic Progression L5 Lesson 5.1 Patterns seen in nature like the petals in a sunflower Lesson 5.2 Look and understand patterns in day to day life Lesson 5.3 Arithmetic Progression (general form) Lesson 5.4 Derivation of the nth term of A.P. Lesson 5.5 Common difference: d Lesson 5.6 Last term: l Lesson 5.7 Sum of the first n terms of A.P. Lesson 5.8 Application (example: sum of the first n positive integers) Lesson 5.9 Application of A.P. and nth term and their sum in solving daily life problems (example: Simple Interest) Chapter : 7.Coordinate Geometry L7 Lesson 7.1 Demonstrate an understanding of: Concept of Coordinate Geometry Lesson 7.2 Demonstrate an understanding of: Graphs of Linear Equations Lesson 7.3 Understand the: Distance Formula Lesson 7.4 Understand the: Section Formula Lesson 7.5 Understand the: Area of a Triangle L14 L15 Develop an understanding of: Mean, median, mode of grouped data Lesson 14.1 Lesson 14.2 Cumulative frequency graph Lesson 14.3 Word problems on above Lesson 14.4 Challenging Questions integrating the above concepts Chapter : 8.Introduction to Trigonometry L8 Lesson 8.1 Demonstrate an understanding of: Trigonometric Ratios Lesson 8.2 Understand: Trigonometric Ratios of some special angles - If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined Lesson 8.3 Understand: Trigonometric Ratios of some special angles - The values of trigonometric ratios for angles 0°, 30°, 45°, 60° and 90°. Lesson 8.4 Trigonometric Ratios of Complementary Angles Lesson 8.5 Demonstrate an understanding of: Trigonometric Identities - The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1 Lesson 8.6 Demonstrate an understanding of: Trigonometric Identities - sin(90° – A) = cos A, cos(90° – A)=sin A Lesson 8.7 Demonstrate an understanding of: Trigonometric Identities - tan(90° – A) = cot A, cot(90° – A)=tan A Demonstrate an understanding of: Trigonometric Identities - sec (90° – A) = cosec A, cosec (90° – A) = sec A Lesson 8.8 Lesson 8.9 Demonstrate an understanding of: Trigonometric Identities - sin²A + cos²A = 1 Lesson 8.10 Demonstrate an understanding of: Trigonometric Identities - sec²A – tan²A = 1 for 0° ≤ A ≤ 90° Lesson 8.11 Demonstrate an understanding of: Trigonometric Identities - cosec²A = 1 + cot²A for 0° ≤ A ≤ 90° Lesson 8.12 Word problems for all the above Chapter : 11.Constructions L11 Demonstrate an understanding to construction of: Division of a line segment in a given ratio (internally) Lesson 11.1 Lesson 11.2 Demonstrate an understanding to construction of: Tangent to a circle from a point outside it Lesson 11.3 Demonstrate an understanding to construction of: Construction of a triangle similar to a given triangle Challenging Questions integrating the above concepts Lesson 11.4 Chapter : 9.Some applications of Trigonometry L9 Lesson 9.1 Demonstrate an understanding of: Simple problems on heights and distances (Problems should not involve more than two right triangles) Lesson 9.2 Demonstrate an understanding of: The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios Lesson 9.3 Demonstrate an understanding of: Angles of elevation / depression should be only 30°, 45°, 60° Lesson 9.4 Demonstrate an understanding of: The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer. Lesson 9.5 Demonstrate an understanding of: The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when we raise our head to look at the object. Lesson 9.6 Demonstrate an understanding of: The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object. Lesson 9.7 Challenging Questions integrating the above concepts Chapter : 10.Circles L10 Demonstrate an understanding of: Tangents to a circle - From chords drawn from points coming closer and closer to the point Demonstrate an understanding of: Number of tangents from a point on a circle - Prove that tangent at any point of a circle is perpendicular to the radius through the point of contact Challenging Questions integrating the above concepts Demonstrate an understanding of: Number of tangents from a point on a circle - Prove the lengths of tangents drawn from an external point to circle are equal Chapter : 6.Triangles L6 Lesson 6.1 Demonstrate an understanding of: Similar figures -Two figures having the same shape but not necessarily the same size are called similar figure Lesson 6.2 Demonstrate an understanding of: Similar figures - All the congruent figures are similar but the converse is not true Lesson 6.3 Demonstrate an understanding of: Similar figures - Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio(i.e., proportion). Lesson 6.4 Demonstrate an understanding of: Similarity of Triangles - If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio Chapter : 12.Areas related to Circles L12 Lesson 12.1 An understanding of the following: The area of a circle – review Lesson 12.2 An understanding of the following:Areas of sectors and segments of a circle Lesson 12.3 An understanding of the following: Length of an arc of a sector of a circle with radius r and angle with degree measure θ Lesson 12.4 Understanding of the following: Problems based on areas and perimeter/ circumference of the above said plane figures (in calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only) Lesson 12.5 Understanding of the following: Plane figures involving triangles, simple quadrilaterals and circle should also be taken Lesson 12.6 Challenging Questions integrating the above concepts Chapter : 13.Surface Area and Volume L13 Lesson 13.1 Develop an understanding of: Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones Lesson 13.2 Develop an understanding of: Frustum of a cone Lesson 13.3 Word problems on: Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken). Lesson 13.4 Challenging Questions integrating the above concepts Lesson 15.1 Classical definition of probability (a theoretical approach) Lesson 15.2 The difference between experimental probability and theoretical probability Lesson 15.3 The theoretical(classical)probability of an event E, written as P(E), is defined as [P (E) = Number of outcomes favourable to E / Number of all possible outcomes of the experiment] where we assume that the outcomes of the experiment are equally likely. Probability of an event: The probability of a sure event (or certain event) is 1 Probability of an event: The probability of an impossible event is 0 Lesson 15.4 Lesson 15.5 Probability of an event:The probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1 Lesson 15.6 Probability of an event: An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1. Lesson 15.7 Probability of an event: For any event E, P (E) + P (E') = 1, where E' stands for 'not E'. E and E' are called complementary events Lesson 15.8 Simple problems on single events (not using set notation) Lesson 15.9 Challenging Questions integrating the above concepts Chapter : 14.Statistics Chapter : 15.Probability Lesson 6.5 Demonstrate an understanding of: Similarity of Triangles - If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side Lesson 6.6 Criteria for Similarity of Triangles - If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion) Lesson 6.7 Criteria for Similarity of Triangles - If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AA similarity criterion) Lesson 6.8 Criteria for Similarity of Triangles - If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar (SSS similarity criterion). Lesson 6.9 Criteria for Similarity of Triangles - If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar(SAS similarity criterion) Lesson 6.10 Understand the: Areas of Similar Triangles - The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides Lesson 6.11 Understand the: Areas of Similar Triangles - If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other Lesson 6.12 Demonstrate an understanding of: Similarity of Triangles - If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. Lesson 6.13 Pythagoras Theorem - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem) Lesson 6.14 Pythagoras Theorem - If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle Lesson 6.15 Word problems on all the above Lesson 4.5 Lesson 4.7 Discriminant and nature of roots - No real roots Situational problems based on quadratic equations related to day-to-day activities to be incorporated Lesson 4.8 Lesson 10.1 Lesson 10.2 Lesson 10.4 Lesson 10.3 PixelMath Make Math practice as fun and engaging as Games Chapter : 1.Real Numbers LESSON LEVELS CONCEPT GRADE 10 Lesson 7.6 Challenging Questions integrating the above concepts www.pixelmath.org [email protected] 8280723657 Lesson 15.10
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L1 Lesson 1.1 Euclid's division algorithm based on Euclid'sdivision lemma
Lesson 1.2 Fundamental Theorem of Arithmetic
Lesson 1.3Revisiting irrational numbers: proof of results:irrationality of √2, √3, √5 and their representationon number line
Lesson 1.4Revisiting Rational Numbers (in terms ofterminating/non terminating recurring decimals)and other Decimal Expressions
Lesson 1.5 Challenging Questions integrating the aboveconcepts
Chapter : 2.Polynomials
L2 Lesson 2.1 The degrees of Linear polynomials
Lesson 2.2 The degrees of Quadratic polynomials
Lesson 2.3 The degrees of Cubic polynomials
Lesson 2.4 Zeroes of a quadratic polynomial
Lesson 2.5 Zeroes of a cubic polynomial
Lesson 2.6 Geometrical meaning of the zeroes of apolynomial
Lesson 2.7 Relationship between zeroes and coefficients of apolynomial
Lesson 2.8 Statement and simple problems on divisionalgorithm for polynomials with real coefficients
Lesson 2.9 Challenging Questions integrating the aboveconcepts
Chapter : 4.Quadratic Equations
L4 Lesson 4.1 Standard form of a quadratic equation ax2 +bx+c=0, (a ≠ 0)
Lesson 4.2 Solution of the quadratic equation (only realroots) by: Factorization
Lesson 4.3 Solution of the quadratic equation (only realroots) by: Completing the squares
Lesson 4.4Solution of the quadratic equation (only realroots) by: Using quadratic formula
Chapter : 3.Pair of Linear Equations in Two Variables
L3 Lesson 3.1Pair of Linear Equations in two variables (Eachsolution (x, y) of a Linear Equation in two variablesax + by + c = 0 corresponds to a point on the linerepresenting the equation and vice versa)
Lesson 3.2Graphical Method of solution of a pair of LinearEquations (Consistent and inconsistent solutionsdepending on whether the lines are intersecting,coincident or parallel)
Lesson 3.3 Geometric representation of different possibilitiesof solutions/inconsistencies
Lesson 3.4
Discriminant and nature of roots - Two distinctreal roots
Lesson 4.6 Discriminant and nature of roots - Two equalreal roots
Algebraic Method of solving a pair of LinearEquations with Substitution Method
Lesson 3.5 Algebraic Method of solving a pair of LinearEquations with Cross – Multiplication Method
Lesson 3.6
Lesson 3.7
Algebraic Method of solving a pair of LinearEquations with Verification for all the above three
Equations reducible to a pair of Linear Equationsin two variables
Lesson 3.8
Lesson 3.9
Equations reducible to a pair of Linear Equationsin two variables
Word problems on all the above
Chapter : 5.Arithmetic Progression
L5 Lesson 5.1 Patterns seen in nature like the petals in asunflower
Lesson 5.2 Look and understand patterns in day to day life
Lesson 5.3 Arithmetic Progression (general form)
Lesson 5.4 Derivation of the nth term of A.P.
Lesson 5.5 Common difference: d
Lesson 5.6 Last term: l
Lesson 5.7 Sum of the first n terms of A.P.
Lesson 5.8 Application (example: sum of the first n positiveintegers)
Lesson 5.9Application of A.P. and nth term and their sum insolving daily life problems (example: SimpleInterest)
Chapter : 7.Coordinate Geometry
L7 Lesson 7.1 Demonstrate an understanding of: Concept ofCoordinate Geometry
Lesson 7.2 Demonstrate an understanding of: Graphs of Linear Equations
Lesson 7.3 Understand the: Distance Formula
Lesson 7.4 Understand the: Section Formula
Lesson 7.5 Understand the: Area of a Triangle
L14
L15
Develop an understanding of: Mean, median, mode of grouped dataLesson 14.1
Lesson 14.2 Cumulative frequency graph
Lesson 14.3 Word problems on above
Lesson 14.4 Challenging Questions integrating the aboveconcepts
Chapter : 8.Introduction to Trigonometry
L8 Lesson 8.1 Demonstrate an understanding of: Trigonometric Ratios
Lesson 8.2Understand: Trigonometric Ratios of some special angles - If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined
Lesson 8.3Understand: Trigonometric Ratios of some special angles - The values of trigonometric ratios for angles 0°, 30°, 45°, 60° and 90°.
Lesson 8.4 Trigonometric Ratios of Complementary Angles
Lesson 8.5Demonstrate an understanding of: TrigonometricIdentities - The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1
Lesson 8.6 Demonstrate an understanding of: TrigonometricIdentities - sin(90° – A) = cos A, cos(90° – A)=sin A
Lesson 8.7 Demonstrate an understanding of: Trigonometric Identities - tan(90° – A) = cot A, cot(90° – A)=tan A
Demonstrate an understanding of: TrigonometricIdentities - sec (90° – A) = cosec A, cosec (90° – A)= sec A
Lesson 8.8
Lesson 8.9 Demonstrate an understanding of: TrigonometricIdentities - sin²A + cos²A = 1
Lesson 8.10 Demonstrate an understanding of: Trigonometric Identities - sec²A – tan²A = 1 for 0° ≤ A ≤ 90°
Lesson 8.11 Demonstrate an understanding of: Trigonometric Identities - cosec²A = 1 + cot²A for 0° ≤ A ≤ 90°
Lesson 8.12 Word problems for all the above
Chapter : 11.Constructions
L11Demonstrate an understanding to construction of: Division of a line segment in a given ratio (internally)
Lesson 11.1
Lesson 11.2 Demonstrate an understanding to construction of: Tangent to a circle from a point outside it
Lesson 11.3Demonstrate an understanding to construction of: Construction of a triangle similar to a given triangle
Challenging Questions integrating the above conceptsLesson 11.4
Chapter : 9.Some applications of Trigonometry
L9 Lesson 9.1Demonstrate an understanding of: Simple problems on heights and distances (Problemsshould not involve more than two right triangles)
Lesson 9.2Demonstrate an understanding of: The height orlength of an object or the distance between two distant objects can be determined with the help of trigonometric ratios
Lesson 9.3 Demonstrate an understanding of: Angles ofelevation / depression should be only 30°, 45°, 60°
Lesson 9.4Demonstrate an understanding of: The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
Lesson 9.5Demonstrate an understanding of: The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it isabove the horizontal level, i.e., the case when we raise our head to look at the object.
Lesson 9.6Demonstrate an understanding of: The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object.
Lesson 9.7 Challenging Questions integrating the above concepts
Chapter : 10.Circles
L10Demonstrate an understanding of: Tangents to acircle - From chords drawn from points comingcloser and closer to the point
Demonstrate an understanding of: Number of tangents from a point on a circle - Prove that tangent at any point of a circle is perpendicularto the radius through the point of contact
Challenging Questions integrating the above concepts
Demonstrate an understanding of: Number oftangents from a point on a circle - Prove the lengths of tangents drawn from an external point to circle are equal
Chapter : 6.Triangles
L6 Lesson 6.1Demonstrate an understanding of: Similar figures-Two figures having the same shape but not necessarily the same size are called similar figure
Lesson 6.2Demonstrate an understanding of: Similar figures- All the congruent figures are similar but the converse is not true
Lesson 6.3Demonstrate an understanding of: Similar figures - Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio(i.e., proportion).
Lesson 6.4Demonstrate an understanding of: Similarity of Triangles - If a line is drawn parallel to one side ofa triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio
Chapter : 12.Areas related to Circles
L12 Lesson 12.1 An understanding of the following: The area of a circle – review
Lesson 12.2 An understanding of the following:Areas of sectorsand segments of a circle
Lesson 12.3An understanding of the following: Length of an arc of a sector of a circle with radius r and angle with degree measure θ
Lesson 12.4Understanding of the following: Problems based on areas and perimeter/ circumference of the above said plane figures (in calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only)
Lesson 12.5Understanding of the following: Plane figures involving triangles, simple quadrilaterals and circle should also be taken
Lesson 12.6 Challenging Questions integrating the above concepts
Chapter : 13.Surface Area and Volume
L13 Lesson 13.1Develop an understanding of: Problems on findingsurface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres,hemispheres and right circular cylinders/cones
Lesson 13.2 Develop an understanding of: Frustum of a cone
Lesson 13.3Word problems on: Problems involving convertingone type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).
Lesson 13.4 Challenging Questions integrating the above concepts
Lesson 15.1 Classical definition of probability (a theoretical approach)
Lesson 15.2 The difference between experimental probability and theoretical probability
Lesson 15.3
The theoretical(classical)probability of an event E,written as P(E), is defined as [P (E) = Number of outcomes favourable to E / Number of all possible outcomes of the experiment] where we assume that the outcomes of the experiment are equally likely.
Probability of an event: The probability of a sure event (or certain event) is 1
Probability of an event: The probability of an impossible event is 0
Lesson 15.4
Lesson 15.5
Probability of an event:The probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1Lesson 15.6
Probability of an event: An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events ofan experiment is 1.
Lesson 15.7
Probability of an event: For any event E, P (E) + P (E') = 1, where E' stands for 'not E'. E and E' are called complementary events
Lesson 15.8
Simple problems on single events (not using set notation)Lesson 15.9
Challenging Questions integrating the above concepts
Chapter : 14.Statistics
Chapter : 15.Probability
Lesson 6.5Demonstrate an understanding of: Similarity of Triangles - If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side
Lesson 6.6Criteria for Similarity of Triangles - If in twotriangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion)
Lesson 6.7
Criteria for Similarity of Triangles - If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AAsimilarity criterion)
Lesson 6.8Criteria for Similarity of Triangles - If in two triangles, corresponding sides are in the sameratio, then their corresponding angles are equal and hence the triangles are similar (SSS similaritycriterion).
Lesson 6.9
Criteria for Similarity of Triangles - If one angle of a triangle is equal to one angle of another triangleand the sides including these angles are in the same ratio (proportional), then the triangles are similar(SAS similarity criterion)
Lesson 6.10Understand the: Areas of Similar Triangles - Theratio of the areas of two similar triangles is equalto the square of the ratio of their corresponding sides
Lesson 6.11
Understand the: Areas of Similar Triangles - If aperpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other
Lesson 6.12
Demonstrate an understanding of: Similarity of Triangles - If a line is drawn parallel to one side ofa triangle to intersect the other two sides indistinct points, then the other two sides are divided in the same ratio.
Lesson 6.13Pythagoras Theorem - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem)
Lesson 6.14Pythagoras Theorem - If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle
Lesson 6.15 Word problems on all the above
Lesson 4.5
Lesson 4.7 Discriminant and nature of roots - No real roots
Situational problems based on quadraticequations related to day-to-day activities to beincorporated
Lesson 4.8
Lesson 10.1
Lesson 10.2
Lesson 10.4
Lesson 10.3
PixelMathMake Math practice as fun and engaging as Games
Chapter : 1.Real Numbers
LESSON LEVELS CONCEPT
GRADE10
Lesson 7.6 Challenging Questions integrating the above concepts
www.pixelmath.org [email protected] 8280723657
Lesson 15.10
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