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Year 10
Linear Equations in Two Variables
Word Problems on Linear Equations in Two Variables
Problems on Boats and Stream

Year 10

1. Real numbers

1.1. Euclid's Division Lemma

1.2. Fundamental Theorem of Arithmetic, LCM, HCF

1.3. Rational Numbers

1.4. Irrational Numbers

2. Polynomials

2.1. Zeros of a Quadratic Polynomial

2.2. Zeros of a Cubic Polynomial

2.3. Division Algorithm for Polynomials

3. Linear Equations in Two Variables

3.1. Forming Linear Equations Under the Given Conditions

3.2. Solutions of a Linear Equation

3.3. Solving a System of Simultaneous Linear Equations

3.3.1. Graphical Method

3.3.2. Algebraic Method

3.3.2.1. Substitution Method

3.3.2.2. Elimination Method

3.3.2.3. Cross Multiplication Method

3.4. Conditions for Solvability of a System of Linear Equations

3.4.1. System of Equations with Unique Solution

3.4.2. System of Equations with Infinitely Many Solutions

3.4.3. System of Equations with No Solution

3.4.4. To Identify the Number of Solutions of a System of Simultaneous Linear Equations

3.4.5. To Find the Unknown Variable When the Equation of Two Lines is Given

3.4.6. Graph of Consistent and Inconsistent System of Linear Equations

3.5. Word Problems on Linear Equations in Two Variables

3.5.1. Problems on Numbers

3.5.2. Problems on Ages

3.5.3. Problems on Time and Distance

3.5.4. Problems on Boats and Stream

3.5.5. Problems on Time and Work

3.5.6. Problems on Geometry

4. Triangles

4.1. Basic Proportionality Theorem (Thales's Theorem) and its Applications

4.2. Angle-Bisector Theorem and its Applications

4.3. Similar Triangles

4.3.1. Theorems and Problems Related to Similar Triangles

4.3.2. Ratio of the Areas of Two Similar Triangles

4.4. Pythagoras Theorem

5. Trigonometry

5.1. Trigonometric Ratios

5.1.1. Trigonometric Ratios of an Acute Angle of a Right-Triangle

5.1.2. Relation Between Trigonometric Ratios

5.1.3. Various Trigonometric Ratios of an Angle

5.1.4. Evaluate Expressions Involving Trigonometric Ratios

5.1.5. Square Relation of Trigonometric Ratios

5.2. Trigonometric Ratios of Angles 0, 30, 45, 60, and 90 degrees

5.3. Trigonometric Ratios of Complementary Angles

5.4. Trigonometric Identities

5.4.1. Trigonometric Identities to solve Expressions Involving Trigonometric Ratios

5.4.2. Elimination of Trigonometric Ratios Using Identities

5.5. Heights and Distances

6. Statistics and Probability

6.1. Statistics

6.1.1. Mean of Grouped and Ungrouped Data

6.1.1.1. Mean for Exclusive and Inclusive Series

6.1.1.1.1. Direct Method

6.1.1.1.2. Assumed-Mean Method

6.1.1.1.3. Step-Deviation Method

6.1.2. Median for Grouped Data

6.1.2.1. Median for an Exclusive Series

6.1.2.2. Median for an Inclusive Series

6.1.3. Mode of Grouped Data

6.1.3.1. Mode for an Exclusive Series

6.1.3.2. Mode for an Inclusive Series

6.1.3.3. Using Empirical Formula

6.1.4. Miscellaneous Questions on Mean, Mode and Median of Grouped Data

6.2. Probability

6.2.1. Card Problems

6.2.2. Dice Problems

6.2.3. Coin Problems

6.2.4. Other Problems

7. Quadratic Equations

7.1. Identify Quadratic Equations

7.2. Solutions of a Quadratic Equation

7.3. Solve Quadratic Equations by Factorization

7.4. Solve Quadratic Equations by Completing the Square

7.5. Solve Quadratic Equations by Using Quadratic Formula

7.6. Nature of Roots of a Quadratic Equation

7.7. Word Problem on Quadratic Equations

7.7.1. Word Problems on Numbers

7.7.2. Word Problems on Ages

7.7.3. Word Problems on Money

7.7.4. Word Problems on Speed, Time and Distances

7.7.5. Word Problems on Time and Work

7.7.6. Word Problems Geometry

8. Arithmetic Progression (AP)

8.1. Tell if a Progression is an Arithmetic Progression (AP)

8.2. Find the Unknown Variable(s) in an AP

8.3. Find the Numbers in AP Under Specified Conditions

8.4. General Term (n^th Term) of an AP

8.4.1. General Term of an AP

8.4.2. Number of Terms in an AP

8.4.3. Middle Term of an Arithmetic Progression

8.4.4. Position and Number of Terms of an Arithmetic Progression

8.5. General Term (n^th Term) from the End of an AP

8.6. Arithmetic Mean

8.7. Sum of n Terms of an Arithmetic Progression (AP)

8.7.1. Find the General Term of an AP When the Sum of n Terms is Given

8.7.2. Find the Common Difference when the Sum of the Series is Given (AP) and the First and the Last Term is Given

8.7.3. Find the Number of Terms in an AP When the Sum of the Series is Given

8.7.4. Find the Sum of an AP Under Different Conditions

8.8. Word Problems on Arithmetic Progressions (AP)

9. Circles

9.1. Theorems and Results Related to Tangents of Circles

10. Coordinate Geometry

10.1. Distance Formula

10.1.1. Distance Between Two Points

10.1.2. Miscellaneous Problems

10.2. Section Formula and Midpoint Formula

10.3. Centroid of a Triangle

10.4. Area of Triangle and Parallelogram

11. Mensuration

11.1. Perimeter and Area of Plane Figures

11.1.1. Measuring Areas of Triangles

11.1.1.1. Area of a Triangle Using Base and Altitude

11.1.1.2. Area of a Triangle Using Heron's Formula

11.1.2. Measuring Areas of Quadrilaterals

11.1.2.1. Area Between Two Rectangles

11.1.2.2. Area of a Quadrilateral

11.1.2.3. Area of a Parallelogram

11.1.2.4. Area of a Rhombus

11.1.2.5. Area of a Trapezium

11.1.2.6. Area of a Quadrilateral Using Heron's Formula

11.1.2.7. Application of Results on Area of Polygonal Regions

11.1.3. Area of circles, sectors and segments

11.1.3.1. Area and Circumference of a Circle

11.1.3.2. Area of a Sector, Segment and Length of the Arc

11.1.4. Areas of Combinations of Plane Figures

11.2. Surface Areas and Volumes

11.2.1. Volume and Surface Area of Solids

11.2.2. Volume and Surface Area of Conical Frustum

11.2.3. Volume and Surface Area of Combination of Solids

11.2.4. Mixed Problems on Volume and Surface Area

Year 10 Australian School Math Problems on Boats and Stream

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