Textbook of Mathematics Science Group Grade 10 PDF

# Textbook of Mathematics Science Group Grade 10 ## Details - Based on National Curriculum 2006 - Published by National Book Foundation as Federal Textbook Board, Islamabad - Copyright 2024 - ISBN: 978-969-37-1601-6 - Price: 400/- - Quantity: 33000 - First Edition - First Impression: March, 2024...

# Textbook of Mathematics Science Group Grade 10 ## Details - Based on National Curriculum 2006 - Published by National Book Foundation as Federal Textbook Board, Islamabad - Copyright 2024 - ISBN: 978-969-37-1601-6 - Price: 400/- - Quantity: 33000 - First Edition - First Impression: March, 2024 ## Authors - Dr. Khalid Mahmood - Dr. Saleem Ullah Satti ## Review Committee Member - Mr. Shahzad Ahmed - Mr. Muhammad Dabeer Mughal - Mr. Naveed Akmal ## Desk Officer (NCC) - Ms. Sikandra Ali ## Contents - **Unit 1**: Quadratic Equations - **Unit 2**: Theory of Quadratic Equations - **Unit 3**: Variation - **Unit 4**: Partial Fractions - **Unit 5**: Set - **Unit 6**: Basic Statistics - **Unit 7**: Introduction to Trigonometry - **Unit 8**: Projection of Sides of a Triangle - **Unit 9**: Chord of a Circle - **Unit 10**: Tangent to a Circle - **Unit 11**: Chord and Arcs - **Unit 12**: Angle in a Segment of a Circle - **Unit 13**: Practical Geometry Circles ## Preface The Mathematics Science Group Grade 10 textbook is developed to cover the learning outcomes of the revised Mathematics National Curriculum 2006 comprehensively. The Mathematics Science Group Grade 10 textbook builds a strong foundation of the subject through the use of well-researched and sound pedagogical principles. Adopting the popular Concrete- Pictorial-Abstract approach widely used in revised Mathematics Curriculum 2000, learners are introduced to new concepts through concrete manipulatives and engaging pictorials before they are led to see their abstract symbolic representations. This allows learners to have a deeper understanding of key mathematical concepts, thus motivating them to learn. Content is also clearly structured and spiralled across the levels to ensure a gradual build-up and review of skills as learner's progress up the grades. At the same time, emphasis is given on developing learners' problem-solving skills, critical thinking, as well as other 21st century skills. The Mathematics Science Group Grade 10 textbook also develops pupils' confidence for examinations through Check points, Exercises and Review Exercises for every concept. Every Chapter begins with a chapter opener which motivates learner's interest. Interesting real life situations and applications are used to develop learner's interest and curiosity so that they can appreciate the beauty of Mathematics in their environments. The National Book Foundation endeavours to keep quality enhancement at the heart of textbooks development. Likewise, it strives to keep improving its textbooks by incorporation of feedback and suggestions from the students, teachers and the community Preface in subsequent editions of its new textbooks. Some errors pointed out as feedback which are rectified by authors in this edition. As always the National Book Foundation looks forward to receiving feedback on this new textbook for Mathematics Science Group Grade X to align it more closely to the needs of the learners. ## Managing Director - Dr. Raja Mazhar Hameed ## Key Points - **Quadratic Equations**: - The standard ax² + bx + c = 0, where a does not equal zero. - Methods for solving quadratic equations: factorization, completing the square, and quadratic formula. - **Nature of Roots**: - Discriminant (b²-4ac) - Real roots: The discriminant is greater or equals zero. - Rational and Unequal: The discriminant is a perfect square. - Rational and Equal: The discriminant is zero. - Irrational and Unequal: The discriminant is positive, but not a perfect square. - Imaginary roots: The discriminant is negative. - **Cube Roots of Unity**: - Real cube root: 1 - Complex cube roots: -1+√3 / 2 and -1-√3 / 2 - Properties: - The sum of all three cube roots of unity is zero. - The product of all three cube roots of unity is 1. - For any n ∈ Z, ω^n is equivalent to one of the cube roots of unity. - **Relationships between Roots and Coefficients of Quadratic Equations**: - Sum of roots: -b/a - Product of roots: c/a - **Formation of Quadratic Equations**: - Given the roots α and β, the quadratic equation is x² - Sx + P = 0 - S: Sum of roots - P: Product of roots - **Synthetic Division**: - Method for dividing polynomials by linear polynomials to find the quotient and the remainder. - Steps: 1. Write down the coefficients of the dividend in a row. 2. Write the value of 'a' (from divisor x-a) to the left of the coefficients. 3. Bring down the first coefficient. 4. Multiply the first coefficient by 'a' and write the result below the second coefficient. 5. Add the two values in the second column and write the sum below the line. 6. Repeat steps 4 and 5 until all coefficients are used. - **Simultaneous Equations**: - A set of equations with a common solution. - Solving Methods: - Substitution: Solve one equation for one variable and substitute it into the other equation. - Elimination: Multiply the equations by constants to make the coefficients of one variable identical. Then add or subtract the equations to eliminate the variable. - **Variations**: - A relation between two quantities in which the change in one quantity causes a change in the other quantity. - **Direct Variation**: y α x or y = kx - When one quantity increases, the other increases proportionally. - Example: The number of items produced is directly proportional to the number of workers. - **Inverse Variation**: y α 1/x or xy = k - Example: The speed of a car is inversely proportional to the time taken to cover a certain distance. - **Joint Variation**: y α xz or y = k xz - Example: The volume of a gas varies jointly as the temperature and inversely as the pressure. - **Mean and Continued Proportions**: - Mean Proportion: a:b::b:d - Continued Proportion: a:b::b:d ## Additional Notes - The document contains various formulas, equations, and tables that are not suitable to be converted into simple markdown. - The document includes multiple examples and solved problems to illustrate the use of different concepts related to quadratic equations and variations. - The document also contains exercises and an exercise solution key to allow for practice. - Some images were not recognized by the OCR. 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