Questions and Answers
What is the formula for the distance of a line?
√(x₂−x₁)²+(y₂-y₁)²
What is the formula for the midpoint of a line?
(x₁+x₂÷2, y₁-y₂÷2)
What is the formula for slope?
(y₂-y₁)÷(x₂-x₁)
What is the point-slope form of a line?
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What is the equation of a line?
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What is the equation of a circle?
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What is a common factor?
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What is an example of a simple trinomial?
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What is a perfect square?
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What is the formula for the difference of squares?
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What is an example of a complex trinomial?
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What is the vertex form of a quadratic function?
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What is the factored form of a quadratic function?
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What is the standard form of a quadratic function?
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What is the quadratic formula?
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What is the Pythagorean theorem?
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What is the sine of an angle in a right triangle?
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What is the cosine of an angle in a right triangle?
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What is the tangent of an angle in a right triangle?
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What is the sine law (length)?
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What is the sine law (angle)?
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What is the cosine law (length)?
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What is the cosine law (angle)?
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Study Notes
Distance and Midpoint
- Distance between two points can be calculated using the formula: √((x₂ − x₁)² + (y₂ − y₁)²).
- The midpoint of a line segment connecting two points is given by: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).
Slope and Line Equations
- The slope of a line between two points is determined by the formula: (y₂ − y₁) ÷ (x₂ − x₁).
- Point-slope form of a linear equation is expressed as: y₂ − y₁ = m(x₂ − x₁), where m represents the slope.
- The general equation of a line is represented as: y = mx + b, where m is the slope and b is the y-intercept.
Circle and Factorization
- The equation of a circle centered at the origin is: x² + y² = r², where r is the radius.
- Identifying common factors in polynomials like 6x⁴y⁵ + 9x⁵y³ - 3x²y aids in simplification.
- Simple trinomials can be expressed, for example as: 5x² - 5x - 30.
- Perfect squares take the form: 4x² + 12xy + 9y², indicating a specific factorization pattern.
Special Polynomial Forms
- The difference of squares is written as: x² - 16, allowing for factorization into (x - 4)(x + 4).
- A complex trinomial example includes expressions like: 4x² - 100y².
Quadratic Equations
- Vertex form of quadratic equations is given by: y = a(x - h) + k, where (h, k) is the vertex.
- Factored form can be represented as: y = (x - s)(x - r), where s and r are the roots.
- Standard form of a quadratic equation is: y = ax² + bx + c.
Quadratic Formula and Theorems
- The quadratic formula for finding the roots of a quadratic equation is: x = -b ± √(b² - 4ac) ÷ 2a.
- Pythagorean theorem states that for right triangles: a² + b² = c², where c is the hypotenuse.
Trigonometric Ratios
- Sine (sin) is calculated as the ratio of the opposite side to the hypotenuse: O ÷ H.
- Cosine (cos) is defined as the ratio of the adjacent side to the hypotenuse: A ÷ H.
- Tangent (tan) is the ratio of the opposite side to the adjacent side: O ÷ A.
Sine and Cosine Law
- Sine Law for lengths relates the sides of a triangle to the sine of their opposite angles: sin A ÷ a = sin B ÷ b = sin C ÷ c.
- Sine Law for angles states: a ÷ sin A = b ÷ sin B = c ÷ sin C.
- Cosine Law for lengths: a² = b² + c² - 2bc(cos A), useful for finding side lengths.
- Cosine Law for angles can be expressed as: cos A = (b² + c² - a²) ÷ (2bc), enabling angle determination.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of essential math formulas with these flashcards designed for Grade 10 students. Each card features key formulas such as distance, midpoint, slope, and equations for lines and circles. Perfect for quick reviews or studying for exams!
