Grade 10 Math Formulas Flashcards

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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?

y₂-y₁=m(x₂-x₁) Signup and view all the answers

What is the equation of a line?

y=mx+b Signup and view all the answers

What is the equation of a circle?

x²+y²=r² Signup and view all the answers

What is a common factor?

6x⁴y⁵+9x⁵y³-3x²y Signup and view all the answers

What is an example of a simple trinomial?

5x²-5x-30 Signup and view all the answers

What is a perfect square?

4x²+12xy+9y² Signup and view all the answers

What is the formula for the difference of squares?

x²-16 Signup and view all the answers

What is an example of a complex trinomial?

4x²-100y² Signup and view all the answers

What is the vertex form of a quadratic function?

y=a(x-h)+k Signup and view all the answers

What is the factored form of a quadratic function?

y=(x-s)(x-r) Signup and view all the answers

What is the standard form of a quadratic function?

y=ax²+bx+c Signup and view all the answers

What is the quadratic formula?

x=-b±√b²-4ac÷2a Signup and view all the answers

What is the Pythagorean theorem?

a²+b²=c² Signup and view all the answers

What is the sine of an angle in a right triangle?

O÷H Signup and view all the answers

What is the cosine of an angle in a right triangle?

A÷H Signup and view all the answers

What is the tangent of an angle in a right triangle?

O÷A Signup and view all the answers

What is the sine law (length)?

sinA÷a=sinB÷b=sinC÷c Signup and view all the answers

What is the sine law (angle)?

a÷sinA=b÷sinB=c÷sinC Signup and view all the answers

What is the cosine law (length)?

a²=b²+c²-2bc(cosA) Signup and view all the answers

What is the cosine law (angle)?

cosA=b²+c²-a²÷2bc Signup and view all the answers

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.

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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!