9th Grade Math: Real Numbers, Inequalities, Polynomials

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Qual das seguintes opções descreve corretamente um intervalo de números reais?

  • O conjunto de todos os números inteiros entre dois limites.
  • O conjunto de todos os números imaginários entre dois limites.
  • O conjunto de todos os números racionais entre dois limites.
  • O conjunto de todos os números reais entre dois limites. (correct)

A solução para a inequação $x + 5 > 10$ inclui todos os números menores que 5.

False (B)

Simplifique a seguinte expressão: $(3x^2 + 2x - 1) + (x^2 - 5x + 4)$.

4x^2 - 3x + 3

O produto de um monómio por um polinómio é encontrado multiplicando o monómio por ______ termo do polinómio.

<p>cada</p> Signup and view all the answers

Associe cada tipo de função à sua forma algébrica correspondente:

<p>Função Afim = $y = ax + b$ Função de Proporcionalidade Inversa = $y = \frac{k}{x}, x &gt; 0$ Função Quadrática = $y = ax^2, a \neq 0$</p> Signup and view all the answers

Qual método é usado para resolver equações do 2º grau?

<p>Fatoração e lei do anulamento do produto. (D)</p> Signup and view all the answers

Em uma sequência, o termo geral é uma fórmula que permite encontrar qualquer termo sem conhecer os anteriores.

<p>True (A)</p> Signup and view all the answers

Num triângulo retângulo, se os catetos medem 3 cm e 4 cm, qual é a medida da hipotenusa?

<p>5 cm</p> Signup and view all the answers

A fórmula para o volume de um cubo é $V = l^3$, onde $l$ representa o comprimento da ______ do cubo.

<p>aresta</p> Signup and view all the answers

Qual razão trigonométrica é definida como o lado oposto sobre a hipotenusa?

<p>Seno. (B)</p> Signup and view all the answers

Flashcards

Real Number Intervals

A set of real numbers between two given endpoints, which can be open, closed, or half-open.

Inequalities in ℝ

Mathematical statements that show the relationship between two non-equal values.

Operations with Real Numbers

Combining numbers using operations like addition, subtraction, multiplication, and division following the order of operations.

Monomials and Polynomials

An algebraic expression consisting of one term (monomial) or the sum of multiple terms (polynomials).

Signup and view all the flashcards

Functions

A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Signup and view all the flashcards

Equation

A mathematical statement that asserts the equality of two expressions.

Signup and view all the flashcards

Sequences and Successions

An ordered list of numbers (or other elements), called terms, that often follow a specific pattern or rule.

Signup and view all the flashcards

Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Signup and view all the flashcards

Trigonometry

Techniques to measure the angles and sides of triangles

Signup and view all the flashcards

Circumference

A round plane figure whose boundary consists of points equidistant from the center.

Signup and view all the flashcards

Study Notes

  • Study notes for a 9th-grade math test scheduled for March 2025.

Real Number Intervals

  • Determine intervals of real numbers, including intersections and unions.
  • Identify numbers belonging to intervals of real numbers.

Inequalities in IR (Real Numbers)

  • Solve first-degree inequalities.

Operations with Real Numbers

  • Perform operations in the set of real numbers (R).

Monomials and Polynomials

  • Determine the algebraic sum and product of two monomials.
  • Write a polynomial in reduced form.
  • Determine the algebraic sum of polynomials.
  • Determine the product of a monomial and a polynomial.

Functions

  • Identify algebraic and graphical representations of:
    • Affine functions (y = ax + b).
    • Inverse proportionality functions (y = k/x, x > 0).
    • Quadratic functions (y = ax², a ≠ 0).
  • Solve problems involving affine, inverse proportionality, and quadratic functions.

Equations

  • Solve incomplete 2nd-degree equations using the zero-product property.
  • Solve complete 2nd-degree equations.

Sequences and Successions

  • Solve problems involving sequences and successions, finding general terms.

Pythagorean Theorem

  • Determine the measure of one side of a right triangle when the measures of the other two sides are known.

Areas and Volumes of Solids

  • Solve problems involving calculating volumes of geometric solids.

Trigonometry in Right Triangles

  • Determine the exact or approximate value of an angle's amplitude using its trigonometric ratios.
  • Solve problems determining distances using trigonometric ratios.

Circle/Circumference

  • Understand and apply the relationship between the amplitude of a central angle and the amplitude of the arc it subtends.
  • Understand and apply the relationship between the amplitude of an inscribed angle and the amplitude of the arc it subtends.
  • Recognize that inscribed angles subtending the same arc have the same amplitude.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

More Like This

Use Quizgecko on...
Browser
Browser