Entrance Tricks

አስረኛ ክፍል Mathematics ምን ያህል ታስታውሳላቹ ። በ Entrance Tricks የተዘጋጀ !!! #አብረን_እናስታውስ 🇪🇹Unit 1: Relations and Function • Relation: A relation is a set of ordered pairs, typically defined as a subset of the Cartesian product of two sets. • Domain: The set of all possible inputs (first elements) for a relation. • Range: The set of all possible outputs (second elements) for a relation. • Function: A special type of relation where each element in the domain is associated with exactly one element in the range. • Notation: A function is often denoted as  f(x) , where  x  is the input variable. • One-to-One Function: A function where each element of the range is mapped by at most one element of the domain. • Onto Function: A function where every element in the range is mapped by at least one element of the domain. • Inverse Function: A function that reverses the mapping of the original function. If  f(x) = y , then  f⁻¹(y) = x . 🇪🇹 Unit 2: Polynomial Function • Polynomial Function: A function of the form  f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ , where  aₙ, aₙ₋₁, ..., a₀  are constants and  n  is a non-negative integer. 📬Operations on Polynomial Functions • Addition: Combining polynomials by adding their corresponding coefficients. • Subtraction: Combining polynomials by subtracting their corresponding coefficients. • Multiplication: Using the distributive property to multiply polynomials. • Division: Dividing polynomials using long division or synthetic division. 📭Theorem on Polynomial Functions • Remainder Theorem: If a polynomial  f(x)  is divided by  x - c , the remainder is  f(c) . • Factor Theorem: A polynomial  f(x)  has a factor  x - c  if and only if  f(c) = 0 . 📭 Zeros of Polynomial Functions • Zero of a Polynomial: A value  x = c  such that  f(c) = 0 . • Multiplicity: The number of times a particular zero occurs as a root. 📭 Graphs of Polynomial Functions • End Behavior: Describes how the graph behaves as  x  approaches positive or negative infinity. • Turning Points: Points where the graph changes direction, determined by the degree of the polynomial. 🇪🇹Unit 3: Exponential and Logarithmic Functions • Exponent: A number that indicates how many times to multiply a base by itself (e.g.,  aⁿ = a × a × ... × a  (n times)). • Logarithm: The inverse operation to exponentiation, defined as  logᵦ(a) = c  if and only if  bᶜ = a . 📬 The Exponential Functions and Their Graphs • Exponential Function: A function of the form  f(x) = abˣ , where  a ≠ 0  and  b > 0 . • Graph Characteristics: Exponential functions grow rapidly; they have horizontal asymptotes. 📬 The Logarithmic Functions and Their Graphs • Logarithmic Function: A function of the form  f(x) = logᵦ(x) , which is the inverse of the exponential function. • Graph Characteristics: Logarithmic functions increase slowly; they also have vertical asymptotes. 📬 Solving Exponential and Logarithmic Equations • Methods include using properties of exponents and logarithms, such as:     –  b^(logᵦ(x)) = x     –  logᵦ(xy) = logᵦ(x) + logᵦ(y) 📬 Relation between Exponential and Logarithmic Functions • The relationship is defined by the equations:     – If  y = bˣ , then  x = logᵦ(y) . – They are inverses of each other, reflecting across the line  y = x . ክፍል 2 ይቀጥላል ...