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所在平台: Udemy |
课程主页: https://www.udemy.com/course/clep-college-mathematics-exam-algebra-functions/
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课程名称：CLEP大学数学考试 - 数字、代数与函数 课程概述：该课程涵盖了大学数学CLEP考试中数字与代数与函数两个类别的基本概念。这两个主题合计占考试内容的约30%。无论你是在复习数学基础知识，还是准备通过考试获得大学学分，这门课程都将帮助你建立扎实的基础，内容包括：核心数字概念（约占考试的10%）和代数推理与函数（约占考试的20%）。许多大学和学院承认CLEP考试的学分，学分政策因机构而异，请确认你的学校如何将CLEP学分应用于你的学位课程。 通过掌握这两个内容领域，你将能够自信地应对大学数学CLEP考试近三分之一的内容。课程涵盖的主要讲座包括： - **实数**：定义、实数的性质、运算顺序、实数的组成部分 - **分数与数字规则**：适当和不适当的分数、奇偶数规则、因子与倍数、质数与合数 - **指数**：负指数、零指数、分数指数、负分数指数及指数法则 - **不等式与绝对值**：定义、实数的顺序性质、不等式的传递性质、不等式的加法性质、不等式的图示法、数轴上的区间、绝对值的定义及绝对值的解法 - **虚数与复数**：虚数的定义、复数的定义、复数的加法、减法、乘法及除法 - **科学记数法**：科学记数法的定义与形式、如何转为标准记数法、科学记数法的乘法与除法 - **测量系统**：英制与公制的长度、重量和体积单位；时间单位；如何进行单位换算 - **方程**：如何在方程中求解未知数、如何解分数方程及指数方程 - **对数**：如何找出对数、常用对数及对数规则 - **线性方程**：线性方程的定义、含有一个未知数的线性方程求解、两个未知数的线性方程的一般形式、斜截式和线性方程的图示 - **现实问题建模**：线性函数建模及使用表格形式写线性函数的方程 - **点-斜率与截距形式**：点-斜率式、如何用点-斜率形式找出给定两点的线性方程、截距形式及如何找到给定x和y截距的线性方程 - **联立线性方程**：使用代入法、加法或减法及图示法求解联立线性方程 - **其他方程系统**：相关方程、一致与不一致线性方程组、平行线与垂直线 - **不等式与绝对值方程**：如何解不等式、线性不等式的图示法及绝对值方程的求解 - **二次方程**：定义、一个未知数的二次方程、两个未知数的二次方程及使用因式分解、二次差法和二次公式解决一个未知数的二次方程 - **二次公式**：二次公式示例、判别式定义及对二次方程根的性质影响 - **关系**：有序对、关系及关系的定义域与值域 - **函数**：函数定义、函数的三种表示方式、如何判断关系是否为函数、函数的图形表示、竖线测试、符号表示及分段函数 - **函数的定义域**：指定函数定义域的五个选项及定义域规则和示例 - **其他函数**：函数的逆函数和指数函数 - **组合函数**：函数的复合及代数结合 - **图形变换**：常见图形变换及对函数的影响 本课程的学习将有助于巩固数学基础知识，提升考试信心，并为未来的学术发展打下坚实的基础。
This course covers the essential concepts from the Numbers and Algebra & Functions categories of the College Mathematics CLEP exam. Together, these two topics account for approximately 30% of the exam content, based on guidance from the College Board.Whether you're brushing up on math fundamentals or preparing to earn college credit by exam, this course will help you build a strong foundation in:Core number concepts (≈10% of the exam)Algebraic reasoning and functions (≈20% of the exam)The College Mathematics CLEP exam is accepted for credit at many colleges and universities. Credit policies vary by institution, so please check with your school to confirm how CLEP credit may apply to your degree program.By mastering these two content areas, you'll be well on your way to confidently tackling nearly one-third of the College Mathematics CLEP exam.The following lectures are included:Real numbers - definition, properties of real numbers, order of operations, components of real numbersFractions and number rules - proper and improper fractions, rules of odd and even numbers, factors and multiples, prime numbers and composite numbersExponents - negative exponents, exponent of zero, fractional exponents, negative fractional exponents, the laws of exponentsInequalities and absolute value - definition, order property of real numbers, transitive property of inequalities, addition property of inequality, graphing inequalities, intervals on a number line, absolute value definition, how to solve expressions with absolute values, the rules of absolute valuesImaginary and complex numbers - define imaginary numbers, define complex numbers, adding complex numbers, subtracting complex numbers, multiplying complex numbers, dividing complex numbersScientific notation - definition/form of scientific notation, how to convert to standard notation, how to convert from standard notation to scientific notation, multiplication of numbers in scientific notation, division of numbers in scientific notationSystems of measurement - imperial system and metric system units of length, weight and volume; units of time; how to convert unitsEquations - how to solve for unknown variable in equations, how to solve equations in fractional form, and how to solve exponential equationsLogarithms - how to find logarithms, common logarithm, and logarithm rulesLinear equations - define linear equation, solve linear equations with one unknown, general format for linear equations with two unknowns, slope-intercept form, and how to graph linear equationsModeling real-world problems - modeling linear functions and using tabular form to write an equation for a linear functionPoint-Slope and Intercept Form - point-slope form, how to find linear equation given two points using point-slope form, intercept form, how to find linear equation given the x and y intercepts using intercept form, horizontal lines, and vertical linesSimultaneous linear equations - how to solve simultaneous linear equations using substitution, addition or subtraction, and graphingOther systems of equations - dependent equations, consistent vs inconsistent system of linear equations, parallel lines and perpendicular linesInequality and absolute value equations - how to solve inequalities, graphing linear inequalities, and solving absolute value equationsQuadratic equations - define quadratic equations, quadratic equations with one unknown, quadratic equations with two unknowns, and solving quadratic equations with one unknown using factoring, difference of two squares, and quadratic formulaQuadratic formula - quadratic formula examples, discriminant definition, and impact of the discriminant on the nature of the roots of a quadratic equationRelations - ordered pairs, relations, and domain and range of a relationFunctions - function definition, the three ways that functions can be represented, numerical representation of functions, how to identify relations that are functions, graphical representation of functions, the vertical line test, symbolic representation of functions, evaluating functions to find y with a given x value, and piecewise functionsDomain of functions - 5 options for specifying domain of a function, domain of function rules, and domain of function examplesOther functions- inverses of a function and exponential functionsCombining functions - Composition of functions and combining functions algebraicallyTransformation of graphs - common graph transformations and their impact on the function in functional notation
