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课程名称：核心数学 课程概述：核心数学课程旨在为学生打下坚实的基础，以便为大学数学课程做准备。此外，该课程特别设计为可替代CSEC数学的通过要求。课程采用基于能力的教学与学习原则进行授课。 课程描述：该课程涵盖了数学原理的基本知识，并逐渐深入到更高级的应用，以帮助学生有效应对课程中将遇到的其他数学内容。课程内容包括算术运算、基本统计、三角学和图形。 一般目标：为学生在大学数学方面打下坚实基础。 课程学习成果：完成本课程后，学生应能够： - 解决口头和数值表达的数学问题。 - 图形和分析性地解决数学问题。 - 讨论数学对国家发展的重要性。 - 应用数学概念有效处理现实世界中的情况。 课程内容摘要： 单元1：计算 - 区分实数的子集（自然数、整体数、整数、有理数、无理数） - 说明并应用数的性质（结合律、交换律） - 通过四舍五入近似小数 - 用科学记数法表示小数 - 区分质数和合数 - 解决典型的比例问题 单元2：消费者数学 - 比较简单利息和复利投资 - 解决分期付款和盈亏问题 - 应用货币兑换技巧 单元3：统计学 - 区分离散数据和连续数据 - 从给定的统计图表（饼图、线图、条形图）解读数据 - 计算分组和未分组数据的统计平均数（均值、中位数、众数） - 确定最适合特定情况的平均数 单元4：代数 - 通过分组相似项简化表达式 - 简化代数分数 - 因式分解代数表达式 - 解决包括分数的线性方程 - 解决线性不等式并在数轴上表示 - 解决线性联立方程 单元5：集合 - 理解和使用集合术语（如相等集合、等价集合、子集等） - 应用集合符号（包括并集、交集和补集符号） - 解读和应用维恩图以识别区域并解决典型的两个集合的问题 单元6：三角学与矩阵 - 识别三角形的类型（等边、等腰、斜边、直角） - 使用毕达哥拉斯定理求解直角三角形中未知边的长度 单元7：图形 - 绘制线性方程的图形 - 通过图形解决一对线性联立方程 学习资源：教材、讲义 所需教材： Toolsie, R. (2010). Mathematics a Complete Course with CXC Questions Vol. 1. San Fernando, Trinidad & Tobago. Caribbean Educational Publishers
RATIONALE:Core Mathematics was developed to offer students a sound base, in preparation for the University's Mathematics courses. Additionally, the course is specifically designed so that it may be used as a substitute for a pass in CSEC mathematics. Core Mathematics is delivered along the principles of competency- based teaching and learning.COURSE DESCRIPTION:The course sets out the basics of mathematical principles and moves into more advanced applications which will equip students to effectively cope with other mathematics courses they will encounter throughout their program. Topics include arithmetic operations, and basic statistics, trigonometry, and graphs.GENERAL OBJECTIVE:To prepare students for a sound base in College MathematicsCOURSE LEARNING OUTCOMES:After completing this course students should be able Solve worded and numerically expressed mathematical problems.Solve graphically and analytically mathematical problems.Discuss the importance of mathematics to national development.Apply mathematical concepts to effectively deal with real world situations.SUMMARY OF COURSE CONTENTUnit 1 Computation Differentiate among subsets of real numbers [natural, whole, integer, rational, irrational]State and apply number properties[associative, commutative laws]Approximate decimal numbers by rounding off [decimal places, significant figures.]Represent decimal numbers in scientific notation.Differentiate between prime and composite numbers.Differentiate between prime and composite numbers..Solve typical ratio/proportion problemsUnit 2 Consumer Mathematics Compare simple interest and compound Interest investmentsSolve hire-purchase and profit/loss problemsApply currency conversion techniqueUnit 3 Statistics Topics to include only: Computation and Consumer MathematicsDistinguish between discrete and continuous dataInterpret data from given statistical diagrams [Pie chart, Line, Bar graph)Calculate statistical averages for grouped and ungrouped data [Mean, Mode, Median]Determine which average is best suited for particular situationsUnit 4 Algebra Simplify expressions by grouping like termsSimplify algebraic fractionsFactorize algebraic expressions [By factor, Grouping, The difference of two squares, Quadratic factorization]Solve linear equations including those containing fractionsSolve linear inequalities and represent them on number lines Solve linear simultaneous equationsUnit 5 Sets Appreciation and use of set terminology [Equal sets; Equivalent sets; Subsets including the 2n formula; Set builder notation]Apply set symbols [Including union, intersection, and complement symbols]Interpret and apply Venn- diagrams to identify regions and to solve typical 2 set wordedUnit 6 Trigonometry & MatricesTopics to include only: Algebra (solving simultaneous equations and solving quadratic equations by factorization and formula) &SetsIdentify the types of triangles [equilateral, isosceles, scalene, right]Use Pythagoras' theorem to find the length of an unknown side in a right triangleUnit 7 Graphs Plot graphs of linear equationsSolve a pair of linear simultaneous equations graphicallyLEARNING RESOURCES:Text Books; Lecture NotesREQUIRED TEXT(S):Toolsie, R. (2010). Mathematics a Complete Course with CXC Questions Vol. 1.San Fernando, Trinidad & Tobago. Caribbean Educational Publishers
