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完整版高中数学必修一全册课件目录•高中数学必修一概述•集合与函数概念•基本初等函数（Ⅰ）•函数的应用•空间几何体•点、直线、平面之间的位置关系01高中数学必修一概述包括集合的基本概念、集合间的关系与运算、函数的概念与性质等。
集合与函数概念包括指数函数、对数函数、幂函数等基本初等函数的图像与性质。
基本初等函数包括函数与方程、函数模型及其应用等，通过实例探究函数的性质与应用。
函数的应用教材内容与结构过程与方法通过观察、思考、探究、归纳等活动，培养学生的数学思维能力、创新能力和解决问题的能力。
知识与技能掌握集合与函数的基本概念，理解基本初等函数的图像与性质，能够运用函数知识解决一些实际问题。
情感态度与价值观激发学生学习数学的兴趣和热情，培养学生的数学素养和审美情趣。
教学目标与要求总结归纳定期对所学知识进行总结归纳，形成知识网络，便于记忆和提取。
通过大量的练习，熟练掌握解题方法和技巧，提高解题速度和准确性。
课后复习及时复习巩固所学知识，独立完成作业和练习题，加深对知识点的理解和记忆。
课前预习提前阅读教材，了解本节课的知识点和重点难点，为听课做好准备。
课中听讲认真听讲，积极思考，及时记录重要知识点和解题方法。
学习方法与建议02集合与函数概念03元素与集合的关系属于、不属于。
01集合的概念集合是由一个或多个确定的元素所构成的整体。
02集合的表示方法列举法、描述法、图像法。
集合及其表示方法集合之间的关系与运算集合之间的关系子集、真子集、相等。
集合的运算并集、交集、补集。
集合运算的性质交换律、结合律、分配律等。
函数是一种特殊的对应关系，它使得每个自变量对应唯一的因变量。
函数的概念函数的表示方法函数的三要素解析法、列表法、图像法。
定义域、值域、对应法则。
030201函数及其表示方法1 2 3单调性、奇偶性、周期性等。
函数的性质解决实际问题，如最优化问题、数学建模等。
函数的应用通过函数可以研究方程和不等式的解的性质和范围。
Summary of key points in S1Chapter 1: Binomial distribution1. （重点***）计算二项分布的概率：（1）公式法（**），由),(~p n B X ，则有x n x n x p p x X P --==)1()()( （2）查表法（***）：利用书中135-139页中的)()(x X P x F ≤=，其中p 是0.05的倍数、一直到0.50，n 最小是5、最大是50。
2. （重点**）计算二项分布的期望和方差：),(~p n B X ，则有n p X E =)( )1()(p n p X V a r -=3. （考点*）二项分布的条件：● A fixed number of trials,n .● Each trial should be success or failure.● The trials are independent.● The probability of success,p , at each trial is constant.其中，n 为指数（index ），p 为参数（parameter ）。
难点是要求根据题意写出二项分布的条件，如果有题意背景的，要根据题意写。
4. （考点*）如果),(~p n B X ，其中5.0>p ，则)1,(~p n B Y -，那么5.01≤-p ；如果p 是0.05的倍数，则可以用查表法求概率。
5. 典型例题：例7/8/9*/10/11/12/13(a)/14*6. 复习题：Review Exercise 1: 1/4/87. 练习册部分题目：12-01-2, 10-01-1, 08-01-2Chapter 2: Representation and summary of data – location1、Frequency tables and grouped datacumulative frequency ：to add a column to the frequency table showing the running total of the frequencies.A grouped frequency distribution consists of classes and their related class frequencies.Classes 30-31 32-33 34-35For the class 32-33Lower class boundary is 31.5Upper class boundary is 33.5Class width is 33.5-31.5=2Class mid-point is (31.5+33.5)/2=32.52、The measurements of location of the centre of a set of data – mode, median and mean● The mode is the value that occurs most often.● The median is the middle value or the half of the two middle values, when thedata is put in order.● The mean is the sum of all the observations divided by the total number of theobservations. The mean of a sample of data in a frequency distribution, is x where∑∑=ffx x 3、Coding for large data valuesCoding is normally of the formba x y -= where a andb are to be chosen.To find the mean of the original data; find the mean of the coded data , equate this to the coding used and solve.Chapter 3:Representation and summary of data – measures if dispersion1、The range of a set of data is the difference between the highest and lowest value in the set.The quartiles, ,1Q ,2Q ,3Q split the data into four parts. To calculate the lower quartile , divide n by 4.For discrete data for the lower quartile, ,1Q divide n by 4. To calculate the upper quartile, ,3Q divide n by 4 and multiply by 3. When the result is a whole numberfind the mid-point of the corresponding term and the term above. When the result is not a whole number round the number up and pick the corresponding term.For continuous grouped data for ,1Q divide n by 4, for 3Q divide n by 4 and multiply by 3. Use interpolation to find the value of the corresponding term.The inter-quartile range is .13Q Q -2、The standard deviation and variance of discrete data variance=222)(⎪⎪⎭⎫ ⎝⎛-=-∑∑∑n x n x n x x standard deviation= VarianceIf you let f stand for the frequency, then ∑=f n andVariance=222)(⎪⎪⎭⎫ ⎝⎛-=-∑∑∑∑∑∑f fx f fx f x x f 3、Adding or subtracting numbers does not change the standard deviation of the data. Multiplying or dividing the data by a number does affect the standard deviation.To find the standard deviation of the original data, find the standard deviation of the coded data and either multiply this by what you divide the data by, or divide this by what you multiplied the data by.Chapter 4: Representation of data1. A stem and leaf diagram is used to order and present data given to two or three significant figures. Each number is first split into its stem and leaf .Two set of data can be compared by using back-to-back stem and leaf diagrams.2、An outlier is an extreme value that lies outside the overall pattern of the data, which is⏹ greater that the upper quartile +1.5⨯inter-quartile rangeor⏹ less that the lower quartile -1.5⨯inter-quartile range.3、Box plotUsing box plots to compare two sets of data4、HistogramA histogram gives a good picture of how data are distributed. It enables you to see a rough location, the general shape of the data and how spread out the data are.A histogram is similar to a bar chart but are two major differences● There are no gaps between the bars.● The area of the bar is proportional to the frequency.To calculate the height of each bar (the frequency density ) use the formulaArea of bar=⨯k frequency.1=k is the easiest value to use when drawing a histogram thenFrequency density=ClassWidthFrequency 5、The shape (skewness) of a data setThe ways of describing whether a distribution is skewed:⏹ You can use the quartiles.If 2312Q Q Q Q -=- then the distribution is symmetrical .If 2312Q Q Q Q -<- then the distribution is positively skewed .If 2312Q Q Q Q ->- then the distribution is negatively skewed .⏹ You can use the measures of locationmode=median=mean describes a distribution which is symmetrical .mode<median<mean describes a distribution with positive skew .mode>median>mean describes a distribution with negative skew .6、Comparing the distributions of data sets● The IQR is often used together with the median when the data are skewed .● The mean and standard deviation are generally used when the data are fairlysymmetrical .Chapter 5: Probability1、Vocabulary used in probabilityA sample space is the set of all possible outcomes of an experiment.The probability of an event is the chance that the event will occur as a result of an experiment. Where outcomes are equally likely the probability of an event is the number of outcomes in the event divided by the total number of possible outcomes in the sample space.2、Venn diagramsYou can use Venn diagrams to solve probability problems for two or three events. A rectangle represents the sample space and it contains closed curves that represent events.3、Using formulae to solve problemsAddition Rule)()()()(B A P B P A P B A P -+=Conditional probabilityThe probability of B given A , written )|(A B P , is called the conditional probability of B given A and so:)()()|(A P A B P A B P =Multiplication Rule)()|()(A P A B P A B P ⨯=4、Tree diagrams5、Mutually exclusive and independent eventsWhen A and B are mutually exclusive, then Φ=B A , so .0)(=B A PThe Addition Rule applied to mutually exclusive events:)()()(B P A P B A P +=If A and B are independent, then:)()()(B P A P B A P ⨯=Chapter 6: Correlation6.1 Scatter diagramsIf both variables increase together they are said to be positively correlated . For a positive correlation the points on the scatter diagram increase as you go from left to right. Most points lie in the first and third quadrants.If one variable increases as the other decreases they are said to be negatively correlated . For a negative correlation the points on the scatter diagram decrease as you go from left to right. Most points lie in the second and fourth quadrants.If no straight line (linear) pattern can be seen there is said to be no correlation . For no correlation the points on the scatter diagram lie fairly evenly in all four quadrants. Examples: 1/2/3 6.2 You can calculate measures for the variability of bivariate data()()()()∑∑∑∑∑∑∑∑∑∑-=--=-=-=-=-=ny x y y y x x S n y y y S n x x x S ii i i i xy ii yy i i xx i 22i 222i 2x ))((y )(x )(注：上面的公式在公式本中有。
