VCE 数学考前一周复习计划
2011 年 10 月 31 日

10
EXAM1
EXAM2
• EXAM1 的重点还是集中在近五年的高考题，
在本周内让所有的同学重新再做一遍，有
针对性地进行个别辅导，争取让每一位同
学均能有所提高，另外还有就是要把握题
目的意思理解，有必要自己归纳一下各种
各样题型的方法和思路。

概
率
密
度
函
数
1 定积分为 1
2.Pr(x>a)
3.Pr(a<x<b)
1.Given
2.If
3. Next
条件
概率
树状图
概率 2006
正态
分布
1.Mean
2.Standard deviation
3.Normally distribution
4.Pr(x>a)
5.Pr(x>a|x>b)

EXAM1 中的概率问题重思
• 2006 年
• Question 5
• Let X be a normally distributed random variable with a mean of 72 and a standard deviation of 8.
Let Z be the
• standard normal random variable.
• Use the result that Pr(Z < 1) = 0.84, correct to two decimal places , to find
• a. the probability that X is greater than 80
• b. the probability that 64 < X < 72
• c. the probability that X < 64 given that X < 72.

EXAM1 中的概率问题重思
• 2006 年
• Question 6
• The probability density function of a continuous random variable X is given by
• a. Find Pr (X < 3).
• b. If Pr (X ≥ a) = 5/8 , find the value of a.

EXAM1 中的概率问题重思
• 2006 年
• Question 10
• Jo has either tea or coffee at morning break. If she has tea one morning, the probability she has tea the next morning is 0.4.
If she has coffee one morning, the probability she has coffee the next morning is 0.3. Suppose she has coffee on a
Monday morning . What is the probability that she has tea on the following Wednesday
• morning?

韦恩图和表格
独
立
重
复
试
验
1. n
2.
p
3.
公式
4.
注意 at least /more than less than / no more than
概率
A
A’
B B’
1

EXAM1 中的概率问题重思
• 2007 年
• Question 5
• It is known that 50% of the customers who enter a restaurant order a cup of coffee. If four customers enter the restaurant, what is the probability that more than two of these customers order coffee?
(Assume that what any
• customer orders is independent of what any other customer orders.)

EXAM1 中的概率问题重思
• 2007 年 Question 6
• Two events, A and B, from a given event space, are such that Pr (A) =1/5 and Pr (B)
=1/3 .
• a. Calculate Pr (A′ ∩ B) when
• Pr (A ∩ B) = 1/8.
• b. Calculate Pr (A′ ∩ B) when A and B are mutually exclusive events.

EXAM1 中的概率问题重思
• 2008 年 Question 4
• The function
• is a probability density function for the continuous random variable X .
• a. Show that k =π/2.
• b. Find

EXAM1 中的概率问题重思
• 2008 年 Question 7
• Jane drives to work each morning and passes through three intersections with traffic lights. The number X of
• traffic lights that are red when Jane is driving to work is a random variable with probability distribution given
• By
• a. What is the mode of X?
• b. Jane drives to work on two consecutive days. What is the probability that the number of traffic lights that
• are red is the same on both days?

EXAM1 中的概率问题重思
• 2008 年 Question 8
• Every Friday Jean-Paul goes to see a movie. He always goes to one of two local cinemas – the Dandy or the Cino. If he goes to the Dandy one Friday, the probability that he goes to the Cino the next Friday is
0.5
. If he goes tothe Cino one Friday, then the probability that he goes to the Dandy the next Friday is 0.6. On any given Friday the cinema he goes to depends only on the cinema he went to on the previous Friday. If he goes to the Cino one Friday, what is the probability that he goes to the Cino on exactly two of the next three Fridays?

EXAM1 中的概率问题重思
• 2009 年 Question 5
• Four identical balls are numbered 1, 2, 3 and 4 and put into a box. A ball is randomly drawn from the box, and not returned to the box. A second ball is then randomly drawn from the box.
• a. What is the probability that the first ball drawn is numbered 4 and the second ball drawn is numbered 1?
• b. What is the probability that the sum of the numbers on the two balls is 5?

EXAM1 中的概率问题重思
• Question 7
• The random variable X has this probability distribution.
• Find
• a. Pr ( X > 1| X ≤ 3)
• b. Var( X ), the variance of X .

EXAM1 中的概率问题重思
• 2010 年 Question 7
• The continuous random variable X has a distribution with probability density function given by
• where a is a positive constant.
• a. Find the value of a.
• b. Express Pr( X < 3) as a definite integral. (Do not evaluate the definite integral.)

EXAM1 中的概率问题重思
• 2010 年 Question 8
• The discrete random variable X has the probability distribution
• Find the value of p.

PDF 中的特殊图形面积算法
• 2011 年模拟卷
• The continuous random variable X has a distribution with probability density function shown by the graph below.
• Find the value of a
• Determine the value of the median, m , for the continuous random variable,x

EXAM2
• 利用计算器可以做到：
• 代入求特定的函数值
• 代入求方程的解
• 代入求不等式的解集
• 代入求积分
• 代入求导数
• 定义一个函数的形式
• 求反函数
• 输入可以画图
• 画图可以分析拐点的
性质
• 画图可以分析定义域，
区间，渐近线
• 画图可以找出截距，
值域
• 画图可以看出区域面
积

EXAM2