alevel数学具体学什么？alevel数学真题

从alevel选课这个角度看，没有比数学更好用的的学科。无论是理工类专业还是金融类专业，都明确写了需要提供alevel数学成绩。接下来跟锦秋alevel培训辅导小编一起看看alevel数学学什么？alevel数学真题。

一、alevel数学具体学什么？
数学的内容有四大模块:
模块1.纯数学(pure mathematics)，有7个单元，分别是C1、C2、C3、C4、FP1、 FP2、 FP3。
模块2.统计数学(statistics)有4个单元，分别是S1、S2、S3、S4。
模块3.机械数学 (mechanics)有5个单元，分别是M1、M2、M3、M4、M5。
模块4.决策数学 (decision mathematics)有2个单元，分别是D1、D2。

IAL基础数学和进阶数学都必须按组合要求各考够6个单元，IAL数学共有14个单元，如果同时考基础数学和进阶数学，需要完成12个单元的学习考试。
基础数学的必须单元为P1、P2、P3、P4，再从其余的10个单元中，选择两个单元，搭配6个单元，进行学习考试。基础数学一般选择P1+P2+P3+P4+S1+M1这样的组合。

二、alevel数学真题
1. A machine makes screws with a mean length of 30mm and a standard deviation of 2.5mm.
A manager claims that, following some repairs, the machine is now making screws with
a mean length of less than 30mm. The manager takes a random sample of 80 screws and
finds that they have a mean length of 29.5mm.
Use a suitable test, at the 5% level of significance, to determine whether there is evidence
to support the manager's claim. State your hypotheses clearly.
2. Andy has some apple trees. Over many years she has graded each apple from her trees as
A, B, C, D or E according to the quality of the apple, with A being the highest quality and
E being the lowest quality.
She knows that the proportion of apples in each grade produced by her trees is as follows.
Grade A B C D E
Proportion 4% 28% 52% 10% 6%
Raj advises Andy to add potassium to the soil around her apple trees.
Andy believes that adding potassium will not affect the distribution of grades for the
quality of the apples.
To test her belief Andy adds potassium to the soil around her apple trees. The following
year she counts the number of apples in each grade. The number of apples in each grade
is shown in the table below.
Grade A B C D E
Frequency 9 71 136 21 3
Test Andy's belief using a 5% level of significance. Show your working clearly, stating
your hypotheses, expected frequencies and degrees of freedom.
3. A cafe owner wishes to know whether the price of strawberry jam is related to the taste of
the jam. He finds a website that lists the price per 100 grams and a mark for the taste, out
of 100, awarded by a judge, for 9 different strawberry jams A, B, C, D, E, F, G, H and I.
He then ranks the marks for taste and the prices.
The ranks are shown in the table below.
Rank 1 2 3 4 5 6 7 8 9
 Price A B E C D F G H I
 Taste A B F E H G I C D
(a) Calculate Spearman’s rank correlation coefficient for these data.
(5)
(b) Test, at the 5% level of significance, whether or not there is a relationship between the
price and the taste of these strawberry jams. State your hypotheses clearly.
(3)
A friend suggests that it would be better to use the price per 100 grams, c, and the mark
for the taste, m, for each strawberry jam rather than rank them.
Given that
Scc = 2.0455 Smm = 243.5556 Scm = 16.4943
(c) calculate the product moment correlation coefficient between the price and the mark
for taste of these strawberry jams, giving your answer correct to 3 decimal places.
(2)
(d) Use your value of the product moment correlation coefficient to test, at the 5% level
of significance, whether or not there is evidence of a positive correlation between the
price and the mark for taste of these 9 strawberry jams.
State your hypotheses clearly.
(3)
(e) State which of the tests in parts (b) and (d) is more appropriate for the cafe owner to
use. Give a reason for your answer.
(1)
4. A local village radio station, LSB, decides to survey adults in its broadcasting area about
the programmes it produces.
LSB broadcasts to 4 villages A, B, C and D.
The number of households in each of the villages is given below.
Village Number of households
A 41
B 164
C 123
D 82
LSB decides to take a stratified sample of 200 households.
(a) Explain how to select the households for this stratified sample.
(3)
One of the questions in the survey related to the age group of each member of the
household and whether they listen to LSB. The data received are shown below.
Age group
18–49 50–69 Older than 69
Listen to LSB 130 162 65
Do not listen to LSB 78 98 62
The data are to be used to determine whether or not there is an association between the
age group and whether they listen to LSB.
(b) Calculate the expected frequencies for the age group 50–69 that
(i) listen to LSB
(ii) do not listen to LSB
(2)
Given that for the other 4 classes
O E
E
    
2
4.657 to 3 decimal places,
(c) test at the 5% level of significance, whether or not there is evidence of an association
between age and listening to LSB. Show your working clearly, stating the degrees of
freedom and the critical value.
(6)
5. Assam produces bags of flour. The stated weight printed on the bags of flour is 3kg.
The weights of the bags of flour are normally distributed with standard deviation 0.015kg.
Assam weighs a random sample of 9 bags of flour and finds their mean weight is 2.977kg.
(a) Calculate the 99% confidence interval for the mean weight of a bag of flour. Give your
limits to 3 decimal places.
(3)
Assam decides to increase the amount of flour put into the bags.
(b) Explain why the confidence interval has led Assam to take this action.
(1)
After the increase a random sample of n bags of flour is taken. The sample mean weight
of these n bags is 2.995kg. A 95% confidence interval for μ gave a lower limit of less
than 2.991 kg.
(c) Find the maximum value of n.
(4)

以上是alevel数学S3真题，更多关于alevel数学真题、数学学习的内容，可以咨询锦秋客服。