Level 3
Level 2
Level 1
Introduction (http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/understanding-ncea/the facts/factsheet-4/)
The chart below shows the distribution of credits
gained during 2010 by year 11, 12 and 13
students.
Subject Reference
Mathematics and Statistics
Title

Level
Credits
Apply xxxxxxxx in solving problems.
Assessment
Achievement
Achievement with Merit


Apply xxxxxxxx in solving
problems.
Internal/external
Achievement with Excellence
Apply xxxxxxxxxxx, using relational 
thinking, in solving problems.
Apply xxxxxxxxxxx, using extended
abstract thinking, in solving problems.
.
Level 1
Level 2
AS91026
1.1
Apply numeric reasoning in solving problems
AS91256
Apply co-ordinate geometry methods in solving
problems
4
credits
2
credits
Internal
AS91027
1.2
Apply algebraic procedures in solving problems
Internal
AS91257
Apply graphical methods in solving problems
4 credits
4
credits
External (CAT)
Level 3
2.1
3.1
Apply the geometry of conic sections in solving
problems
3
credits
Internal
2.2
3.2
Apply linear programming methods in solving problems
2
credits
Internal
AS91028
1.3
Investigate relationships between tables, equations
and graphs
Internal
AS91258
Apply sequences and series in solving problems
2.3
3.3
Apply trigonometric methods in solving
problems
4
credits
2
credits
External
AS91029
1.4
Apply linear algebra in solving problems
Internal
AS91259
2.4
Apply trigonometric relationships in solving problems
3
credits
3
credits
4 credits
Internal
3.3
Apply trigonometric methods in solving problems
4
credits
Internal
Internal
AS91030
1.5
Apply measurement in solving problems
AS91260
Apply network methods in solving problems
Internal
3
credits
2
credits
Internal
AS91031
1.6
Apply geometric reasoning in solving problems
Internal
AS91261
Apply algebraic methods in solving problems
4
credits
4
credits
External
AS91032
1.7
Apply right-angled triangles in solving measurement
problems
External
AS91262
Apply calculus methods in solving problems
3
credits
5
credits
2.5
3.4
Use critical path analysis in solving problems
2 credits
Internal
2.6
3.5
Apply algebraic methods in solving problems
5
credits
External
2.7
3.6
Apply differentiation methods in solving problems
6
credits
External
AS91033
1.8
Apply knowledge of geometric representations in
solving problems
AS91263
Design a questionnaire
3
credits
3
credits
Internal
Internal
2.8
3.8
Investigate times series data
4
credits
Internal
3.9
Investigate bivariate measurement data
4 credits
AS91034
1.9
Apply transformation geometry in solving problems
2
credits
AS91264
Use statistical methods to make an inference
Internal
2.9
3.10
Use statistical methods to make a comparison
4
credits
5
credits
Internal
AS91265
2.10
Conduct an experiment to investigate a situation using
statistical methods
Internal
AS91035
1.10
Investigate a given multivariate data set using the
statistical enquiry cycle
4
credits
3
credits
3
credits
Internal
AS91036
1.11
Investigate bivariate numerical data using the statistical
enquiry cycle
Internal
AS91266
Evaluate a statistically based report
3
credits
2
credits
Internal
AS91037
1.12
Demonstrate understanding of chance and data
Internal
AS91267
Apply probability methods in solving problems
4
credits
4
credits
4
credits
External
AS91038
1.13
Investigate a situation involving elements of chance
External
AS91268
2.13
Investigate a situation involving elements of chance
using a simulation
External
2
credits
4
credits
Internal
3
credits
3.11
Conduct an experiment using experimental design
principles
Internal
2.11
3.12
Critically evaluate statistically based reports
4
credits
External
2.12
3.13
Apply probability concepts in solving problems
3.14
Apply probability distributions in solving problems
Internal
Internal
AS91269
Apply systems of equations in solving problems
External
2.14
3.15
Apply linear systems in solving problems
A New Zealand tour company collected data over a period of a year to investigate information about its
passengers.
(a) It found that:
• 48% of its passengers were male
• 63% of its female passengers came from overseas
• 21% of all passengers were males from overseas.
You may assume that the event that a passenger is male and the event that a passenger is from overseas
are independent.
Find the probability that a randomly selected male passenger was from overseas.
The tour company decides to analyse its data in more depth.
(a) It finds that:
• the probability of an overseas passenger coming from Australia is 2/3
• the probability of an overseas passenger coming from Australia or aged over 30 is 3/4
• the probability of an overseas passenger coming from Australia and aged over 30 is 1/10.
Find the probability that an overseas passenger is aged over 30.
In 2006, a survey was conducted on households in Hamilton, Canada.
(a) Let the random variable X represent the number of cars in a randomly chosen household at the time of
the survey. The survey gave the following probability distribution for X.
x
0
1
2
3
4
P(X = x)
0.059
0.383
0.377
0.153
0.028
Find the expected value of X.