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Port Moresby International School
P.O. Box 276, Boroko, Papua New Guinea
Phone +675 325 3166, Fax +675 325 4439
Owned and operated by the International Education Agency.
Unit & Assessment Semester Outline for Students & Parents Grades 11 – 12.
2015
Year
Curriculum
Subject Title/s
Course Name
Unit Name
Course Code
12
Semester 1
Grade
ACT/IB
Mathematics
Mathematical Methods/ Mathematics SL
Further Calculus and Statistics
1297
Unit Code
Assessment Tasks
Week Due
Topic(s)
7
Statistics
15
Statistics Investigation
16
Calculus
18
Summative Assessment
Unit Value
1.0
12979
Type of Task
Test
Portfolio
Test
Examination
Weighting
15%
25%
25%
35%
Learning outcomes against which the students will be reported
Can calculate the probability of independent and dependent events and describe the features
of a probability distribution
Can apply the binomial distribution to find probabilities and use the normal distribution to
model data sets of continuous random variables
Can differentiate exponential, logarithmic and trigonometric functions and apply differential
calculus to solve problems
Can find indefinite and definite integrals, use integral calculus to find areas and volumes
Can use integration to solve problems.
Assessment Criteria
This course should enable students to:
describe a data set in terms of its summary statistics
calculate the probability of independent and dependent events
describe the features of a probability distribution
apply the binomial distribution to find probabilities
use the normal distribution to model data sets of continuous random variables
investigate models of growth and decay
differentiate exponential, logarithmic and trigonometric functions
apply dfferential calculus to solve problems
find indefinite and definite integrals
use integral calculus to find areas and volumes
use integration to solve problems.
Regulations governing Late Submission of Work, Non-Submission of Work, Attendance, Cheating/Plagiarism,
Grade Descriptors, Moderation Procedures, Method of unit score calculation, meshing procedures, Course
information, Procedures for calculating course scores & Rights of Appeal may be found in the Grade 11-12
Curriculum Handbooks, or from the POMIS website;
www.pmis.iea.ac.pg
Summary of Content
Weeks Content Outline
Statistics.Concepts of population, sample, random sample and
1-2
frequency distribution of discret and continuous data.
Presentation of data: frequency tables and diagrams, box and
whisker plots. Grouped data mid-interval values, interval width,
upper and lower interval boundaries, frequency histograms.
Mean, median, mode, quartiles, percentiles. Range, interquartile
3-4
range, variance, standard deviation (both of population and
sample). Measures of both spread and central tendency
Linear correlation of bi-variate data, including Pearson's PMCC.
Curriculum Links
IB 5.1
ACT This is a
NARC
accredited course
5-6
IB 5.3, 5.5
ACT All
references are on
NARC document
7-8
Cumulative frequency and CF graphs. Use these to find median,
quartiles and percentiles. Probability. Concepts of trial, outcome,
equally likely outcomes, sample space and event.
Complementary events A and A', P(A) + P(A') = 1. Combined
events P(A or B) = P(A) + P(B) - P(A and B).
Mutually exclusive and independent events.
Conditional probability P(A|B).Use of Venn diagrams.
Concept of discrete random variables (drv), expected value,
mode, median, variance and sd of these.
IB 5.2, 5.4
ACT It forms 2
0.5 combined
units
IB 5.6, 5.7
9-10
Binomial distribution.
IB 5.8
Expected value and standard deviation.
Application of the binomial distribution to find the probability of
events (both pdf and cdf).
11-12
Normal distribution.
Properties, standard normal distribution, normal distribution as
an approximation to the binomial distribution.
Standardisation of normal variables.
IB 5.9
13-14
Calculus. Derivative of sin x, cos x, tan x, e^x and ln x.
Use of chain, product and quotient rules. Local maximum and
minimum problems, using first and second derivatives.
Indefinite integration as anti-differentiation.
IB 6.2, 6.4
15-16
Anti differentiation with boundary condition.
Definite integrals.
Areas between curves.
Volumes of revolution (about x axis only.)
IB 6.4, 6.5
17-18
Kinematic problems involving s, v, a.
IB 6.6
19-20
Review of semester material
Port Moresby International School
P.O. Box 276, Boroko, Papua New Guinea
Phone +675 325 3166, Fax +675 325 4439
Owned and operated by the International Education Agency.