CANADIAN INTERNATIONAL SCHOOL OF HONG KONG
STANDARD LEVEL MATHEMATICS
GRADE 11
Teacher:
PIERRE LACOSTE – Office 210
Telephone: 2525-7088 ext. 3206
Email: [email protected]
COURSE DESCRIPTION / AIMS
This course caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the
skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound
mathematical background as they prepare for future studies in subjects such as chemistry, economics, psychology and business
administration.
Students are expected to know and use mathematical concepts and principles. In particular, students must be able to:
• read, interpret and solve a given problem using appropriate mathematical terms
• organize and present information and data in tabular, graphical and/or diagrammatic forms
• know and use appropriate notation and terminology
• formulate a mathematical argument and communicate it clearly
• select and use appropriate mathematical strategies and techniques
• demonstrate an understanding of both the significance and the reasonableness of results
• recognize patterns and structures in a variety of situations, and make generalizations
• recognize and demonstrate an understanding of the practical applications of mathematics
• use appropriate technological devices as mathematical tools
• demonstrate an understanding of and the appropriate use of mathematical modelling.
EVALUATION
Coursework:
70%
Exam:
30%
Application, Knowledge and Understanding, Thinking Inquiry, Communication
Tasks include: problem sets/assignments, quizzes, IB portfolio assignments, and unit tests
Paper 1 (no calculator) & Paper 2 (with calculator)
Homework: This is assigned each class. The average time spent between classes on homework should be 45 minutes. Students are
required to do the assigned work to ensure their success in the course. This is an integral part of the learning process.
IB FINAL GRADE
(END OF GRADE 12)
Internal Assessment – Portfolio: 20%
A collection of two pieces of work assigned by the teacher and completed by the student
during the course. The pieces of work must be based on different areas of the syllabus and represent the two types of tasks:
• mathematical investigation
• mathematical modelling.
The portfolio is internally assessed by the teacher and externally moderated by the IBO
External Assessment - Exam: 80% Paper 1 - 1.5 hrs (no calculator) & Paper 2 – 1.5 hrs (with calculator)
EXTRA HELP
A math teacher will be available every Monday, Wednesday, Friday during the lunch period as well as after school on Tuesdays
and Thursdays. All are held on the second floor. Appointments and extra help sessions may be set-up when the need arises.
TEXTBOOKS & RESOURCES
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Mathematics for the International Student, Mathematics SL, Haese and Harris
TI 84 Graphing Calculator
Math Software: Geogebra, Logger Pro, Mathtype, Excel/Numbers
Websites: Moodle: http://moodle.cdnis.edu.hk/login/index.php ,
Blog: http://sites.cdnis.edu.hk/teachers/pierrelacoste/
CANADIAN INTERNATIONAL SCHOOL OF HONG KONG
STANDARD LEVEL MATHEMATICS
UNITS OF STUDY
UNITS
0
TOPICS
•
Presumed Knowledge/TOK
x=−
(IB:1.2,2.1,2.2,2.3,2.4,2.5,2.6
,2.7,2.8 Ch.1,3,5)
1
Matrices
(IB:4.1,4.2,4.3,4.4, Ch.11)
2
Sequences & Series,
Binomial Expansion
(IB:1.1,1.3, Ch.2,7)
3
Functions, Exponents,
Logarithms, Polynomials
(IB:1.2,2.1,2.2,2.3,2.4,2.5,2.6
,2.7,2.8 Ch.1,3,4,5,6)
Quadratic function review
x  ax 2 + bx + c : its graph, y-intercept (0,c) , axis of symmetry
b
, the form x  a(x − h)2 + k : vertex (h,k) , the form x  (x − p)(x − q) ; x-intercepts
2a
•
(p,0) and (q,0) .
The solution of ax 2 + bx + c = 0, a ≠ 0 , the quadratic formula.
•
•
•
Use of the discriminant Δ = b − 4ac .
Distance between two points, midpoints
Definition of tan θ , cos θ and sin θ in terms of the unit circle.
•
Given
•
•
•
•
•
•
•
•
Definition of matrix, element, row, column, order
Algebra of matrices: equality, addition, subtraction, multiplication by a scalar
Multiplication of matrices, identity, zero matrices
Determinant of a square matrix
2 × 2, 3 × 3 determinants
Inverse of a 2 × 2 matrix
Conditions for the existence of the inverse of a matrix
Solutions of systems of linear equations using inverse matrices (max. 3 equations and three unknowns)
•
•
•
•
Arithmetic sequences and series; sum of finite arithmetic series.
Geometric sequences and series; sum of finite and infinite geometric series.
Sigma notation.
The binomial theorem: expansion of ( a + b )n , n ∈Ν .
•
Concept of function f : x  f (x) : domain, range; image (value).
•
Composite functions
•
Inverse function
−1
•
•
The graph of a function; its equation y= f(x) .
Function graphing skills: use of a GDC to graph a variety of functions; investigation of key features of
graphs. Identification of horizontal and vertical asymptotes. Solution of equations graphically.
•
The function: x  a x , a > 0 , Graphs of y
•
The exponential function y
•
•
Laws of logarithms, change of base formula.
The inverse function x  log a x, x > 0 , graph of y
•
•
Solution of a = b using logarithms.
The logarithmic function x  ln x, x > 0 .
•
Transformations of graphs: translations; stretches; reflections in the axes.
•
The graph of
•
The reciprocal function x  1 , x ≠ 0 ; its graph; its self-inverse nature.
x
Polynomial functions
Rational Function
•
•
2
sin θ
, finding possible values of
f
f g
cosθ
without finding
θ
.
identity function.
.
= ax .
= ex .
= log a x .
x
y = f −1 (x) as the reflection in the line y = x
of the graph of y = f (x) .
4
Trigonometry and Circular
Functions
(IB:3.1,3.2,3.3,3.4,3.5,3.6
Ch.8,9,10)
5
One Variable Statistics and
Probability
(6.1,6.2,6.3,6.4,6.5,6.6,6.7,6.
8,6.9,6.10,6.11 Ch.14,15)
•
•
•
The circle: radian measure of angles; length of an arc; area of a sector.
Radian measure may be expressed as multiples of π , or decimals.
Definition of cos θ and sin θ in terms of the unit circle.
The reciprocal trigonometric functions sec θ ,
csc θ
•
sin θ .
Definition of tan θ as
cosθ
•
Lines through the origin can be expressed as y
= x tan θ , with gradient tan θ .
•
2
and cot θ .
θ + cos θ = 1 .
2
•
The identity sin
•
Double angle formulae: sin 2θ = 2 sin θ cos θ ; cos 2θ = cos 2 θ − sin 2 θ .
•
•
The circular functions sin x , cos x , tan x : their domains and ranges; their periodic nature; and their
graphs.
Composite functions of the form f (x) = a sin b ( x + c ) + d .
•
•
Solution of trigonometric equations in a finite interval.
Equations of the type a sin b ( x + c ) + d = k .
•
•
•
Equations leading to quadratic equations in, for example, sin x .
Solution of triangles.
2
2
2
The cosine rule: c = a + b − 2ab cosC .
•
The sine rule: a
•
The ambiguous case of the sine rule.
•
Area of a triangle as A =
•
•
•
•
•
Concepts of population, sample, random sample and frequency distribution of discrete 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 range; variance; standard deviation.
Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles.
Concepts of trial, outcome, equally likely outcomes, sample space (U) and event.
•
The probability of an event A as P(A) =
•
The complementary events A and A′ (not A); P(A)+P(A′)=1.
•
•
(
(
sin A
=
)
)
b
c .
=
sin B sin C
1
ab sin C .
2
n(A) .
n(U )