CURRICULUM SUMMARY – September to December 2014
SUBJECT: Mathematics SL
Week Learning objectives
PROBABILITY - revision
1
2
3
PROBABILITY – revision
 Normal distribution.
x

Agata Piskorz
Using tables of probability distributions
Using the formula: E( X )  xP( X  x) .

Revising the coefficients from the binominal expansion. Using GDC.
n
r
Using the formula X ~ B(n, p)  P( X  r )    p r (1  p) n  r
Use of calculator to find normal probabilities; the reverse process

PROBABILITY , PROBABILITY DISTRIBUTIONSrevision
TRIGONOMETRIC FUNCTIONS
Students will understand and use:
 The basic sine and cosine curves

5
Standardized normal variable. z 
TEACHER:
Solving past papers questions
PROBABILTY DISTRIBUTIONS
Students will understand and use:
 discrete random variables and their
probability distributions.
 expected value (mean), E(X ) for discrete
data.
 applications of expectation, for example,
games of chance.
 Binomial distribution. Mean of the binomial
distribution. E ( X )  np .

4
YEAR GROUP: IB2
Activities (in brief)
Amplitude, period, , equation of the principal
axis of functions :
y=Asin B(x+C)+D, y=Acos B(x+C)+D,
The tangent function y=Atan B(x+C)+D
TRIGONOMETRY – revision
 Sine and cosine models to solve practical
problems
 The Pythagorean identity cos2θ + sin2θ =1.
 Double angle identities for sine and cosine
Solving past papers questions.
Test.
Using the unit circle to investigate the basic sine, cosine and tangent curves.
Drawing graphs of trigonometric functions without using technology.
Trigonometric functions graphs transformations : vertical stretch, horizontal stretch, vertical and
horizontal translation, reflections in .
Using GDC (Graphic Display Calculator) to sketch and analyze graphs of the trigonometric
functions;
Solving past papers questions.
Investigation – mean monthly temperature modeling;
Using sine and cosine models to solve practical problems;
Using DGC to solve equations involving trigonometric functions;
6


Relationship between trigonometric ratios.
Trigonometric equations
TRIGONOMETRY, TRIGONOMETRIC FUNCTIONS revision
7
8
VECTORS
Students will understand and use:
 Tied vectors and free vectors
 Equal vectors, opposite vectors, the null
vector; parallel vectors. Operations with
vectors.

Standard basis vectors: i, j , k .
A vector as a linear combination of the
standard basis vectors.

OV -the position vector of a point V and its

coordinates. Coordinates of any vector in the
Cartesian 2 and 3-dimensional coordinate
system.
Magnitude of a vector.
INTERNAL ASSESSMENT – students ideas
 The scalar product of two vectors.
 Parallel and perpendicular vectors
 The angle between two vectors.
9
DESCRIPTIVE STATISTICS - revision
 Vector equation of a line in two and three
dimensions: r = a + tb .
10
LINEAR MODELLING - revision
 Relationship between lines
 The angle between two lines.
11
VECTORS AND LINES - revision
INTERNAL ASSESSMENT – first draft feedback
Solving trigonometric equations in a finite interval analytically.
Solving questions leading to quadratic equations in sin x, cos x or tan x .
Using of technology to solve a variety of equations, including those where there is no appropriate
analytic approach.
Solving past papers questions.
Test.
Multiplication of a vector by a scalar;
Adding and subtracting vectors (the triangle low, the parallelogram low )
Calculating coordinates of a vector AB when coordinates of points A and B are given. (Vector
AB expressed as OB  OA ).
 v1 
 
Using column representation: v   v2   v1 i  v2 j  v3 k .
v 
 3
Calculating distances between points in two and three dimensions
Investigating algebraic properties of a scalar product.
Finding angle between two vectors.
Writing and interpreting equations of lines in 2D and 3D.
Solving constant velocity problems - interpretation of t as time and b as velocity, with |b|
representing speed.
Distinguishing between coincident and parallel lines.
Finding the point of intersection of two lines.
Determining whether two lines intersect.
Finding the shortest distance from a line to a point.
Solving past papers questions.
Test.
DIFFERENTIAL CALCULUS
Students will understand and use:



Informal ideas of limit and convergence.
Limit notation.
Definition of derivative at a point from first
principles as
Using technology to investigate limits and convergence.
Investigating behavior of the gradient of the line through two points P and Q,
on the graph of a function, as Q approaches P.
Drawing tangent to a curve at a point.
Finding some simple gradient functions from first principles.
 f ( x0  h )  f  x0  
f ' ( x0 )  lim 

h 0
h



12
13
14
15
The derivative (gradient) function.
FUNCTIONS - revision
 Simple rules of differentiation
 The chain rule
 The product rule
 The quotient rule.
 The second and higher derivatives.
FUNCTIONS - revision
 Tangents and normals, and their equations.
 Local maximum and minimum points.
 Increasing and decreasing functions.
FUNCTIONS - revision
 Concave-up” and “concave-down” graphs .
 Points of inflexion with zero and non-zero
gradients.
 Graphical behavior of functions, including the
relationship between the graphs of f , f ′ and f
′′
 Optimization.
 Rates of change.
FUNCTIONS, DIFFERENTIAL CALCULUS - revision
Using technology to illustrate derivatives: derivative of 𝑥 𝑛 sin x , cos x , tan x ,𝑒𝑥 and ln x .
Differentiation of a sum and a real multiple of these functions.
Using rules of differentiation to find derivatives.
Using both forms of notation: f ' ( x ) and
𝑑𝑦
𝑑𝑥
for the first derivative.
Finding equations of tangents and normal at a point.
Testing for maximum or minimum - using change of sign of the first derivative and using sign of
the second derivative.
Investigating necessary and sufficient conditions for a point of inflexion:
Testing for stationary points and finding their nature.
Sketching graphs
Solving optimisation problems that include profit, area, volume…
Motion on a line - using derivatives to find displacement, velocity and acceleration.
Solving practical problems.