Mathematics Standard Level Year 11 Outcomes
Topic
Algebra
Objectives
Know
Arithmetic sequences and series; sum of finite arithmetic series;
Geometric sequences and series; sum of finite and infinite series.
Sigma notation
Exponents and logarithms
Laws of exponents; laws of logarithms.
Change of base.
The binomial theorem: expansion of
Concept of function f : x
Composite functions f
Inverse function f
1
( a  b) n , n 
f ( x) :domain, range; image (value).
g ; identity function
.
The graph of a function; its equation y  f ( x)
Function graphing skills:
 Use of GDC to graph a variety of functions
 Investigation of key features of graph
 Solution of equations graphically
Transformations of graphs: translations; stretches; reflections in the
axes.
1
The graph of y  f ( x) as the reflection in the line y = x of the
graph of y  f ( x) .
The reciprocal function x
1
; x  0 : its graph; its self-inverse
x
nature.
Functions and Equations
The quadratic function x
(0, c).
ax2  bx  c ; its graph, y-intercept
The form x
b
.
2a
a ( x  h) 2  k : vertex (h, k)
The form x
a( x  p)( x  q) : x-intercepts (p, 0) and (q, 0)
Axis of symmetry x  
The solution of ax  bx  c  0, a  0 .
The quadratic formula.
Use of the discriminant   b2  4ac .
2
ax , a  0 .
The inverse function: x
log a x, x  0 .
The function: x
x
Graphs of y  a and y  log a x .
Solution of a x  b using logarithms.
Circular Functions and
Trigonometry
The exponential function x
ex .
The logarithmic function x
ln x, x  0 .
The circle: radian measures of angles; length of an arc; area of a
sector.
Definition of cos and sin  in terms of the unit circle.
sin 
.
cos 
cos2   sin 2   1 .
Definition of tan  as
The identity
Double angle formulae:
sin 2  2sin  cos
cos 2  cos2   sin 2 
07/13/17
Needs
Work
Mathematics Standard Level Year 11 Outcomes
The circular functions sin x, cos x and 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 .
Circular Functions and
Trigonometry
continued
Solutions of trigonometric equations in a finite interval.
Equations of the type a sin(b( x  c))  k.
Equations leading to quadratic equations in, for example, sin x.
Graphical interpretation of the above.
Solutions of triangles.
The sine rule:
a
b
c


sin A sin B sin C
The cosine rule:
c 2  a 2  b2  2ab cos(C ); cos(C ) 
The area of a triangle: A 
Matrices
a 2  b2  c 2
2ab
1
ab sin(C )
2
Definition of a matrix: the terms “element”, “row”, “column” and
“order”.
Algebra of matrices: equality; addition; subtraction; multiplication
by a scalar.
Multiplication of matrices.
Identity and zero matrices.
Determinant of a square matrix.
Calculation of a 2 X 2 and 3 X 3 determinants.
Inverse of a 2 X 2 matrix.
Conditions for the existence of the inverse of a matrix.
Solution of systems of linear equations using inverse matrices (a
maximum of three equations in three unknowns).
Vectors as displacements in the plane and in three dimensions.
Distance between two points in three dimensions
Components of a vector; column representation.
 v1 
 
v   v2   v1i  v2 j  v3k
v 
 3
Algebraic and Geometric approaches to the following topics:
The sum and difference of two vectors;
Vectors
The difference of
v
w
and
is
v  w  v    w
The zero vector
The vector
v
Multiplication by a scalar,
Magnitude of a vector,
v
Unit vectors; base vectors
Position vectors
07/13/17
kv
i, j , k
OA  a ; AB  OB  OA  b  a
Mathematics Standard Level Year 11 Outcomes
The scalar product of two vectors
v  w  v w cos
v  w  v1w1  v2 w2  v3 w3
The scalar product is also known as the "dot product" or "inner
product".
Perpendicular vectors; parallel vectors
For non-zero perpendicular vectors
For non-zero parallel vectors
Vectors
continued
vw  0
vw   v w
The angle between two vectors
cos 
vw
v w
Representation of a line as
r  a  tb
Lines in the plane and in three-dimensional space.
The angle between two lines
Distinguish between coincident and parallel lines.
Finding points where lines intersect.
Awareness that non-parallel lines may not intersect.
Concepts of population, sample, random sample and frequency
distribution of discrete and continuous data.
(Elementary treatment only)
Presentation of data: frequency tables and diagrams, box and
whisker plots.
Treatment of both continuous and discrete data.
Grouped data, Mid-interval values, Interval width,
Upper and lower interval boundaries,
Frequency histograms using only equal class intervals
Mean, median, mode; quartiles, percentiles.
Statistics and Probability
Awareness that the population mean,
and that the sample mean,
quantity.
 , is generally unknown
x , serves as an estimate of this
Range; inter-quartile range; variance; standard deviation.
Awareness of the concept of dispersion and an understanding of
the significance of the numerical value of the standard deviation.
Using the GDC is expected
Awareness that the population standard deviation,
 , is generally
unknown, and that the standard deviation of the sample,
as an estimate of this quantity.
07/13/17
sn , serves
Mathematics Standard Level Year 11 Outcomes
Cumulative frequency; cumulative frequency graphs; use graph to
find median, quartiles, percentiles.
Concepts of trial, outcome, equally likely outcomes, sample space
(U ) and event.
P  A 
The probability of an event
A
as
The complementary events
A
and
A'
(not
n  A
n U 
A );
P  A  P  A '   1
Combined events, the formula:
P  A  B   P  A  P  B   P  A  B  .
Statistics and Probability
continued
P  A  B   0 for mutually exclusive events.
Use of
P  A  B   P  A  P  B 
for mutually exclusive
events.
Conditional Probability; the definition
P  A / B 
P  A  B
P  B
.
Independent events; the definition
P  A / B   P  A  P  A / B '  .
Use of Venn diagrams, tree diagrams and tables of outcomes to
solve problems.
Informal ideas of limits and convergence
Definition of derivative as
 f ( x  h)  f ( x) 
f ( x)  limh0 
.
h


n
x
Derivative of x (n  ) , sin x, cos x, tan x, e , and ln x.
Calculus
Derivative interpreted as gradient function and as rate of change.
Differentiation of a sum and a real multiple of functions.
The Chain Rule for composite functions.
The product and quotient rules
The second derivative.
Local maximum and minimum points.
Use of the first and second derivatives in optimization problems.
07/13/17
Mathematics Standard Level Year 11 Outcomes
Indefinite integration as anti-differentiation.
Indefinite integral of
xn  n 
 ,sin x, cos x,
1 x
,e .
x
The composites of any of these with the linear function ax  b .
Anti-differentiation with a boundary condition to determine the
constant term.
Definite integrals
Areas under curves (between the curve and the
between curves.
Calculus
continued
x - axis), areas
Volumes of revolution. Revolution about the x - axis only.
Kinematics problems involving displacement, s , velocity, v , and
acceleration, a .
v
s
 v 2s
, a

t
 t t 2
Area under a velocity-time graph represents distance.
Graphical behaviour of functions; tangents and normals, behaviour
for large x , horizontal and vertical asymptotes.
The significance of the second derivative; distinction between
maximum and minimum points.
Points of inflection with zero and non-zero gradients.
07/13/17