Download IB SL Studies Grade 12 Outcomes

Mathematical Studies Year 12 Outcomes
Topic
Objectives
Know
The set of natural numbers,
; integers, ; rational numbers,
; and real numbers, .
Approximation: decimal places; significant figures. Percentage
errors.
Estimation
Expressing numbers in the form a10k where 1  a  10 and
k
Number and Algebra
Operations with numbers expressed in the form a10k where
1  a  10 and k 
SI (System International) and other basic units of measurement:
(grams, metres, seconds, litres, etc..
Arithmetic sequences and series, and their applications.
Use of the formula for the nth nth term and the sum of the first n
terms.
Geometric sequences and series, and their applications.
Use of the formula for the nth nth term and the sum of the first n
terms.
Solutions of quadratic equations: by factorizing; by GDC.
Basic concepts of set theory: subsets; intersection; union;
complement.
Venn diagrams and simple applications.
Sample Space: event, A; complementary event, A’.
Basic concepts of symbolic logic: definition of a proposition;
symbolic notation of propositions.
Compound statements: implication,; equivalence,  ; negation,;
conjunction, disjunction.
Sets, Logic, and
Probability
Translation btwn verbal statements, symbolic form and Venn
diagrams.
Truth tables: the use of truth tables to provide proofs for the
properties of connectives; concepts of logical contradiction and
tautology.
Definition of implication: converse; inverse; contrapositive.
Logical equivalence.
Equally likely events.
n( A)
.
n(U )
Probability of a complementary event, P( A)  1  P( A) .
Probability of an event A given by P( A) 
Venn diagrams; tree diagrams; tables of outcomes. Solutions of
problems using “with replacement”and “without replacement”.
Laws of Probability.
Combined events:
P( A  B)  P( A)  P( B)  P( A  B)
Mutually exclusive events:
P( A  B)  P( A)  P( B)
Conditional Probability: P( A B) 
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P(A  B)
P(B)
Needs
Work
Mathematical Studies Year 12 Outcomes
Topic
Objectives
Know
Concept of a function as a mapping.
Domain and Range. Mapping diagrams
Linear functions and their graphs, for example,
f :x
mx  c
The graph of the quadratic function:
f ( x)  ax 2  bx  c
Properties of symmetry; vertex; intercepts
The exponential expression: ab ; b 
Graphs and properties of exponential functions.
Functions
f ( x)  a x ;
f ( x)  a  x
f ( x)  ka  x  c
k , a , c,  
Growth and decay; basic concepts of asymptotic behaviour.
Graphs and properties of the sine and cosine functions:
f ( x)  a sin bx  c
f ( x)  a cos bx  c; a, b, c 
Amplitude and period.
Accurate graph drawing.
Use of GDC to sketch and analyse some simple, unfamiliar
functions.
Use of GDC to solve equations involving simple combinations of
some simple, unfamiliar functions.
Right-angled trigonometry
Use of the ratios sine, cosine and tangent
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 
Geometry and
Trigonometry
Statistics
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a 2  b2  c 2
2ab
1
ab sin(C )
2
Geometry of three dimensional shapes: cuboid; prism; pyramid;
cylinder; sphere; hemisphere; cone.
Lengths of lines joining vertices with vertices, vertices with
midpoints and midpoints with midpoints; sizes of angles between
two lines and between lines and planes.
Coordinates in two dimensions; points; lines; midpoints.
Distances between points.
Equation of a line in two dimensions; the forms y = mx+c and
ax + by +d = 0.
Gradient; intercepts
Points of intersection of lines; parallel lines; perpendicular lines.
Classification of data as discrete or continuous.
Simple discrete data: frequency tables; frequency polygons
Grouped discrete or continuous data: frequency tables; mid-interval
values; upper and lower boundaries.
Frequency histograms.
Stem and leaf diagrams (stem plots).
Cumulative frequency tables for grouped discrete data and for
grouped continuous data; cumulative frequency curves.
Box and whisker plots (box plots).
Percentiles; quartiles
Needs
Work
Mathematical Studies Year 12 Outcomes
Topic
Objectives
Know
Measures of central tendency.
For simple discrete data: mean, median, mode.
For grouped discrete and continuous data: approximate mean;
modal group; 50th percentile.
Measures of dispersion; range; inter-quartile range; standard
deviation.
Scatter diagrams; line of best fit, by eye, passing through mean
point.
Bivariate data: the concept of correlation.
Pearson’s product-moment correlation coefficient: use of the
formula
r
Statistics
S xy
Sx S y
.
Interpretation of positive, zero and negative correlations.
The regression line for y on x : use of the formula
y y 
S xy
Sx2
( x  x)
Use of the regression line for prediction purposes.
The  test for independence: formulation of null and alternate
hypotheses; significance levels; contingency tables; expected
frequencies; use of the formula
2
 calc 2  
( f0  fe )2
; degrees of freedom; use of tables for
fe
critical values; p-values.
Gradient of the line through two points, P and Q, that lie on the
graph of a function.
Behaviour of the gradient of the line through two points, P and Q,
on the graph of a function as Q approaches P.
(the derivative as the gradient function:
dy
 f ( x  h)  f ( x) 
)
f '( x)  limh0 
 ; f '( x) 
h
dx


Tangent to a curve
The principle that
f ( x)  ax" n  f '( x)  anx n 1
Introductory Differential
Calculus
 f "( x)  an( n  1) x n  2
The derivative of functions of the form
f ( x)  ax n  bx n 1  ..., n  .
Gradients of curves for given values of x.
Values of x where f '( x) is given.
Equation of the tangent at a given point.
Increasing and decreasing functions.
Graphical interpretation of
f '( x)  0, f '( x)  0, f '( x)  0 .
Values of x where the gradient of a curve is 0 (zero ); solution of
f '( x)  0 .
Local maximum and minimum points.
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Needs
Work
Mathematical Studies Year 12 Outcomes
Topic
Objectives
Know
Currency conversions
Simple interest; use of formula I 
Financial Mathematics
Crn
100
Where C =capital, r = % rate, n = number of time periods, I =
interest.
Compound interest; use of the formula
n
r 

I  C  1 
 C .
100


Depreciation.
The value of r can be positive or negative.
Construction and use of tables: loan and repayment schemes;
investment and saving schemes; inflation.
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Needs
Work