# Math Studies SL e-Learning Course

This new e-learning course completely covers the IB Diploma Programme in Mathematical Studies SL and will help students achieve the highest grade possible for their examination. It supplements textbooks and teaching notes. Sound combinations of visual and audio aid allow the students either while in class or on their own to be exposed on a different type of learning. The use of such a digital set of aids shows once more that technological applications as such can on a rather straightforward but well focused manner aid learners to master mathematics on a young age as possible in the most effective and less stressful way.

It contains the following e learning courses

**NUMBER AND ALGEBRA**- Number systems
- Approximation: decimal places; significant figures.
- Percentage errors
- Estimation
- Expressing numbers in scientific notation
- SI (Système International) and other basic units of measurement
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Quadratic equations, factorization

**LOGIC**- Venn diagrams
- Compound statements: implication, equivalence, negation, conjunction, disjunction, exclusive disjunction.
- Translation between verbal statements, symbolic form and Venn diagrams.
- Truth tables
- concepts of logical contradiction and tautology.
- Definition of implication: converse; inverse; contrapositive.
- Logical equivalence.

**PROBABILITY**- Probability of an event A

P(A)= - Probability of a complementary event,

P(A')=1-P(A) - Venn diagrams; tree diagrams; tables of outcomes. Solution of problems using "with replacement" and "without replacement".
- Combined events:

P(A B)=P(A) + P(B) - P(A B) - Mutually exclusive events:

P(A B)=P(A) + P(B) - Independent events:

P(A B)=P(A) P(B) - Conditional probability:

P(A|B)=

- Probability of an event A
**FUNCTIONS**- Domain and range. Mapping diagrams.
- Linear functions and their graphs, for example,

f: xmx + c - The graph of the quadratic function: f(x) = αx
^{2}+ bx +c - Properties of symmetry; vertex; intercepts.
- The exponential expression:

α^{b}; b - Graphs and properties of exponential functions

f(x)=a^{x};, f(x)=a^{λx};

f(x)=ka^{λx}+ c; k, a, c, λ - 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 a GDC to sketch and analyse some simple, unfamiliar functions.
- Use of a GDC to solve equations involving simple combinations of some simple, unfamiliar functions.

**GEOMETRY & TRIGOMOMETRY**- Coordinates in two dimensions: points; lines; midpoints.
- Distances between points.
- Equation of a line in two dimensions:

the forms y = mx + c

& ax + by + d =0 - Gradient; intercepts. Points of intersection of lines; parallel lines; perpendicular lines.
- Right-angled trigonometry. Use of the ratios of sine, cosine and tangent.
- The sine rule:

== - The cosine rule

a^{2}= b^{2}+ c^{2}– 2bc cos A;

cosA= - Area of a triangle:

ab sinC - Construction of labelled diagrams from verbal statements.
- 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.

**STATISTICS**- 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.
- Measures of central tendency.
- For simple discrete data: mean; median; mode.
- For grouped discrete and continuous data: approximate mean; modal group; 50
^{th}percentile. - Measures of dispersion: range; interquartile range; standard deviation.
- Scatter diagrams; line of best fit, by eye, passing through the mean point.
- Bivariate data: the concept of correlation.
- Pearson’s product–moment correlation coefficient:use of the formula

r= - Interpretation of positive, zero and negative correlations.
- The regression line for y on x: use of the formula

*y*-= - Use of the regression line for prediction purposes.
- The x
^{2}test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; use of the formula

X calc^{2}=; degrees of freedom; use of tables for critical values;*p*-values.

**CALCULUS**- Gradient of the line through two points. Tangent to a curve.
- The principle that

f(x)=ax^{n}f'(x) = anx^{n-1}

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

**FINANCIAL MATHEMATICS**- Currency conversions.
- Simple interest: use of the formula

I = where C = capital, r = % rate, n = number of time periods, I = interest - Compound interest: use of the formula

I = C x (1 + )^{n}- C - Depreciation.
- Construction and use of tables: loan and repayment schemes; investment and saving schemes; inflation.

Available April 2010 - DEMO SOON