How can we find the mean
of the weight of a population of students which is found to be normally distributed with standard deviation 2 Kg and the 10% of the students weigh at least 53 Kg.
the answer is here
http://www.ibmaths4u.com/
Wednesday, March 27, 2013
IB Mathematics HL – Continuous Probability Distribution, Normal Distribution
How can we find the mean
of the weight of a population of students which is found to be normally distributed with standard deviation 2 Kg and the 10% of the students weigh at least 53 Kg.
the answer is here
http://www.ibmaths4u.com/
May 2013 examination schedule
May 2013 examination schedule
http://www.wis.edu.na/sites/default/files/pagefiles/may2013examinationschedule11.pdf
http://www.wis.edu.na/sites/default/files/pagefiles/may2013examinationschedule11.pdf
Sunday, March 24, 2013
IB mathematical Studies
Number and algebra, Descriptive statistics, Logic, sets and probability, Statistical applications, Geometry and trigonometry, Mathematical models, Introduction to differential calculus.
IB Mathematics SL
Algebra
Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series. Sigma notation. Elementary treatment of exponents and logarithms. Laws of exponents; laws of logarithms. Change of base.
The binomial theorem.
Functions and equations
Domain, range, image of a function. Composite functions. Identity function. Inverse function.
The graph of a function, Function graphing skills., Investigation of key features of graphs, such as
maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.
Use of technology to graph a variety of functions, including ones not specifically mentioned.
The graph of inverse function as the reflection in the line y = x of the graph of y = f (x) .
Transformations of graphs , Translations, Reflections, Vertical stretch with scale factor p, Stretch in the x-direction, Composite transformations.
The quadratic function, The reciprocal function, The rational function, Vertical and horizontal asymptotes.
Exponential functions and their graphs, Logarithmic functions and their graphs.
Solving equations, both graphically and analytically.
Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.
The quadratic formula, The discriminant, Solving exponential equations, Applications of graphing skills and solving
equations that relate to real-life situations.
Circular functions and trigonometry
The circle: radian measure of angles; length of an arc; area of a sector. Definition of cosθ and sinθ in terms of the
unit circle. Exact values of sin, cos and tan of
The Pythagorean identity, Double angle identities for sine and cosine, Relationship between trigonometric ratios.
The circular functions sin x , cos x and tan x :their domains and ranges; amplitude, theirperiodic nature; and their graphs.
Composite functions of the form f (x) = asin (b(x + c) ) + d . Transformations.
Solving trigonometric equations in a finite interval, both graphically and analytically.
Equations leading to quadratic equations in sin x, cos x or tan x .
Solution of triangles, The cosine rule, The sine rule, including the ambiguous case, Area of a triangle.
Vectors
Vectors as displacements in the plane and in three dimensions.
Components of a vector, The scalar product of two vectors, Perpendicular vectors; parallel vectors, The angle between two vectors,
Vector equation of a line in two and three dimensions, The angle between two lines, Distinguishing between coincident and parallel
lines. Finding the point of intersection of two lines. Determining whether two lines intersect.
Statistics and probability
Concepts of population, sample, random sample, discrete and continuous data.
Presentation of data: frequency distributions, frequency histograms with equal class intervals, box-and-whisker plots, outliers.
Grouped data: use of mid-interval values for calculations, interval width; upper and lower interval boundaries, modal class.
Statistical measures and their interpretations. Central tendency: mean, median, mode. Quartiles, percentiles.
Dispersion: range, interquartile range, variance, standard deviation. Effect of constant changes to the original data.
Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles.
Linear correlation of bivariate data, Pearson’s product–moment correlation coefficient r.
Scatter diagrams; lines of best fit., Equation of the regression line of y on x. Use of the equation for prediction purposes.
Mathematical and contextual interpretation. Concepts of trial, outcome, equally likely
outcomes, sample space (U) and event. The probability of an event A, The complementary events A and A′ (not A).
Use of Venn diagrams, tree diagrams and tables of outcomes.
Combined events, Mutually exclusive events, Conditional probability, Independent events, Probabilities with and without replacement.
Concept of discrete random variables and their probability distributions. Expected value (mean), E(X ) for discrete data.
Binomial distribution. Mean and variance of the binomial distribution. Normal distributions and curves. Standardization of normal variables (z-values, z-scores). Properties of the normal distribution.
Calculus
Informal ideas of limit and convergence, Limit notation, Definition of derivative from first principles, Derivative interpreted as gradient function and as rate of change. Tangents and normals, and their equations. The chain rule for composite functions.
The product and quotient rules. The second derivative. Extension to higher derivatives. Local maximum and minimum points.
Testing for maximum or minimum. Points of inflexion with zero and non-zero gradients. Graphical behaviour of functions,
including the relationship between the graphs of f , f ′ and f ′′ . Optimization. Indefinite integration as anti-differentiation.
The composites of any of these with the linear function ax + b . Integration by inspection, or substitution.
Anti-differentiation with a boundary condition to determine the constant term. Definite integrals, both analytically and using
technology. Areas under curves (between the curve and the x-axis). Areas between curves. Volumes of revolution about the x-axis.
Kinematic problems involving displacement s, velocity v and acceleration a. Total distance travelled.
IB Mathematics HL
Big overall changes are that matrices have been removed. The two portfolio
pieces have been replaced by a more open-ended mathematical exploration. Applications are mentioned
much more than previously.
Algebra
Arithmetic sequences and series, sum of finite arithmetic series, geometric sequences and series, sum of finite and infinite geometric series,Sigma notation.
Exponents and logarithms,Laws of exponents, laws of logarithms,Change of base.
Counting principles, including permutations and combinations.
The binomial theorem
Proof by mathematical induction.
Complex numbers: the number i
terms real part, imaginary part, conjugate,modulus and argument.
Cartesian form z = a + ib
Sums, products and quotients of complex numbers
Modulus–argument (polar) form, The complex plane.Powers of complex numbers: de Moivre’s theorem.
nth roots of a complex number
Conjugate roots of polynomial equations with real coefficients.
Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinity of solutions or no solution.
Functions and equations
Concept of function (domain, range, image),Odd and even functions,Composite functions, Identity function,One-to-one and many-to-one functions
Inverse function, The graph of a function, Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes and symmetry,and consideration of domain and range.
Transformations of graphs: translations, stretches, reflections in the axes. The graph of the inverse function as a reflection in y = x. Rational function, exponential function and logarithmic function.
Polynomial functions and their graphs. The factor and remainder theorems. The fundamental theorem of algebra.
Solving quadratic equations using the quadratic formula. Use of the discriminant to determine the nature of the roots.
Solving polynomial equations both graphically and algebraically. Sum and product of the roots of polynomial equations.
Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.
Graphical or algebraic methods, for simple polynomials up to degree 3. Use of technology for these and other functions.
Circular functions and trigonometry
The circle: radian measure of angles. Length of an arc; area of a sector.Definition of cosθ , sinθ and tanθ in terms of the unit circle.
Exact values of sin, cos and tan of
Definition of the reciprocal trigonometric ratios secθ , cscθ and cotθ . Pythagorean identities.
Compound angle identities. Double angle identities.
Composite functions of the form f (x) = asin(b(x + c)) + d .
The inverse functions arcsin x ,arccos x , arctan x , their domains and ranges, their graphs.
Algebraic and graphical methods of solving trigonometric equations in a finite interval, including the use of trigonometric identities and factorization.
The cosine rule. The sine rule including the ambiguous case. Area of a triangle
Vectors
Concept of a vector. Representation of vectors using directed line segments. Unit vectors; base vectors i, j, k.Components of a vector.
The definition of the scalar product of two vectors.
Properties of the scalar product:
The angle between two vectors. Perpendicular vectors; parallel vectors. vVector equation of a line in two and three dimensions: r = a +λb .
Simple applications to kinematics. The angle between two lines.Coincident, parallel, intersecting and skew lines.
Points of intersection. The definition of the vector product of two vectors.
Properties of the vector product. Geometric interpretation of v × w .
Vector equation of a plane r = a +λb + μc .
Use of normal vector to obtain the form r ⋅ n = a ⋅ n.
Cartesian equation of a plane ax + by + cz = d .
Intersections of: a line with a plane; two planes; three planes. Angle between: a line and a plane; two planes.
Statistics and probability
Concepts of population, sample, random sample and frequency distribution of discrete and continuous data.
Grouped data: mid-interval values, interval width, upper and lower interval boundaries. Mean, variance, standard deviation.
Concepts of trial, outcome, equally likely outcomes, sample space (U) and event.
The probability of an event A. The complementary events A and A′ (not A). Use of Venn diagrams, tree diagrams, counting principles and tables of outcomes to solve problems.
Combined events; the formula for P(A∪ B) . Mutually exclusive events. Conditional probability. Independent events, the definition. Use of Bayes’ theorem for a maximum of three events.
Concept of discrete and continuous random variables and their probability distributions. Definition and use of probability density functions.
Expected value (mean), mode, median, variance and standard deviation.
Binomial distribution, its mean and variance. Poisson distribution, its mean and variance.
Normal distribution, Properties of the normal distribution. Standardization of normal variables.
Calculus
Informal ideas of limit, continuity and convergence. Definition of derivative from first principles.
The derivative interpreted as a gradient function and as a rate of change. Finding equations of tangents and normals.
Identifying increasing and decreasing functions.
The second derivative. Higher derivatives.
Derivatives of xn , sin x , cos x , tan x ,
The product and quotient rules. The chain rule for composite functions.
Related rates of change. Implicit differentiation.
Derivatives of sec x , csc x , cot x ,
Local maximum and minimum values. Optimization problems. Points of inflexion with zero and non-zero gradients.
Graphical behaviour of functions, including the relationship between the graphs of f , f ′ and f ′′ .
Indefinite integration as anti-differentiation. Indefinite integral of x^n , sin x , cos x and
Anti-differentiation with a boundary condition to determine the constant of integration. Definite integrals.
Area of the region enclosed by a curve and the x-axis or y-axis in a given interval; areas of regions enclosed by curves.
Volumes of revolution about the x-axis or y-axis.
Kinematic problems involving displacement s, velocity v and acceleration a. Total distance travelled.
Integration by substitution. Integration by parts.
Subscribe to:
Posts (Atom)