Diploma Subject: Mathematical Studies Level: SL

Transcription

1 Diploma Subject: Mathematical Studies Level: SL Topic Content Year 1 Presumed Knowledge Number Sets, Measurement, Approximation, Rounding and Estimation, % Error, Scientific Notation. Number and Algebra Arithmetic Sequences & Series and apllications: use of the formulae for the nth term and the sum of the first n terms of the sequence. Geometric sequences & series. Use of the formulae for the nth term and the sum of the first n terms Currency conversions. Financial applications of geometric sequences and series: compound interest and annual depreciation Descriptive Statistics Discrete and continuous data: concepts of population, sample, random sample. Frequency tables. Grouped discrete or continuous data; mid-interval values, upper and lower interval boundaries, modal class. Frequency histograms. Cumulative frequency tables, median and quartiles. Box-andwhisker diagrams. Measures of central tendency, mean, median

2 and mode. Measures of dispersion: range, interquartile range, quartiles, percentiles, standard deviation. Statistical Applications Bivariate data: correlation. Scatter diagrams; line of best fit, by eye passing through the mean point; Pearson s product-moment correlation coefficient, r. Interpretation of positive, zero and negative, strong or weak correlations. The regression line for y on x and prediction. Using regression line for prediction purposes. The chi-squared test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; p-values. Coordinate Geometry Mathematical models Equation of a line (standard and general form), gradient, intercepts, points of intersection of lines, simultaneous equations, parallel and perpendicular lines Concept of a function, domain, range and graph; interval form. Function notation and concept of a function as mathematical model. Linear models: linear functions and their graphs. Drawing accurate graphs and transferring

3 a graph from GDC to paper. Reading, interpreting and making Quadratic models: quadratic functions and their graphs. Properties of parabola: symmetry; vertex (turning point); intercepts on the x-axis (roots,zeros) and y-axis. Equation of the axis of symmetry. Drawing accurate graphs and transferring a graph from GDC to paper. Reading, interpreting and making Exponential models: exponential functions and their graphs. Concept and equation of veritcal and horizontal asymptote. Drawing accurate graphs and transferring a graph from GDC to paper. Reading, interpreting and making Polymnomial models: functions of this type and their graphs (cubic, quartic, ). Drawing accurate graphs and transferring a graph from GDC to paper. Reading, interpreting and making Rational Functions: vertical and horizontal asymptotes. Domain and Range. Drawing accurate graphs and transferring a graph from GDC to paper. Reading, interpreting and making The y- axis as vertical asymptote.

4 National Curriculum: Conics Introduction to differential Calculus Concept of a derivative as a rate of change. Notation. Tangent to a curve. Deirvative of functions of the form f(x) = ax n + bx n , where all exponents are integers. Gradients of curves for given values of x. Values of x where f (x)is given. Equation of the tangent and normal at a given point. Year 2 Introduction to differential Calculus Geometry & trigonometry Increasing and decreasing functions. Stationary points. Maximum and minimum points. Optimization problems(ex: fence, cylinder(volume and surface area), costs & profit) Trig ratios, angle of elevation and depression, sine rule, cosine rule, area of triangle. 3-D solids, distance between 2 points, angle between 2 lines or between a line and a plane. Volume and surface areas of the three- dimensional solids studied. National Curriculum: Main elements and properties of Periodical Functions.

5 Logic, sets and probability Basic concepts of Set Theory (element, subsets, intersection, union & complement, Venn diagrams and applications. Probability, sample space, complementary event, probability of an event and complimentary event, expected value. Probabiity of combined events, mutually exclusive events, independent events. Use of tree diagrams, venn diagrams, sample space diagrams, lattice. Probability with and without replacement. Conditinal probability. Logic: symbolic logic, compound statements(implication, negation, disjunction, conjunction, exclusive disjunction, translation between verbal sttements & symbolic form, truth tables, concepts of contradiction and tautology, converse, inverse, contrapositive and logical equivalence. National Curriculum: Counting principles: Combinations and Permutaions Statistical Applications Normal Distribution: concept of continuous random variable, diagrammatic represetation and properties of the bell shape, nomal probability calculations using GDC, Expected value and inverse normal calculations using GDC.