IB Math Studies MOCK EXAM STUDY GUIDE, March 2010 You have covered the following topics starting August 2009 up until the present… 1. Arithmetic calculations, use of the GDC to graph a variety of functions. Appropriate choice of “window”; use of “zoom” and “trace” (or equivalent) Entering data in lists. 2. The sets of natural numbers, ; integers, ; rational numbers, ; and real numbers, . 3. Approximation: decimal places; significant figures. Percentage errors. Estimation. 4. Expressing numbers in the form a ×10 k where 1 ≤ a < 10 and k . Operations with numbers expressed in the form a×10 k where 1≤a<10andk 5. SI (Système International) and other basic units of measurement: for example, gram (g), meter (m), second (s), liter (l), meter per second (m s 1 ), Celsius and Fahrenheit scales 6. Arithmetic sequences and series, and their applications. Use of the formulas for the nth term and the sum of the first n terms. 7. Geometric sequences and series, and their applications. Use of the formulas for the nth term and the sum of n terms. 8. Solutions of pairs of linear equations in two variables by use of a GDC. Solutions of quadratic equations: by factorizing; by use of a GDC. 9. Basic concepts of set theory: subsets; intersection; union; complement. 10. Venn diagrams and simple applications. 11. Sample space: event, A; complementary event, A. 12. Basic concepts of symbolic logic: definition of a proposition; symbolic notation of propositions. 13. Compound statements: implication, ⇒; equivalence, ; negation, ¬ ; conjunction, ; disjunction, ; exclusive disjunction, . 14. Translation between verbal statements, symbolic form and Venn diagrams. 15. Knowledge and use of the “exclusive disjunction” and the distinction between it and “disjunction”. 16. Truth tables: the use of truth tables to provide proofs for the properties of connectives; concepts of logical contradiction and tautology. 17. Definition of implication: converse; inverse; contrapositive. Logical equivalence. 18. Equally likely events. Probability of an event A given by P(A) = n(A) . n(U) Probability of a complementary event, P(A)=1−P(A). 19. Venn diagrams; tree diagrams; tables of outcomes. Solution of problems using “with replacement” and “without replacement”. 20. Laws of probability. Combined events:P(AB)=P(A)+P(B)−P(AB). Mutually exclusive events: P(AB)=P(A)+P(B). Independent events: P(AB)=P(A)P(B). P A B P B 21. Concept of a function as a mapping. Domain and range. Mapping diagrams. 22. Linear functions and their graphs, for example, f : x mx + c . 2 23. The graph of the quadratic function: f(x)=ax +bx+c; Properties of symmetry; vertex; intercepts. 24. The exponential expression: a b ; b Graphs and properties of exponential x x x functions. f (x) = a ; f (x) = a ; f(x)=ka +c; k,a,c,λ Growth and decay; basic concepts of asymptotic behavior. 25. Graphs and properties of the sine and cosine functions: f (x) = asinbx + c ; f(x)=acosbx+c; a,b,c, . Amplitude and period. 26. Accurate graph drawing. 27. Use of a GDC to sketch and analyze some simple, unfamiliar functions. 28. Use of a GDC to solve equations involving simple combinations of some simple, unfamiliar functions. 29. Coordinates in two dimensions: points; lines; midpoints. Distances between points. 30. 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. 31. Right-angled trigonometry. Use of the ratios of sine, cosine and tangent. a b c 32. The sine rule: = = ; The cosine rule a 2 =b 2 +c 2 −2bccosA; sin A sin B sin C 2 2 2 1 b c a cos A ; Area of a triangle: ab sin C 2 2bc 33. 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. 34. Classification of data as discrete or continuous. 35. Simple discrete data: frequency tables; frequency polygons. 36. Grouped discrete or continuous data: frequency tables; mid-interval values; upper and lower boundaries. Frequency histograms. Stem-and-leaf diagrams. 37. Cumulative frequency tables for grouped discrete data and for grouped continuous data; cumulative frequency curves. Box and whisker plots (box plots). Percentiles; quartiles. 38. Measures of central tendency. For simple discrete data: mean; median; mode. For grouped discrete and continuous data: approximate mean; modal group; 50th percentile. 39. Measures of dispersion: range; interquartile range; standard deviation. 40. Scatter diagrams; line of best fit, by eye, passing through the mean point. Bivariate data: the concept of correlation. Pearson’s product–moment correlation Conditional probability: P( A | B) = coefficient: Use of the formula r = s xy sx sy ; Interpretation of positive, zero and negative correlations. 41. The regression line for y on x: use of the formula y y sxy sx2 x x Use of the regression line for prediction purposes. 42. The 2 test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; use of the formula 2 f o fe 2 ; degrees of freedom; use of tables for critical values; p-values. calc fe