IB Math Studies Learning Targets
Topic 1 – Numbers and algebra
1.1: Recognize and use different number systems and units of measurement
- Identify and/or sort numbers based on appropriate number set (integer, rational, ...)
- Recognize and use common units of measure.
- Conversion between different units of measure.
- Appropriate demonstration of decimal places.
- Appropriate demonstration of significant figures.
- Calculate percentage error.
- Evaluate the reasonableness of an answer through estimation.
- Write numbers in scientific notation.
- Conducting arithmetic operations using numbers in scientific notation.
- Find the nth term of an arithmetic sequence.
- Find the term number of a given value in an arithmetic sequence. c. Find the sum of the terms of an arithmetic series.
- Find the nth term of a geometric sequence.
- Find the term number of a given value in a geometric sequence. f. Find the sum of the terms of a geometric series.
- Apply sequences to financial and other situations.
- Solve a pair of simultaneous linear equations graphically.
- Solve a pair of simultaneous linear equations algebraically.
- Solve a quadratic equations by factoring or using quadratic formula.
- Simplify exponential expressions.
- Solve radical and rational equations.
- Convert currency.
- Use formula to calculate simple interest.
- Use formula to calculate interest rate, capital, or number of periods. d. Use formula to calculate compound interest.
- Use formula to calculate interest, capital, or number of time periods. f. Use the formula to solve depreciation problems.
Topic 2: Descriptive Statistics
2.1: Present and interpret data
- Determine whether data is discrete or continuous.
- Create and/or interpret a frequency table.
- Create or interpret a grouped frequency table.
- Create or interpret a frequency histogram.
- Use a cumulative frequency graph to find quartiles and/or percentiles.
- Create or interpret a cumulative frequency curve.
- Create or interpret a box and whisker plot.
- Use GCD to enter and view graphical data displays.
- Calculate mean, median, and/or mode for simple discrete data.
- Approximate mean, find modal group and median for grouped discrete data.
- Find the range and/or interquartile range.
- Calculate the standard deviation.
- Use GCD to enter and analyze data.
Topic 3: Sets, logic, and probability.
3.1: Use set theory to solve problems
- Define basic concepts of set theory: subsets, intersection, union, complement.
- Use Venn diagram to solve problems.
- Construct Venn diagram to represent given information.
- Identify subsets and/or complements based on given information
- Identify union and/or intersection of two sets
- Define proposition and identify symbolic notation.
- Write logic statement in symbolic form and vise versa.
- Translate between logic statements and Venn diagrams.
- Explain the difference between disjunction and exclusive disjunction. e. Complete truth tables.
- Determine whether a statement is a tautology or contradiction.
- Identify converse, inverse, and/or contrapositive of a statement.
- Determine whether two statements are logically equivalent.
- Testing the validity of simple statements.
- Find the probability of a simple event.
- Find the probability of the complement of an event.
- Find probability using a Venn diagram, tree diagram, or table. d. Solve problems using with and without replacement.
- Find the probability of the union of two events.
- Determine if two events are mutually exclusive.
- Determine if two events are independent.
- Find the probability of independent events.
- Calculate conditional probability.
Topic 4: Statistical Applications
4.1: Analyze quantitative data
- Draw line of best fit by eye.
- Identify positive/negative/zero correlation and the strength of the correlation. c. Use GDC to calculate and interpret correlation coefficient from data.
- Use formula to calculate and interpret correlation coefficient from data.
- Find and interpret regression line using GDC.
- Find and interpret regression line using formula
- Use regression line for prediction.
- Understand and use concepts of interpolation and extrapolation.
- Formulate null and alternative hypotheses.
- Interpret contingency tables for use in chi-square test.
- Conduct hypothesis test using GDC.
- Conduct hypothesis test using formula.
- Conduct hypothesis test from given information (no contingency table). f. Construct expected value table.
- Represent a normal distribution situation graphically.
- Calculate probabilities using the normal distribution.
- Solve problems using the inverse normal distribution.
- Calculate expected values.
Topic 5 – Geometry and trigonometry
5.1 Solve problems involving lines on the coordinate plane
- Find the distance between two points.
- Calculate the slope of a line.
- Find the x-and y-intercepts of a line.
- Solve problems involving parallel and/or perpendicular lines.
- Find the point of intersection of two lines.
- Use the sine, cosine, and tangent ratios to solve triangle problems.
- Use inverse sine, cosine, and tangent functions to solve for angles.
- Use sine rule to solve triangle problems.
- Use cosine rule to solve triangle problems.
- Find the area of a triangle.
- Find surface area of 3-D figures.
- Find volume of 3-D figures.
- Find lengths of edges of 3-D figures.
- Find midpoints of edges of 3-D figures.
- Find measures of angles between lines.
- Find measures of angles between lines and planes.
Topic 6: Mathematical models
6.1: Recognize and use various functional notations and forms
- Recognize different representations of functions.
- Complete mapping diagrams.
- Identify domain and range of a function.
- Write linear functions in form y = mx + c
- . Interpret solutions to linear equations from graph.
- Find axis of symmetry, vertex, and intercepts from graph.
- Find axis of symmetry, vertex, and intercepts algebraically.
- Identify properties of functions: intercepts, asymptotes.
- Write exponential equation from graph.
- Applications of exponential equations.
- Identify amplitude and period from equations.
- Write circular function from graph
- Draw accurate graphs.
- Models using functions of the form f (x) = axm + bxn + ...; m, n ∈Ζ o.
- Use GDC to sketch graphs and analyze functions.
- Use GDC to solve equations.
Topic 7: Introductory differential calculus
7.1: Calculate derivatives
- Describe idea of limit informally.
- Calculate derivative of simple function from definition of derivative.
- Draw a tangent line to a curve.
- Use the power rule to find the derivative of a function.
- Use the power rule to find the second derivative of a function.
- Find and interpret the value of f’(x) for a given value of x.
- Find the equation of the line tangent at a given point.
- Find coordinates of a point of tangency.
- Find the function with given point of tangency.
- Find the solution to f’(x) = 0.
- Find local maximum and minimum points.
- Find the function with given critical points.
Topic : Internal Assessment
Communicate data analysis
- Complete introduction and statement of task.
- Complete information/measurement.
- Complete mathematical process.
- Complete sophisticated mathematical process.
- Complete interpretation of results.
- Complete comprehensive interpretation of results.
- Complete validity.
- Adequately structure and communicate the project.
- Show sufficient commitment to project.