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How to learn High school: Mathematics

Alabama academic standards: Mathematics, High school

0 of 25 concepts ready to learn · Markdown, for your AI

1. Precalculus · Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity.

  1. Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

2. Applications of Finite Mathematics · Use vertex and edge graphs to model mathematical situations involving networks.

  1. Sets & Venn Diagrams: Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes

3. Applications of Finite Mathematics · Using application-based problems, develop formulas for permutations, combinations, and combinations with repetition and compare student-derived formulas to standar

  1. Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
  2. Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable

4. Mathematical Modeling · Perform inference procedures based on the results of samples and experiments.

  1. Estimating by rounding: Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values

5. Mathematical Modeling · Construct a sampling distribution for a random event or random sample.

  1. Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

6. Mathematical Modeling · Construct a probability distribution based on empirical observations of a variable.

  1. Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers
  2. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

7. Mathematical Modeling · Use regression with statistical graphing technology to determine an equation that best fits a set of bivariate data, including nonlinear patterns.

  1. Scatter Graphs & Correlation: Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions
  2. Scatter Graphs: Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate

8. Mathematical Modeling · Plot coordinates on a three-dimensional Cartesian coordinate system and use relationships between coordinates to solve design problems.

  1. Plotting Linear Graphs: Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line

9. Mathematical Modeling · Construct a two-dimensional visual representation of a three-dimensional object or structure.

  1. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

10. Algebra II With Statistics · Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, t

  1. Quadratic Graphs: Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions
  2. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context

11. Algebra II With Statistics · Explain why the <em>x</em>-coordinates of the points where the graphs of the equations <em>y = f(x)</em> and <em>y = g(x)</em> intersect are the solutions of the equation

  1. Simultaneous Equations: Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations

12. Algebra I With Probability · Generate a two-way categorical table in order to find and evaluate solutions to real-world problems.

  1. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

13. Algebra I With Probability · Define sequences as functions, including recursive definitions, whose domain is a subset of the integers.

  1. Generating Sequences: Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither

14. Algebra I With Probability · Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

  1. Factorising Expressions: Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

15. Geometry with Data Analysis · Discover and apply relationships in similar right triangles.

  1. Types of angles (age 13+): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
  2. Trigonometry basics: Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem
  3. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

16. Geometry with Data Analysis · Justify whether conjectures are true or false in order to prove theorems and then apply those theorems in solving problems, communicating proofs in a variety of ways, inc

  1. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

17. Geometry with Data Analysis · Verify criteria for showing triangles are similar using a similarity transformation (sequence of rigid motions and dilations) that maps one triangle to another.

  1. Angles in triangles (age 12+): Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent

18. Geometry with Data Analysis · Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

  1. Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

19. Geometry with Data Analysis · Evaluate possible solutions to real-life problems by developing linear models of contextual situations and using them to predict unknown values.

  1. Estimating answers (age 13+): Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts