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How to learn High school: Mathematics

Tennessee academic standards: Mathematics, High school

0 of 15 concepts ready to learn · Markdown, for your AI

1. Precalculus · Find inverse functions (including exponential, logarithmic, and trigonometric).

  1. Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable
  2. 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. Precalculus · Multiply a vector by a scalar.

  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

3. Integrated Math III · Understand and apply the Addition Rule.

  1. Venn Diagrams and Counting Outcomes: Construct and interpret Venn diagrams with two or three sets to organise and count outcomes; use systematic listing and the product rule for counting to enumerate all possible outcomes of combined events

4. Integrated Math III · Use set notation to represent contextual situations.

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

5. Integrated Math III · Solve triangles.

  1. 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

6. Integrated Math III · Use units as a way to understand real-world problems.

  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. 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

7. Integrated Math II · Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

  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

8. Integrated Math II · Solve quadratic equations and inequalities in one variable.

  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

9. Integrated Math II · Extend the properties of integer exponents to rational exponents.

  1. Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers

10. Integrated Math I · Distinguish between situations that can be modeled with linear functions and with exponential functions.

  1. 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 · Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

  1. Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations

12. Geometry · Solve triangles.

  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

13. Algebra I · Interpret expressions that represent a quantity in terms of its context.

  1. Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)