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How to learn High school: Mathematics

New Hampshire academic standards: Mathematics, High school

0 of 13 concepts ready to learn · Markdown, for your AI

1. High School — Statistics and Probability · (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

  1. The Probability Scale: Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible

2. High School — Statistics and Probability · Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

  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

3. High School — Geometry · Verify experimentally the properties of dilations given by a center and a scale factor:

  1. Coordinates (age 12+): Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids

4. High School — Functions · 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

5. High School — Functions · Find inverse functions.

  1. Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable

6. High School — Functions · Write a function that describes a relationship between two quantities

  1. Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios

7. High School — Functions · 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. High School — Algebra · Solve quadratic equations 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. High School — Algebra · Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

  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
  2. 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)

10. High School — Algebra · 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)

11. High School — Number and Quantity · (+) 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

12. High School — Number and Quantity · (+) Add and subtract vectors.

  1. Proportion: Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations