How to learn High school: Mathematics
California academic standards: Mathematics, High school
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1. Higher Mathematics Course — Statistics and Probability · (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
- 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. Higher Mathematics Course — Statistics and Probability · Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- 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. Higher Mathematics Course — Geometry · Verify experimentally the properties of dilations given by a center and a scale factor:
- 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. Higher Mathematics Course — Functions · Distinguish between situations that can be modeled with linear functions and with exponential functions.
- 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. Higher Mathematics Course — Functions · Find inverse functions.
- Using inverse operations: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations
- Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable
6. Higher Mathematics Course — Functions · Write a function that describes a relationship between two quantities
- Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
7. Higher Mathematics Course — Functions · Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- 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. Higher Mathematics Course — Algebra · Solve quadratic equations in one variable.
- 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. Higher Mathematics Course — Algebra · Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- 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
- 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. Higher Mathematics Course — Number and Quantity · (+) Multiply a vector by a scalar.
- 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