How to learn High school: Mathematics

Idaho academic standards: Mathematics, High school

0 of 14 concepts ready to learn · Markdown, for your AI

1. Statistics and Probability (9-12) · (+) 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. Statistics and Probability (9-12) · 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. Geometry (9-12) · (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

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. Functions (9-12) · 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. Functions (9-12) · Find inverse functions algebraically and graphically.

1. Using inverse operations: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations
2. Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable

6. Functions (9-12) · Write a function that describes a relationship between two quantities. Functions could include linear, exponential, quadratic, simple rational, radical, logarithmic, and trigonometr

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. Functions (9-12) · Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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

8. Functions (9-12) · Graph functions expressed symbolically and show key features of the graphs, by hand in simple cases and using technology for more complicated cases.

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

9. 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

10. Algebra · Interpret the relationship between two or more quantities.

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
2. 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

11. Algebra · Demonstrate understanding that polynomials form a system analogous to the integers; namely, they are closed under certain operations.

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

12. Algebra · 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)