How to learn High school: Mathematics
New Jersey academic standards: Mathematics, High school
0 of 12 concepts ready to learn · Markdown, for your AI
1. Vector and Matrix Quantities · 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
2. Seeing Structure in Expressions · Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- 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)
3. Seeing Structure in Expressions · Interpret expressions that represent a quantity in terms of its context.
- Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
4. Reasoning with Equations and Inequalities · 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
5. Linear and Exponential Models · 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
6. Interpreting 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
7. Building 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
8. Building 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
9. Similarity, Right Triangles, and Trigonometry · 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
10. Using Probability to Make Decisions · Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. For example, find the forecasted value of an in
- 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
11. Interpreting Categorical and Quantitative Data · 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