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How to learn High school: Mathematics

South Dakota academic standards: Mathematics, High school

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

1. High School - 4th Year Mathematics · (+)Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding calculating the expected values.

  1. 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

2. High School - 4th Year Mathematics · (+)Analyze conic sections using equations and graphs.

  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
  2. 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

3. High School - 4th Year Mathematics · (+)Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  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

4. High School - Algebra II · 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

5. High School - Algebra II · 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)

6. High School - Geometry · Derive using similarity the length of the arc intercepted by an angle is proportional to the radius.

  1. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
  2. 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

7. High School - Geometry · Use geometric descriptions of rigid motions to transform figures.

  1. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

8. High School - Algebra I · 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

9. High School - Algebra I · Write a function (linear, quadratic, and exponential) that describes a relationship between two quantities.

  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

10. High School - Algebra I · 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

11. High School - Algebra I · 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)

12. High School - Algebra I · Interpret expressions that represent a quantity in terms of its context.

  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