How to learn High school: Mathematics

Kansas academic standards: Mathematics, High school

0 of 11 concepts ready to learn · Markdown, for your AI

1. Functions · Find inverse functions.

1. Using inverse operations: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations

2. Functions · 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
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. 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

4. 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

5. Geometry · Use geometric constructions to verify 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

6. Geometry · Verify experimentally (for example, using patty paper or geometry software) the properties of rotations, reflections, translations, and symmetry:

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

7. Algebra · Analyze and solve pairs of simultaneous linear equations.

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

8. Algebra · Solve quadratic equations and inequalities

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. 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)
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