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How to learn High school: Mathematics

Indiana academic standards: Mathematics, High school

0 of 19 concepts ready to learn · Markdown, for your AI

1. Data Analysis & Statistics · Summarize bivariate categorical data in two-way frequency tables. Interpret relative frequencies in the contexts of the data (including joint, marginal, and conditional re

  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

2. Data Analysis & Statistics · Interpret statistics as a process for making inferences about a population based on a random sample from that population. Recognize the purposes of and differences among s

  1. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

3. Quadratic and Exponential Equations and Functions · Describe the relationships among a solution of a quadratic equation, a zero of the function, an x-intercept of the graph, and the factors of the exp

  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

4. Quadratic and Exponential Equations and Functions · Solve quadratic equations in one variable by inspection (e.g., for x 2 = 49), finding square roots, using the quadratic formula, and factoring, as a

  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

5. Systems of Linear Equations and Inequalities · Represent real-world problems using a system of two linear inequalities in two variables. Graph the solution set to a system of linear inequalities in tw

  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

6. Linear Equations, Inequalities, and Functions · Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables, including with technology. Translate fluen

  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

7. Number Systems, Expressions, and Functions · Add, subtract, and multiply polynomials. Divide polynomials by monomials. Use these operations to rewrite algebraic expressions in equivalent forms, and ju

  1. Expanding Double Brackets: Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms

8. Number Systems, Expressions, and Functions · Simplify square roots of monomial algebraic expressions, including non-perfect squares.

  1. Square and cube numbers: Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations

9. Transformations & Three-Dimensional Solids · Apply geometric methods to create and solve design problems. (E)

  1. 3-D shapes (age 11+): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections

10. Transformations & Three-Dimensional Solids · Use geometric descriptions of rigid motions to transform figures and to predict and describe the results of translations, reflections and rotations on a gi

  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

11. Circles · Solve real-world and other mathematical problems that involve finding measures of circumference, areas of circles and sectors, and arc lengths and related angles (central, inscribed, and int

  1. Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

12. Quadrilaterals & Other Polygons · Develop and use formulas to find measures of interior and exterior angles of polygons.

  1. Angle sums in triangles and polygons: Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons

13. Quadrilaterals & Other Polygons · Prove that given quadrilaterals are parallelograms, rhombuses, rectangles, squares, kites, or trapezoids. Include coordinate proofs of quadrilaterals in the coordinat

  1. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

14. Triangles · Use the relationship between the sides of special right triangles (30° - 60° and 45° - 45°) to solve real-world and other mathematical problems. (E)

  1. Types of angles (age 13+): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts

15. Triangles · Use trigonometric ratios (sine, cosine, tangent, and their inverses) and the Pythagorean Theorem to solve real-world and mathematical problems involving right triangles. (E)

  1. Trigonometry basics: Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem

16. Triangles · Use congruent and similar triangles to solve real-world and mathematical problems involving sides, perimeters, and areas of triangles. (E)

  1. Angles in triangles (age 12+): Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent

17. Geometry Foundations · Use tools to explain and justify the process to construct congruent segments and angles, angle bisectors, perpendicular bisectors, altitudes, medians, parallel and perpendicular

  1. Understanding angles (age 12+): Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle

18. Geometry Foundations · Prove, construct, and apply theorems about parallel and perpendicular lines, parallel lines and transversals, vertical angles, and perpendicular bisectors. (E)

  1. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

19. Geometry Foundations · Describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and theorems) and explain diff

  1. Types of angles (age 11+): Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons