How to learn High school: Mathematics

Arkansas academic standards: Mathematics, High school

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1. Geometry · Students apply congruence criteria to solve problems.

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

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
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

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
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

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
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

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
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
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
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

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
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

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

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

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

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

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

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
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

Algebraic Notation: Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently

Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable