ACT Exam Structure Overview

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ACT Math Test: Comprehensive Topic Breakdown 60 minutes, 60 questions Domain Sub-Domain Topics Included Lesson Name Pre-Algebra Basic Operations & Number Sense Addition, subtraction, multiplication, division, order of operations (PEMDAS), properties of real numbers (commutative, associative, distributive), integers Order of Operations & Number Properties Fractions Simplifying fractions, equivalent fractions, operations with fractions (add, subtract, multiply, divide), mixed numbers, improper fractions Fraction Arithmetic & Conversions Decimals & Percentages Operations with decimals, converting between fractions, decimals, and percents. Percent increase/decrease, percent of a number, sales tax, discounts, simple interest Decimals, Percents & Real-World Apps Ratios, Rates, & Proportions Ratios, unit rates, proportional relationships, solving proportions, scaling, direct variation Ratios, Proportions & Unit Rates Factors & Multiples Factors, multiples, prime and composite numbers, prime factorization, Least Common Multiple (LCM), Greatest Common Factor (GCF) Factors, Multiples & Prime Numbers Mean, Median, Mode, Range Calculating and interpreting measures of central tendency and spread for data sets Statistical Measures: Center & Spread Basic Probability Simple probability (favorable outcomes / total outcomes), complementary events, basic understanding of independent events Introduction to Probability Data Representation Interpreting information from tables, charts, graphs (bar graphs, pie charts, line graphs, pictographs, frequency tables) Interpreting Data Displays Absolute Value Evaluating absolute value expressions, interpreting absolute value as distance on the number line Absolute Value Concepts Expressions Writing and simplifying numeric and basic algebraic expressions, evaluating expressions, combining like terms Writing & Simplifying Expressions Equivalent Expressions Identifying equivalent numeric and algebraic forms, applying the distributive property, basic algebraic manipulation Algebraic Equivalence Number Line & Inequalities Graphing numbers on a number line, comparing numbers, basic inequalities ($ , \le, \ge$), solving simple one-step inequalities Number Line & Basic Inequalities Elementary Algebra Linear Equations Solving one-variable linear equations (including multi-step equations, equations with variables on both sides, equations involving fractions/decimals) Solving Linear Equations Linear Inequalities Solving and graphing linear inequalities in one variable, compound inequalities (e.g., $x>2$ AND $x Solving Linear Inequalities Systems of Linear Equations Solving systems of two linear equations in two variables (graphing, substitution, elimination methods) Solving Systems of Equations Polynomials Operations with polynomials (addition, subtraction, multiplication), degree of a polynomial, basic factoring (GCF, difference of squares, trinomials leading coefficient 1) Polynomial Operations & Basic Factoring Quadratic Equations Solving simple quadratic equations by factoring, using the quadratic formula (for standard cases), understanding roots/zeros Introduction to Quadratic Equations Exponents Laws of exponents (product, quotient, power rules), integer exponents (positive, negative, zero), scientific notation Laws of Exponents & Scientific Notation Radicals Simplifying square roots, operations with square roots, rationalizing denominators (simple cases) Simplifying Radical Expressions Algebraic Manipulation Rewriting algebraic expressions, isolating variables in formulas, working with algebraic fractions (simple) Formula Rearrangement & Variables Intermediate Algebra Functions Function notation ($f(x)$), evaluating functions, domain and range, inverse functions (basic), operations on functions (add, subtract, multiply, divide) Function Concepts & Notation Graphing Functions Graphing linear, quadratic, exponential, radical, and absolute value functions; identifying intercepts, vertex, asymptotes (basic) Graphing Common Functions Complex Numbers Defining $i$ ($i^2 = -1$), operations with complex numbers (addition, subtraction, multiplication, division - basic) Operations with Complex Numbers Logarithms Converting between exponential and logarithmic form, basic logarithmic properties (product, quotient, power rules), solving simple logarithmic equations Logarithms & Exponentials Matrices Adding, subtracting, and scalar multiplication of matrices; multiplying matrices (small dimensions, e.g., $2 \times 2$) Matrix Operations Sequences & Series Arithmetic and geometric sequences (finding terms, sums of finite series), patterns, recursive definitions Arithmetic & Geometric Sequences/Series Advanced Systems of Equations Solving systems with linear and quadratic equations, systems of three linear equations in three variables Advanced Systems of Equations Coordinate Geometry Distance & Midpoints Distance formula, midpoint formula between two points in the coordinate plane Distance & Midpoint Formulas Lines & Slopes Calculating slope, equations of lines (slope-intercept, point-slope, standard form), parallel and perpendicular lines, intercepts Equations of Lines & Slope Conic Sections (Basic) Equation of a circle (center-radius form), identifying center and radius. Basic recognition of parabolas, ellipses, hyperbolas from equations Introduction to Conic Sections Geometric Figures in Coordinate Plane Calculating area and perimeter of polygons in the coordinate plane, proving properties of figures using coordinates Coordinate Geometry of Polygons Transformations Translations, rotations, reflections, dilations (identifying and performing on figures in the coordinate plane) Geometric Transformations Vectors Representing vectors in the coordinate plane, calculating magnitude and direction (basic operations like addition/subtraction) Introduction to Vectors Inequalities in Two Variables Graphing linear inequalities in two variables, identifying solution regions Graphing Linear Inequalities Plane & Solid Geometry Angles & Lines Types of angles (acute, obtuse, right, straight), complementary/supplementary angles, vertical angles, angles formed by parallel lines and transversals Angle & Line Relationships Triangles Types of triangles (equilateral, isosceles, scalene, right), angle sum theorem, triangle inequality theorem, properties of medians, altitudes, angle bisectors Triangle Properties & Theorems Polygons Properties of quadrilaterals (parallelograms, rectangles, squares, trapezoids, rhombuses), sum of interior/exterior angles of polygons Properties of Polygons & Quadrilaterals Circles Circumference, area, arcs, sectors, inscribed angles, central angles, tangents, chords Circle Properties & Formulas Area & Perimeter (2D) Calculating area and perimeter of triangles, quadrilaterals, circles, and composite shapes Calculating 2D Area & Perimeter Surface Area & Volume (3D) Calculating surface area and volume of prisms, cylinders, cones, spheres, pyramids Calculating 3D Surface Area & Volume Trigonometry Right Triangle Trigonometry SOH-CAH-TOA (sine, cosine, tangent) definitions, solving for sides and angles in right triangles Right Triangle Trig Ratios Trigonometric Identities Pythagorean identity ($\sin^2 \theta + \cos^2 \theta = 1$), reciprocal identities ($\csc \theta, \sec \theta, \cot \theta$) Fundamental Trig Identities Unit Circle & Radians Understanding angles in degrees and radians, values of trigonometric functions for common angles (e.g., $0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}$) Unit Circle & Radian Measure Trigonometric Functions & Graphs Basic graphs of sine, cosine, and tangent functions (period, amplitude, phase shift, vertical shift), interpreting graphs Graphing Trig Functions Law of Sines & Cosines Applying the Law of Sines and Law of Cosines to solve non-right triangles Law of Sines & Cosines