# Guide to ACT® Math

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## Number & Quantity

Review basic foundational math skills including mathematical operations, order of operations, and factoring values. Then continue to explore more advanced functions including exponents, matrices, and ratios.

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### Basic Operations and Place Value

Review order of operations to evaluate simple numerical expressions and revisit place values from integers to decimals.
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### Exponents and Roots

Apply exponent rules to evaluate roots or exponential expressions.
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### Matrices

Learn to perform operations on matrices of data sets.
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### Complex Numbers

Following exponents, learn how we can express quantities that contain the root of a negative value.
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### Ratios, Proportions, and Percents

With the power of proportional relationships, use these to convert and scale measures or quantities.
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## Algebra

Review the bulk of algebra through practice with equations, inequalities, and expressions. Remember how to apply concepts like absolute value, quadratic formula, roots, and evaluation of systems of equations to both calculations and word-based problems. Master graphical depictions and analyses of expressions, inequalities, and functions on the coordinate plane.

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### Algebraic Expressions

Simplify expressions by combining like terms, factoring, and simplifying.
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### Linear Equations

Evaluate equations with two variables to solve for unknown quantities in real-world applications.
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### Inequalities

Evaluate inequalities with one or two variables to determine all possible solutions given constants.
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### Polynomial Expressions

Find solutions and simplify expressions with multiple variables containing exponents.
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### Properties of Exponents and Square Roots

Use exponent rules to evaluate expressions and equations with exponents and radicals.
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### Systems of Equations

Find the solution to a system of equations using substitution, addition or subtraction, elimination, or graphing.
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### Equations and Graphs

Apply different linear and quadratic equations to their coordinate plane representations to determine distance and transformations.
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## Functions

Utilize functions and evaluate their solutions through substitution. Analyze sequences and patterns as well as evaluate logarithms to practice for the exam.

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### Function Writing and Evaluation

Fluently read and use function notation to determine solutions at specific values.
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### Analyzing Functions

Compare values of modeled functions to determine best fit and behavior on the coordinate plane.
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### Sequences and Patterns

Explore expansion of sequences to determine patterns either linear or geometric.
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### Logarithms

Exhibit knowledge of logarithms and powers of base 10.
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## Geometry

Explore geometry in 3-dimensional shapes and solids by applying surface area and volume calculations of cylinders, prisms, spheres, and cones. Rediscover polygon conventions including those for triangles and quadrilaterals to help prove polygon congruence. Practice using trigonometric functions to angle measurements or triangle figures.

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### Angles and Lines

Explore properties of angles and what intersections of lines convey about their relationship to each other.
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### Properties of Shapes

Analyze different polygons and the relationships between angles, side lengths, perimeters, and areas.
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### Geometry in Three Dimensions

Taking into account the third dimension, turn polygons into prisms, spheres, pyramids, and cylinders to evaluate surface area, volume, and unknown measurements.
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### Proofs

Use logic and known theorems to evaluate if various arguments and relationships are valid.
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### Special Triangles

Based on special cases, analyze and evaluate unknowns in special instances of the simplest polygon: the triangle.
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### Trigonometry

Test your knowledge of trigonometry including trig functions, laws, graphs, and evaluation of unknowns.
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### Conic Sections

Explore equations of circles, ellipses, and parabolas to evaluate unknown solutions.
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## Statistics & Probability

Discover the power of statistics to analyze a set of data and also make predictions based on probability. Based on a variety of data visualizations, pull out trends and make conclusions based on them while also checking to see if the methods to gather them were sound.

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### Descriptive Statistics

Calculate and infer from basic descriptive statistics to describe the data sample.
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### Counting and Probability

Use basic probability methods to determine likelihood of outcomes.
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### Data Interpretation

Given graphical representations or numerical data, determine the trends or conclusions that can be made from them.
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### Data Collection

Evaluate the methods and potential errors that occur when collecting data and if it will affect the validity of the conclusions.
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