• Date created

July 1, 2020

• Last updated

July 1, 2020

# Course Overview

The ACT Mathematics course was developed by aligning Plato Courseware with the
topics that are assessed on the 2016 ACT Test. Each unit aligns to one or more topics
within the test. This course focuses on the study of algebraic problem-solving skills and
concepts related to geometry, probability, and statistics. In this course, you will find a
variety of lessons and activities to improve your knowledge and skills in these areas.

# Course Goals

By the end of this course, you will:
Use addition, subtraction, multiplication, and division to solve real-world problems.
Use fractions to solve real-world problems.
Add, subtract, multiply, and divide decimals using the standard algorithm.
Order rational numbers in real-world situations.
Study absolute values and recognize the difference between absolute value and
Explore common factors and multiples.
Study the use of ratios, and understand ratios and rates as percentages.
Explore properties of exponents and understand the use of scientific notation.
Use square and cube roots.
Understand and interpret statistics and ways to measure data sets.
Understand probability.
Add, subtract, multiply, and divide binomials and monomials.
Evaluate rational expressions and create and solve equations.
Rewrite equations to solve for a single variable.
Apply the rules for exponents when the exponents are rational numbers.
Solve quadratic equations by factoring, and find the solution for the quadratic
equations of the form x²+ bx = 0.
Simplify rational and polynomial expressions.
Simplify rational expressions with exponents and radicals.
Prove and use polynomial identities and the Binomial Theorem.
Use the quadratic formula to find a solution set for a quadratic equation.
Solve linear inequalities by using the addition, subtraction, multiplication, and division method.
Graph the solution sets of associated inequalities.
Solve a system of equations by adding or subtracting.
Solve word problems using a system of two linear equations or inequalities.
Understand, construct, and interpret functions.
Graph absolute value functions.
Explore arithmetic and geometric sequences and series.
Understand matrices and perform matrix operations.
Add, subtract, multiply, and divide complex numbers, and plot complex numbers in the plane.
Graph linear equations in two variables.
Use the slope and intercept of linear functions to write an equation from a graph, and
draw a graph from an equation.
Interpret graphs to solve problems and graph linear inequalities in two variables.
Identify graphs from their equations.
Identify the slope of parallel lines and the slope of a line that is perpendicular to another line.
Divide a line segment based on a ratio.
Use coordinates to compute perimeters and areas.
Derive the equation, center, and radius of a circle.
Understand conic sections while exploring parabolas and their graphs.
Explore ellipses, circles, and their graphs.
Use key features of hyperbolas to graph them.
Understand basic geometric concepts.
Represent transformations in a plane.
Write mathematical proofs and apply them to simple geometric relationships.
Prove theorems about lines, angles, triangles, and parallelograms.
Prove the slope criteria for parallel and perpendicular lines to solve geometric problems.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Identify and describe relationships among inscribed angles, radii, and chords.
Represent three-dimensional figures using nets made up of rectangles and triangles,
and find the surface area of these figures.
Examine trigonometric graphs and trigonometric functions using a unit circle.
Examine and apply the basic trigonometric identities.
Describe and use the relationship between the sine and cosine of complementary angles.
Understand trigonometric ratios and apply the Pythagorean Theorem to solve right triangles.

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