The ACT Math Test typically covers a variety of mathematical concepts, including pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. Here are six common question types that you may encounter on the ACT Math Test:

## Pre-Algebra:

Pre-Algebra is a fundamental area of mathematics tested on the ACT Math Test. Some of the concepts covered in pre-algebra include:

- Arithmetic operations: Addition, subtraction, multiplication, and division of whole numbers, decimals, and fractions.
- Exponents and Roots: Understanding of exponent rules and the use of radical notation to simplify expressions.
- Algebraic expressions: Understanding variables and coefficients and simplifying and evaluating expressions.
- Linear Equations: Understanding of linear equations and how to solve for a specific variable.
- Inequalities: Understanding of how to graph and solve linear inequalities.
- Systems of Equations: Understanding of how to solve systems of linear equations using substitution or elimination.

Here are some examples of pre-algebra concepts that might appear on the ACT Math Test:

- Arithmetic operations:

- Simplify the expression: 2/3 + 1/4
- Multiply: (3 + 2) * 5

- Exponents and Roots:

- Simplify: (3^2)^3
- Simplify: √16 * √9

- Algebraic expressions:

- Simplify: 2x + 3y - 4x
- Evaluate the expression: 3x + 2 when x = 4

- Linear Equations:

- Solve for x: 2x + 3 = 7
- Graph the equation: y = 3x + 2

- Inequalities:

- Solve for x: x + 5 > 12
- Graph the inequality: y < 2x - 1

- Systems of Equations:

- Solve the system by substitution: y = 3x + 2 and y = -x + 7
- Solve the system by elimination: 2x + 3y = 7 and 4x + 6y = 14

## Elementary Algebra

Elementary Algebra focuses on the basic algebraic concepts and techniques for solving more complex problems. Some of the concepts covered in this section include:

- Linear Equations: Understanding of linear equations, including how to solve for a specific variable.
- Quadratic Equations: Understanding quadratic equations, including solving for the roots using the quadratic formula.
- Factoring: Understanding how to factor and simplify expressions using the distributive property.
- Simplifying Expressions: Understanding how to simplify expressions using the rules of exponents and polynomials.

Here are some examples of the types of questions you may encounter in the Elementary Algebra section of the ACT Math Test:

- Linear Equations:

- Solve for x: 3x + 2 = 8
- Graph the equation: y = -3x + 5

- Quadratic Equations:

- Solve for x: x^2 + 3x + 2 = 0
- Factor the expression: x^2 + 7x + 10

- Factoring:

- Factor the expression: 4x^2 + 20x + 25
- Simplify the expression: (x + 5)(x + 3)

- Simplifying Expressions:

- Simplify the expression: (3x + 2)^2
- Simplify the expression: 2x^3 + 4x^2 + 2x

## Intermediate Algebra.

Intermediate Algebra is a more advanced level of algebra that builds on the concepts learned in Elementary Algebra. Some of the concepts covered in this section include:

- Functions: Understanding of functions, including how to graph a function and how to use inverse functions.
- Exponential and Logarithmic Functions: Understanding exponential and logarithmic functions, including graphing and solving related equations.
- Polynomials: Understanding polynomials, including how to factor, simplify, and solve polynomial equations.
- Rational Expressions: Understanding rational expressions, including how to simplify, factor, and solve related equations.

Here are some examples of the types of questions you may encounter in the Intermediate Algebra section of the ACT Math Test:

- Functions:

- Graph the function: f(x) = x^2 + 3
- Determine the inverse of the function: f(x) = 3x + 2

- Exponential and Logarithmic Functions:

- Graph the exponential function: y = 2^x
- Solve the logarithmic equation: log_2(x) = 3

- Polynomials:

- Factor the polynomial: 2x^3 + 5x^2 - 3x
- Simplify the polynomial: (x^2 + 3x + 2)(x - 1)

- Rational Expressions:

- Simplify the rational expression: (x + 2)/(x - 3)
- Solve the equation: (2x + 3)/(x - 1) = 4

## Plane Geometry.

Plane Geometry studies two-dimensional shapes, including points, lines, angles, triangles, quadrilaterals, and circles. Some of the concepts covered in this section include:

- Points, Lines, and Angles: Understanding of points, lines, and angles, including how to measure angles and how to classify angles as acute, right, or obtuse.
- Triangles: Understanding of triangles, including how to classify triangles based on their sides and angles, how to find the area of a triangle, and how to solve for missing lengths and angles in a triangle.
- Quadrilaterals: Understanding of quadrilaterals, including how to classify quadrilaterals based on their sides and angles and how to find the area of a square, rectangle, rhombus, and parallelogram.
- Circles: Understanding circles, including how to find the area, circumference, and radius of a circle and how to solve for missing lengths and angles in a circle.

Here are some examples of the types of questions you may encounter in the Plane Geometry section of the ACT Math Test:

- Points, Lines, and Angles:

- Classify the angle as acute, right, or obtuse: ∠ABC = 75°
- Measure the angle formed by two lines: m∠AB + m∠BC = 90°

- Triangles:

- Classify the triangle based on its sides: side lengths = 5, 6, 7
- Find the area of the triangle: base = 5, height = 3

- Quadrilaterals:

- Classify the quadrilateral based on its sides and angles: sides = 4, 5, 6, 7, angles = 90°, 90°, 60°, 90°
- Find the area of the square: side length = 5

- Circles:

- Find the area of the circle: radius = 7
- Solve for the missing length in the circle: circumference = 44, diameter = 14

## Trigonometry.

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles. Some of the concepts covered in this section include:

- Right Triangles: Understanding right triangles, including how to use the Pythagorean Theorem and solving for missing lengths and angles.
- Trigonometric Functions: Understanding the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, including how to evaluate these functions for given angles and how to use them to solve real-world problems.
- Inverse Trigonometric Functions: Understanding the inverse trigonometric functions, including how to find the inverse of a trigonometric function and how to use the inverse functions to solve for angles.
- Law of Sines and Law of Cosines: Understanding of the Law of Sines and the Law of Cosines, including how to use these formulas to solve for missing lengths and angles in a triangle.

Here are some examples of the types of questions you may encounter in the Trigonometry section of the ACT Math Test:

- Right Triangles:

- Use the Pythagorean Theorem to find the missing length: legs = 3, 4
- Solve for the missing angle in a right triangle: hypotenuse = 5, adjacent side = 3

- Trigonometric Functions:

- Evaluate the sine of an angle: sin 30° = 0.5
- Use the tangent function to find the missing length: opposite side = 4, adjacent side = 3

- Inverse Trigonometric Functions:

- Find the inverse of the sine function: sin x = 0.5
- Use the inverse tangent function to find the missing angle: opposite side = 3, adjacent side = 4

- Law of Sines and Law of Cosines:

- Use the Law of Sines to solve for a missing length: sides = 3, 4, 5
- Use the Law of Cosines to find the missing angle: sides = 7, 8, 9

## Coordinate Geometry.

Coordinate Geometry involves the study of points and shapes in a two-dimensional coordinate plane. Some of the concepts covered in this section include:

- Coordinate Plane: Understanding of the coordinate plane, including how to graph points, lines, and equations.
- Distance and Midpoint Formulas: Understanding the distance and midpoint formulas, including how to find the distance between two points and the midpoint of a line segment.
- Slope: Understanding of slope, including how to find the slope of a line and how to use slope to graph a line.
- Equations of Lines: Understanding of the equation of a line, including how to write the equation of a line in slope-intercept form, point-slope form, and standard form.

Here are some examples of the types of questions you may encounter in the Coordinate Geometry section of the ACT Math Test:

- Coordinate Plane:

- Graph the point: (3, 4)
- Graph the line: y = 2x + 1

- Distance and Midpoint Formulas:

- Find the distance between points: (3, 4) and (7, 10)
- Find the midpoint of the line segment: endpoints = (5, 8) and (11, 14)

- Slope:

- Find the slope of the line: (3, 4) and (7, 10)
- Graph the line using slope: slope = 2, y-intercept = 1

- Equations of Lines:

- Write the equation of the line in slope-intercept form: (3, 4), (7, 10)
- Write the equation of the line in the point-slope form: slope = -1, (5, 6)