ACT Math Intermediate Algebra

Questions and Answers

How should you time yourself on the ACT Math test?

First 20 questions = 10 - 15 minutes; Second 20 questions = 15 - 20 minutes; Last 20 questions = 25 - 35 minutes.

What should you do if your solution does not match any of the answer choices?

Immediately redo your calculations.

What is the formula for the sum of the roots in a quadratic equation?

-b/a

What is the formula for the product of the roots in a quadratic equation?

c/a Signup and view all the answers

What does it mean to isolate the radical when solving equations with radicals?

Get the radical on its own on one side and then square both sides. Signup and view all the answers

How do you simplify a rational expression?

Factor the numerator and denominator completely and remove factors equal to 1. Signup and view all the answers

What is the domain of a function?

The set of all x-values for which the function is defined. Signup and view all the answers

What is a linear function?

A function whose graph is a straight line. Signup and view all the answers

What is the slope-intercept form of a linear equation?

y = mx + b Signup and view all the answers

What is the Quadratic Formula?

x = -b ± √(b² - 4ac) / 2a Signup and view all the answers

What is the defining characteristic of a quadratic equation?

An equation of the form f(x) = ax² + bx + c = 0, where a ≠ 0. Signup and view all the answers

Study Notes

Timing Yourself on the ACT Math Test

Questions increase in difficulty throughout the test.
Allocate 10-15 minutes for the first 20 questions.
Use 15-20 minutes for the second 20 questions.
Reserve 25-35 minutes for the last 20 questions.

Redoing Solutions

If a solution doesn't match any answer choices, redo calculations immediately.
Reworking the problem while it's fresh is more efficient than returning later.

Solving Inequalities Using Addition or Subtraction

Isolate the variable by adding or subtracting from both sides of the inequality.

Solving Inequalities Using Multiplication or Division

Apply multiplication or division across the inequality, being mindful of the direction when multiplying/dividing by a negative number.

Multiplying or Dividing an Inequality by a Negative Number

Multiplying or dividing an inequality by a negative number reverses the inequality sign.
Example: From -4x ≥ 7, after multiplying by -1, it becomes 4x ≤ -7.

Equations with Radicals

To solve, isolate the radical and square both sides.
Example: From √x - 5 = 2, first isolate √x, then square to find x.

Sum of the Roots

The sum of the roots of a quadratic equation can be calculated using the formula -b/a.

Product of the Roots

The product of the roots can be calculated with the formula c/a.

Rational Expressions

A rational expression is a fraction where both the numerator and denominator are polynomials.

Simplifying a Rational Expression

Factor both numerator and denominator completely.
Cancel out common factors to simplify.

Functions

A function relates each x-value to one y-value.
Functions can be expressed as ordered pairs, equations, or graphs.

Domain and Range

The domain is the set of all allowable x-values, while the range is the corresponding y-values.
Exclude values that cause division by zero or negative roots.

Identifying the Correct Type of Function

Linear inequalities focus on moving variable terms to one side.
Quadratic inequalities require factoring and examining the graph.

Linear Function

A linear function produces a straight-line graph.

Slope-Intercept Form

The slope-intercept form is y = mx + b, with m as slope and b as y-intercept.
Parallel lines share the same slope; perpendicular lines have negative reciprocal slopes.

Quadratic Formula

The formula x = -b ± √(b² - 4ac) / 2a is used to find roots of quadratic equations.

Quadratic Equations

A quadratic equation is formatted as f(x) = ax² + bx + c = 0, where a ≠ 0.

Transformations

Various transformations affect the graph of f(x), adjusting its position, width, or orientation.

Complex Numbers

Complex numbers consist of a real part and an imaginary part, expressed as a + bi.

Laws of Logarithms

These rules govern the manipulation of logarithmic expressions and include properties like product, quotient, and power rules.

Description

This quiz provides essential strategies for tackling the ACT Math test, focusing on time management and problem-solving techniques. Learn how to effectively allocate your time and what to do if your solution doesn't match the answer choices. Enhance your preparation for the ACT Math section with these flashcards.