MAT-1033 Flashcards

Questions and Answers

What are natural numbers?

All whole numbers

-1, 0, 1, 2...

1, 2, 3... (correct)

0, 1, 2, 3...

What are whole numbers?

All integers

-1, 0, 1, 2...

1, 2, 3...

0, 1, 2, 3... (correct)

What are integers?

Only positive numbers

Fractions

All whole numbers including their opposites (correct)

Only negative numbers

What is absolute value?

The distance a number is from zero on a number line. Signup and view all the answers

Is absolute value always positive?

True Signup and view all the answers

|X| represents a _______ line.

vertical Signup and view all the answers

The symbol '=' represents a _______ line.

horizontal Signup and view all the answers

What is the process when graphing an inequality?

Finding the boundary line using the y-intercept and the rise over run, then shading based on a test point. Signup and view all the answers

What is the elimination method in solving equations?

Eliminating one of the variables by adding or subtracting equations. Signup and view all the answers

What is the sum of cubes formula?

a^3 + b^3 = (a + b)(a^2 - ab + b^2) Signup and view all the answers

What is the difference of cubes formula?

a^3 - b^3 = (a - b)(a^2 + ab + b^2) Signup and view all the answers

What is the domain of a rational function?

All real numbers except those for which the denominator equals zero. Signup and view all the answers

What is the process of dividing rational expressions?

Factor expressions, identify restricted values, change to multiplication, and reduce common factors. Signup and view all the answers

What should you do before adding or subtracting rational expressions?

Factor first and find the least common denominator (LCD). Signup and view all the answers

What is the method for simplifying a complex fraction?

Multiply every term in the numerator and denominator by the least common multiple of all denominators. Signup and view all the answers

What is long division of polynomials?

A method where you align polynomials and divide step by step, ensuring all terms are accounted for. Signup and view all the answers

What does synthetic division of polynomials involve?

Using the divisor constant in a box and applying multiplication while dropping down exponents. Signup and view all the answers

What is the time word equation format?

Part Glen + Part Paula = Both Signup and view all the answers

How do you express a fraction in radical notation?

Write the fraction exponent inside the radical and simplify. Signup and view all the answers

What does it mean to rationalize the denominator?

Rewriting a fraction by multiplying by a fraction equivalent to 1 to eliminate radicals from the denominator. Signup and view all the answers

How can you eliminate a radical in an equation?

Multiply by the index to both sides of the equation. Signup and view all the answers

What is the square root property?

If b is a real number and if a^2 = b, then a = ±√b. Signup and view all the answers

What does a negative radical number represent?

-(i) * √(number) Signup and view all the answers

What is the quadratic formula?

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

What do negative exponents indicate?

That the base should be moved to the denominator. Signup and view all the answers

Study Notes

Number Types

Natural Numbers: Counting numbers starting from 1 (e.g., 1, 2, 3, ...).
Whole Numbers: Non-negative integers including zero (e.g., 0, 1, 2, 3, ...).
Integers: Whole numbers including their negatives (e.g., -3, -2, -1, 0, 1, 2, 3, ...).

Absolute Value

Represents the distance from zero on a number line; always non-negative.
Can be negative if preceded by a negative sign outside (e.g., |-1| is -1).

Inequalities

When graphing inequalities, find the boundary line using the y-intercept and slope (rise/run).
Perform a test using a point (usually (0,0)); if true, shade that side; if not, shade the opposite.

Elimination Method

Used to solve systems of equations by removing one variable through addition or subtraction.
Multiply equations if necessary to facilitate elimination.

Algebraic Identities

Sum of Cubes: ( a^3 + b^3 = (a + b)(a^2 - ab + b^2) ).
Difference of Cubes: ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) ).

Rational Functions

Domain: All real numbers except where the denominator is zero (e.g., ( { x | x \text{ is real, } x \not= 14, x \not= 2 } )).
Dividing Expressions: Factor expressions, identify restricted values, convert to multiplication using the reciprocal.

Operations on Rational Expressions

Adding/Subtracting: Factor first, find the Least Common Denominator (LCD), and adjust equations accordingly.
Simplifying Complex Fractions: Multiply numerator and denominator by the least common multiple of all denominators.

Polynomial Division

Long Division: Present problem as long division, ensuring all exponents are accounted for and solve akin to numerical division.
Synthetic Division: Use the constant from the divisor; bring down the exponent and multiply until complete.

Time Word Problems

Combine parts of two individuals to find the total, with time calculated based on the context of the question.

Radical Expressions

Radical Notation: Understand the relationship between fractional exponents and radical notation (inside over outside).
Rationalizing Denominators: Multiply fraction by another fraction equivalent to 1 to eliminate radicals in the denominator.

Solving Radicals

Eliminate radicals by multiplying by the index, ensuring radicals are isolated before proceeding. Always remember to check solutions.

Square Root Property

If ( a^2 = b ), then ( a = \pm \sqrt{b} ).

Quadratic Formula

The solution of ( ax^2 + bx + c = 0 ) can be found using ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).

Negative Exponents

Move bases with negative exponents to the opposite part of the fraction, rewriting accordingly.

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Description

Test your knowledge of basic number types with these MAT-1033 flashcards. Covering natural numbers, whole numbers, integers, and absolute value definitions, this quiz is perfect for reinforcing foundational mathematical concepts. Perfect for students looking to solidify their understanding in mathematics.