Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
BASIC MATHEMATICS SOLUTION MANUAL FOR UTAS EXAM WITH QS AND AS|LATEST UPDATE 2025-2026|A+ RATED
Typology: Exams
1 / 59
This page cannot be seen from the preview
Don't miss anything!
Creative Commons License Allows non-commercial use with attribution. Foundation Program Introductory academic program for university students. Real Numbers All numbers on the number line, including fractions. Natural Numbers Counting numbers starting from 1: N = {1, 2, ...}.
Whole Numbers Natural numbers plus zero: W = {0, 1, 2, ...}. Fractions Numbers expressed as a ratio of two integers. Decimals Numbers expressed in base 10, using a decimal point. Ratios Comparison of two quantities, expressed as a fraction. Percent A ratio expressed as a fraction of 100. Exponents Indicates how many times to multiply a number.
Quadratic Equations Polynomial equations of degree two. Coordinate Geometry Study of geometry using a coordinate system. Trigonometry Mathematics dealing with angles and their relationships. U.S. System Measurement system using inches, feet, pounds. Metric System Measurement system using meters, liters, grams. Temperature Measurement Quantifying heat using Celsius or Fahrenheit scales.
Applications of Linear Equations Real-world problems solved using linear equations. Applications of Quadratic Equations Real-world problems solved using quadratic equations. Testing Equations for Symmetry Determining if a graph is symmetric about an axis. Trigonometric Ratios Ratios of sides in a right triangle: sin, cos, tan. Trigonometric Identities Equations involving trigonometric functions that are true.
Closure Property Sum or product of real numbers is real. Commutative Property Order of addition or multiplication doesn't matter. Associative Property Grouping of numbers doesn't affect sum or product. Identity Numbers 0 for addition, 1 for multiplication. Additive Inverse Number that sums to zero with original number.
Multiplicative Inverse Number that multiplies to one with original number. Distributive Property a × (b + c) = a × b + a × c. Properties of Zero Any number times zero equals zero. Finite Decimal Decimal with a limited number of digits. Repeating Decimal Decimal with a finite sequence repeating indefinitely. Indefinite Decimal
Example of Integer -50 is an integer. Example of Negative Integer -80 is a negative integer. Example of Positive Integer 75 is a positive integer. Example of Finite Decimal 10.456 is a finite decimal. Example of Repeating Decimal 0.22¯3 is a repeating decimal. Example of Indefinite Decimal
1.39174 · · · is an indefinite decimal. Identity Property of Addition Adding zero to a number yields the same number. Identity Property of Multiplication Multiplying a number by one yields the same number. Property of Zero Any number multiplied by zero equals zero. Fraction A number expressed as a/b, b =J 0. Proper Fraction Numerator is less than denominator.
Comparison of two quantities with the same unit. Additive Inverse of 8 The number that sums to zero with 8 is -8. Multiplicative Inverse of 8 The number that multiplies to one with 8 is 1/8. Additive Inverse of 0. The number that sums to zero with 0.5 is -0.5. Multiplicative Inverse of 0. The number that multiplies to one with 0.5 is 2. Simplifying Fractions Reducing fractions to their simplest form.
Dividing by Zero Division by zero is undefined. Simplifying Expressions Combining like terms and applying properties. Finding Inverses Determining additive and multiplicative inverses. Multiplying Fractions Multiply numerators and denominators. Dividing Fractions Multiply by the reciprocal of the divisor. Division
Exponent Indicates how many times to multiply the base. Product Rule am × an = am+n for exponents. Quotient Rule am ÷ an = am−n for exponents. Power Rule (am)n = amn for exponents. Zero Exponent a^0 = 1 for any non-zero a. Negative Exponent
a−n = 1/an, reciprocal of positive exponent. Power of Product (ab)n = an × bn for exponents. Power of Quotient (a/b)n = an/bn for exponents. Simplification Reducing an expression to its simplest form. Positive Exponent Indicates a number multiplied by itself. Fraction to Percent Convert a fraction into a percentage.
Multiply by the reciprocal of the divisor. Simplified Form The lowest terms of a fraction. Product rule of Exponents am × an = am+n Quotient rule of Exponents am ÷ an = am−n Power rule of Exponents (am)n = amn Rule of Negative Exponent a−n = 1/an
Property of Zero Exponent a^0 = 1 for any a Exponent rule of power of product (ab)n = a^n b^n Exponent rule of power of quotient (a/b)^n = a^n/b^n Integer Exponents Exponents that are whole numbers Rational Exponents Numerator indicates power, denominator indicates root Simplifying Exponents
