Mathematics in the Modern World Past Paper PDF

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This document contains a Mathematics in the Modern World past paper focusing on exponents, polynomials, and operations on polynomials. The paper includes a variety of questions, from defining polynomials to solving equations using operations on polynomials. The quiz appears to be for an undergraduate-level course.

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Mathematics in the Modern World Topic 05: Exponents, Polynomials, and Operations on Polynomials Name: Score: Section: Date: A. Define the meaning of Polynomials (5 points) What is P...

Mathematics in the Modern World Topic 05: Exponents, Polynomials, and Operations on Polynomials Name: Score: Section: Date: A. Define the meaning of Polynomials (5 points) What is Polynomials? Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations. B. Matching Type: Find the exact meaning of the following. C 1. The power property can easily be extended to include more than one factor within the parentheses. B 2. In words the property says, to raise an A. Product property of exponents exponential expression to a power, keep the same base and multiply the exponents. B. Power property of exponents A 3. In words, the property says, to multiply exponential terms with the same base, keep the C. Product to a power property common base and add the exponents. G 4. If the exponent of the denominator is greater D. Quotient to a power property than the exponent in the numerator, the quotient property yields a negative exponent. E. Quotient property of exponents F 5. Any base raised to the exponent of zero is equal to 1. F. Zero exponent property E 6. In words, the property says, to divide two exponential expressions with the same base, keep G. Property of negative exponents the common base and subtract the exponent of the denominator from the exponent of the numerator. D 7. We can also raise a quotient of exponential terms to a power. C. True or False: Write FALSE if the statement is true, write TRUE if the statement is false. TRUE 1. Polynomial is made up of two terms, namely Poly (meaning “more”) and Nominal (meaning “terms.”) TRUE 2. Adding polynomials simply involves the use of the commutative and associative properties only. TRUE 3. A binomial is a term using only whole number exponents on variables, with no variables in the denominator. TRUE 4. The FOIL method stands for 'First, Outer, Inner, Last,' and is used to divide two binomials. TRUE 5. The square of a binomial (𝑎±𝑏)2 will be 𝑎2+2𝑎𝑏−𝑏2 if expanded. D. Solve the following using Operations on Polynomials. (3 points each) 1. Find the sum: (14𝑦2+6𝑦−4)+(3𝑦2+8𝑦+5) 14𝑦 2 + 6𝑦 − 4 + 3𝑦 2 + 8𝑦 + 5 (combine like terms) 𝟏𝟕𝒚² + 𝟏𝟒𝒚 + 𝟏 2. Find the difference: (8𝑥2+3𝑥−19)−(7𝑥2−14) 8𝑥 2 + 3𝑥 − 19 − 7𝑥 2 + 14 (combine like terms) 𝒙² + 𝟑𝒙 − 𝟓 3. Multiply a Polynomial by a Monomial: 4𝑥2(2𝑥2−3𝑥+5) 𝟖𝒙𝟒 − 𝟏𝟐𝒙𝟑 + 𝟐𝟎𝒙² (distributive property) 4. Multiply a Polynomial by a Binomial: (𝑥+8)(𝑥+9) (𝑥)(𝑥 + 9) + 8(𝑥 + 9) 𝑥 2 + 9𝑥 + 8𝑥 + 72 (combine like terms) 𝒙² + 𝟏𝟕𝒙 + 𝟕𝟐 5. Solve using FOIL method: (4𝑥+3)(2𝑥−5) F: (4𝑥)(2𝑥) = 8𝑥 2 O: (4𝑥)(−5) = −20𝑥 I: (3)(2𝑥) = 6𝑥 L: (3)(−5) = −15 8𝑥 2 − 20𝑥 + 6𝑥 − 15 (combine like terms) 𝟖𝒙² − 𝟏𝟒𝒙 − 𝟏𝟓 E. Factor the following Polynomials. (2 points each) 1. Factoring Binomial: 4𝑥2+28𝑥 𝟒𝒙(𝒙 + 𝟕) 2. Factoring Binomial: 8𝑥4−40𝑥2 𝟖𝒙²(𝒙² − 𝟓) 3. Factoring by group: 𝑥3+2𝑥2−5𝑥−10 (𝒙 + 𝟐)(𝒙² − 𝟓) 4. Factoring Trinomials: 𝑥2−9𝑥+20 (𝒙 − 𝟒)(𝒙 − 𝟓) DON HONORIO VENTURA STATE UNIVERSITY Bacolor, Pampanga COLLEGE OF ENGINEERING AND ARCHITECTURE MMW 113 NAME: ____________________________ SCORE: _____________ COURSE/YEAR/ SEC: _________________ DATE: ______________ Encircle the correct answer. 1. A rational expression is in simplest form or lowest terms when the numerator and denominator have no common factors (other than 1). A. Multiplication of Rational Expressions B. Division of Rational Expressions C. Writing a Rational Expression in Simplest Form D. Addition and Subtraction of Rational Expressions 2. A rational number is one that can be written as the quotient of two integers. Similarly, a rational expression is one that can be written as the quotient of two polynomials. A. Writing a Rational Expression in Simplest Form B. Division of Rational Expressions C. Rational Expression D. Addition and Subtraction of Rational Expressions 3.. The quotient of two rational expressions is computed in the same way. A. Multiplication of Rational Expressions B. Addition of Rational Expressions C. Division of Rational Expressions D. Subtraction of Rational Expressions 4. In many fields of study, formulas and literal equations involve rational expressions and we often need to rewrite them for various reasons. A. Simplifying Compound Rational Expressions B.. Simplifying Compound Fraction C. Simplifying Formulas and Literal Equations D. Addition and Subtraction of Rational Expressions 5. Recall that the addition and subtraction of fractions requires finding the lowest common denominator (LCD) and building equivalent fractions. A. Multiplication of Rational Expressions B. Addition of Rational Expressions C. Addition and Subtraction of Rational Expressions D. Subtraction of Rational Expressions 6. Operations on rational expressions use the factoring skills reviewed earlier, along with much of what we know about rational numbers. A. Subtraction of Rational Expressions B. Multiplication of Rational Expressions C. Multiplication and Division of Rational Expressions D. Addition of Rational Expressions 7. The expression as a whole is called the major fraction, and any fraction occurring in a numerator or denominator is referred to as a minor fraction. A. Simplifying Compound Rational Expressions B.. Simplifying Formulas and Literal Equations C. Simplifying Compound Fraction D. Subtraction of Rational Expressions 8-10. What are the 3 Steps of Multiplication and Division of Rational Expressions? 1. 2. 3. Test II: WRITE YOUR ANSWER BEFORE THE NUMBER 1.Square roots and cube roots come from a much larger family called radical expressions. Expressions containing radicals can be found in virtually every field of mathematical study, and are an invaluable tool for modeling many real world phenomena. 2 2. In section r.1 the square root of a is b only if 𝑏 = 𝑎. All numbers greater than zero have two square roots, one positive and one negative. The positive root is also called the principal square root. 3. As an alternative to radical notation, a rational (fractional) exponent is often used, along with the power property of exponents. 4.The properties used to simplify radical expressions are closely connected to the properties of exponents. 5.The multiplication of radical expressions is simply an extension of our earlier work with the product property of radicals. 6. A right triangle is one that has a angle. The longest side (opposite the right angle) is called the hypotenuse while the other two sides are simply called “legs.” 7. Can also be established using exponential properties, in much the same way as the product property 8. Refers to combining expressions that contain square roots (or other roots). To do this, you must ensure the radicands (the numbers under the radicals) are the same, similar to combining like terms. CHOICES: A. Radical and Rational Expressions B. Simplifying Expressions of the Form C. Radical Expression and Rational Exponents D. Properties of Radicals and Simplifying Radical Expression E. Multiplication and Division of Radical Expression F. Formulas and Literal Equations G. Quotient Property of Radicals H. Adding and Subtracting Radical Expression TEST III: SOLVE THE FOLLOWING. (3PTS EACH) 𝑥+3 𝑥−1 2𝑥−6 4𝑥+8 1. 𝑥−2 − 𝑥+4 3. 𝑥+5 × 𝑥−7 𝑥−2 𝑥+3 5𝑥−15 2𝑥+6 2. 𝑥+5 + 𝑥−4 4. 𝑥+4 ÷ 𝑥−1 Bonus Question (+5 points): What is the exact duration of our presentation? __________. ANSWER KEY Test I 1.C 2.C 3.C 4.C 5.C 6.C 7.C 8. Factor all numerators and denominators completely. 9. Reduce common factors. 10. Multiply numerator x numerator and denominator x denominator. Test 2: 1.A 2.B 3.C 4.D 5.E 6.F 7.G 8.H Test 3: 1.) 2.) 4.) 3.) Bonus Question: 31mins and 13secs Group 7 Quiz in MMW Name: Section: Date: I. Identification C 1. A mathematical a. Linear inequalities statement that expresses the equality b. Solving rational equation between two linear expressions. c. Linear equations A 2. Is an expression that shows the d. Complex number relationship between two expressions using e. Slope-intercept form inequality signs (>, 7 2x+3>7 -3 -3 2x>4 / 2 —> x>2 2. ⅓ x + 4 ≤ 6 ⅓x+4≤6 -4 -4 ( ⅓ x ≤ 2)3 —> x ≤ 6 3. 5 - 3x ≥ -4 5 - 3x ≥ -4 -5 -5 - 3x ≥ -9 / -3 —> x ≥ 3 IV. Solving (Zero Property and Rational Equation) Zero Property Rational Equation 1. (x - 3) (x + 2) = 0 1. ⅝ - ⅗ = x/10 x-3=0, x+2=0 (⅝ - ⅗ = x/10) 40 25-24 = 4x 1 = 4x / 4 2. (3x) (x - 7) = 0 ¼=x 3x=0, x-7=0 or x=0, x-7=0 2. x + 8/x = 6 3. (2x - 3) (3x - 5) = 0 -4 (x + 8/x = 6) x factor 8< x=3/2, x=5/3 x² + = 6x -2 x² - 6x + 8 (x-4) (x-2)=0 x=4, x=2

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