Republic of the Philippines Department of Education Region V-Bicol Schools Division Office of Legazpi City TAYSAN RESETTLEMENT INTEGRATED SCHOOL Taysan, Legazpi City SCORE: MATH 8 QUARTER 3 – ACTIVITY 1 SY: 2021-2022 NAME: Grade & Section: Part I – QUIZ ON MATHEMATICAL SYSTEM: Perform the following set of tests and write your answers on the answer sheet provided. Please refer to the Math 8 Q3 Module 1. TASK 1 – Multiple Choice. (1 point each) 1. What do you call the logical structure composed of undefined terms, defined terms, definitions, postulates, and theorems? A. Mathematical Reasoning C. Mathematical System B. Mathematical Investigation D. Mathematical Statement 2. These terms serve as bases to define other terms hence, these are the building blocks of other mathematical terms. A. Axioms B. Defined Terms C. Theorems D. Undefined Terms 3. Which of these statements does not need proof to be accepted as true? A. An integer is a prime number. B. A triangle is a polygon with 3 sides. C. If you add two integers, the sum will have a bigger value. D. The opposite sides of a quadrilateral are parallel. 4. Which of the following illustrates symmetric property/axiom? A. π = π B. πΌπ π = π, π‘βππ π = π. C. π β (π + π) = (π β π) + (π β π) D. πΌπ π < π, πππ π < π, π‘βππ π < π. 5. Which of the following is not a part of a Mathematical System? A. Expressions B. Axioms or Postulate C. Theorems D. Defined and Undefined Terms TASK 2 – About Mathematical System. (2 points each) Discuss or describe each part of the mathematical system. Show examples of each (with illustrations if possible). a) b) c) d) Undefined Terms Defined Terms Axioms/Postulates Theorems ________________________ Parent’s/Guardian’s Signature TASK 3 – “What’s your Proof?” (2 points each) Prove each statement by supplying reasons in the two-column form below (S-R Table). π π Given: (π + ππ) = − π π π Prove: π = −π Statement 1. 2. 3. 4. 5. π π (π + ππ) = − π π π π π π (π) + (ππ) = − π π π π 1 15 2 π₯ + = − π₯ 3 3 3 π π π+π=− π π π π π π π π + π + π = −ππ + ππ π π π π+π =π π π+π=π 6. π + π − π = π − π 7. π = −π Reason 1. Given 2. _______________________________ 3. By Simplification 4. _______________________________ 5. By Simplification 6. _______________________________ 7. _______________________________ TASK 4 – “What Axiom am I?” (2 points each) Determine the Axiom for Real Numbers applied in the given situation. 1. Kendra has a debt to her Tita Tessy for loading her cellular phone number with a total of P150.00. How much is her change if she pays her aunt P200.00? Her change can be illustrated by this mathematical model: Let π be the change she would get for paying her debt 150 + π = 200 β 150 − 150 + π = 200 − 150 β π = 50 2. An employer needs to pay P500.00 to each of his 10 employees in one working day. If each of the employees has additional P150.00 to be received, how much money shall the employer has to dispense or distribute in total? Apply this mathematical statement: 10(500 + 150) = 10(500) + 10(150) = 5000 + 1500 = 6500 This answer can also be obtained by adding 500 and 150, then multiplying the sum by 10, 500 + 150 = 650 then 10 × 650 = 6500.
