# Final Exam GenMath.pdf

29 de May de 2023
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### Final Exam GenMath.pdf

• 2. San Antonio de Padua College National Highway Brgy. Sta. Clara Sur Pila, Laguna Tel No. (049) 559 – 0501/ 09328564408 FINAL EXAM IN GENERAL MATHEMATICS Name: ________________________________ Date: ____________ Grade and Section: _____________________ Ms. Ellen Mae E. Nasayao Test I. Multiple Choice Read each question carefully and choose the letter of the correct answer. 1. If f(x) = x2 +x+7, then f(-3) equals a. 10 b. 11 c. 12 d. 13 2. Given f(x) = x2 -81 and g(x) = x+9, which of the following will result to 𝑔(𝑥) 𝑓(𝑥) ? a. x-9 b. 1 𝑥−9 c. x+9 d. 1 𝑥+9 3. The product of c(x) and d(x) is x2 -4x-21. What are the two functions? a. c(x) = x-7 ; d(x) = x+3 b. c(x) = x-7 ; d(x) = x-3 c. c(x) = x+7 ; d(x) = x-3 d. c(x) = x+7 ; d(x) = x+3 4. Evaluate (𝑔 ○ 𝑓)(𝑥) ∶ 𝑓(𝑥) = 𝑥2 + 2𝑥 ; 𝑔(𝑥) = 3𝑥 − 8 a. 3x2 -6x+8 b. 3x2 +6x-8 c. 3x2 -6x-8 d. 3x2 +6x+8 5. If g(x) = 5𝑥2+9 3𝑥 find g(3) a. 4 b. 5 c. 6 d. 7 6. Which of the following DOES NOT illustrates a one-to-one function? a. The relation pairing an airport to its airport code. b. The relation pairing a vehicle to its plate number. c. The relation pairing a real number to its square. d. None of the choices 7. The statement “Each SSS number assigned a unique SSS number wherein two different numbers cannot be assigned the SSS number.” What function does it illustrates? a. one-to-one b. one-to-many c. many-to-one d. many-to-many 8. What test will help you to determine if the graph is one-to-one function? a. Vertical Line Test b. Horizontal Line Test c. Slope-Line Test d. None of the choices 9. Which of the following is an exponential function? a. 4𝑥−1 = 16𝑥 b. 𝑦 = 2𝑥+5 c. 15𝑥−1 = 𝑥 d. 729 ≤ 2𝑥−3 10. All are exponential equations EXCEPT; a. 4𝑥−1 = 16𝑥 b. 𝑥 = 2𝑥+5 c. 15𝑥−1 = 𝑥 d. 𝑓(𝑥) = 2𝑥−3 11. Which of the following cannot be represent using exponential function? a. Measuring the population growth b. Measuring interest rates c. Measuring blood pressure d. Measuring depreciation value
• 3. 12. What is the formula for measuring population growth? a. 𝐴 = 𝑃𝑒𝑟𝑡 b. 𝐴 = 𝑃𝑜𝑟𝑡 c. 𝐴 = 𝑃𝑒−𝑟𝑡 d. 𝐴 = 𝑃𝑜−𝑟𝑡 13. Which of the following is a logarithmic inequality? a. 729 ≤ 2𝑥−3 b. 𝑦 = 𝑙𝑜𝑔5𝑥 c. ln 𝑥 ≥ 9 d. 𝑙𝑜𝑔𝑥2 = 4 14. Which of the following is a logarithmic function? a. 729 ≤ 2𝑥−3 b. 𝑦 = 𝑙𝑜𝑔5𝑥 c. ln 𝑥 ≥ 9 d. 𝑙𝑜𝑔𝑥2 = 4 15. Which of the following is true about compound interest? a. The interest that is computed on the principal and then added to it. b. The percentage of the principal that will be charged for a specified period of time. c. The interest of the principal amount earns another interest. d. The interest due when only the principal amount earns interest for the entire life of the transaction. Test II. Identification Identify what is being asked in each set. Choose your answer inside the boxes. A. For numbers 16-18, identify if each given is a RATIONAL EQUATION, RATIONAL FUNCTION or RATIONAL INEQUALITY. ______16. 𝑓(𝑥) = 𝑦2−12𝑦+36 2𝑦 ______17. 2𝑥+3 𝑥−1 = 𝑥 𝑥+5 ______18. 5𝑥−1 𝑥+2 ≠ 2 𝑥 B. For numbers 19-22, find the inverse of the following one-to-one functions. ______19-20. f(x) = 3x-5 ______21-22. g(x) = 𝑥3 + 2 C. For numbers 23-28, solve for x. ______23-24. 8𝑥+4 = 642𝑥−1 ______25-26. 7𝑥+1 = 49 ______27-28. 52𝑥+6 = 125𝑥 D. For numbers 29-33, identify what law of logarithm is being illustrated in each item. ______29.𝑙𝑜𝑔7(53 • 58) = 𝑙𝑜𝑔753 + 𝑙𝑜𝑔758 ______30. 𝑙𝑜𝑔443 = 3𝑙𝑜𝑔44 ______31. 𝑙𝑜𝑔3 ( 9 54 ) = 𝑙𝑜𝑔39 − 𝑙𝑜𝑔354 ______32. 𝑙𝑜𝑔5126 = 6𝑙𝑜𝑔512 ______33.𝑙𝑜𝑔2(63 • 105) = 𝑙𝑜𝑔263 + 𝑙𝑜𝑔2105 E. For numbers 33-36, solve for x. ______34-35. 𝑙𝑜𝑔9(4𝑥 + 1) = 2 ______36-37. 𝑙𝑜𝑔4(5𝑥 − 3) = 𝑙𝑜𝑔4(3𝑥 + 2) A. Rational Equation B. Rational Function C. Rational Inequality A. 2 D. 1 B. 3 E. undefined C. -4 F. 6 A. Product Rule B. Quotient Rule C. Power Rule D. Inverse Rule E. Zero Product Rule A. 𝒇−𝟏(𝒙) = 𝒙+𝟓 𝟑 B. 𝒈−𝟏(𝒙) = √𝒙 − 𝟐 𝟑 C. 𝒈−𝟏(𝒙) = √𝟑𝒙 + 𝟐 𝟑 D. 𝒇−𝟏(𝒙) = 𝒙+𝟑 𝟓 A. 6 D. 5/2 B. 20 E. undefined C. -10 F. -5/2
• 4. F. For numbers 38-40, identify what is being asked in each item ______38. The interest that is computed on the principal and then added to it. ______39. The ideas that the amount of money available at the present time will increase in the future. ______40. “Money makes money, and this is true when it comes to investing.” ----------END OF EXAMINATION---------- “Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.” – Thomas A. Edison A. Simple Interest B. Future Earning Capacity C. Compound Interest D. Time Value of Money E. Time Value of Investment F. Potential Earning Capacity