Basic Calculus Post Test Q3 2025 PDF

BASIC CALCULUS THIRD QUARTERLY POST TEST S.Y. 2024 – 2025 NAME: __________________________________________ SCORE: _______ GRADE AND SECTION: ____________________________ DATE: ___...

BASIC CALCULUS THIRD QUARTERLY POST TEST S.Y. 2024 – 2025 NAME: __________________________________________ SCORE: _______ GRADE AND SECTION: ____________________________ DATE: _________ I. MULTIPLE CHOICE. Directions: Read and analyze the questions carefully. Write the letter of your answer in the space before each number. ____1. What is the relationship between 𝑥→𝑐 lim 𝑓(𝑥) and 𝑓(𝑐)? A. lim 𝑓(𝑥) = 𝑓(𝑐) B. lim 𝑓(𝑥) ≠ 𝑓(𝑐) C. lim 𝑓(𝑥) > 𝑓(𝑐) D.lim 𝑓(𝑥) ≥ 𝑓(𝑐) 𝑥→𝑐 𝑥→𝑐 𝑥→𝑐 𝑥→𝑐 ____2. What is the first theorem to be used to solve the expression lim (2𝑥 3 𝑥→0 + 4𝑥 2 − 1)? A. Addition B. Constant Multiple C. Division D. Multiplication ____3. What is the term to be used to divide the terms in the expression lim 9𝑥 2 ? 𝑥→∞ 𝑥 2 −1 A. 𝑥 B. 𝑥2 C. 𝑥3 D. 𝑥 4 ____4. 1 Given below is the table of values of the expression lim. What is the value of A? 𝑥→∞ 𝑥 Approaching from the left Approaching from the right x f(x) x f(x) -1 -1 1 1 -10 -0.1 100 B -1000 A 10000 0.0001 A. -0.1 B. -0.01 C. -0.001 D. -0.0001 ____5. What property of the function is shown when its graph is can be traced from left side to right side of a given value of x without lifting the pen? A. Flexible B. Accurate C. Reliable D. Continuous ____6. Applying the first condition of continuity, what would be the value of 𝑓(𝑐) at 𝑥 = 0 using 3𝑥 2 +𝑥−2 𝑓(𝑥) = ? 𝑥−1 A. 0 B. 1 C. 2 D. DNE 𝟑 , 𝒊𝒇 𝒙 < −𝟖 𝟐𝒙 − 𝟑 , 𝒊𝒇 − 𝟖 ≤ 𝒙 < 𝟎 For item 7. Consider the function 𝒌(𝒙) = 𝒙𝟐 + 𝟏 , 𝒊𝒇 𝟎 ≤ 𝒙 ≤ 𝟏𝟏 𝟐 { , 𝒊𝒇 𝒙 > 𝟏𝟏 𝒙 ____7. In which interval k(x) is continuous? A. (−∞, −2] B. [13, +∞) C. [−9, −4] D. (−6,5 ] ____8. In IVT, the value of m is one of the important values that should be present. In what interval should the value of m fall? A. (a, b) B. [a, b] C. (f(a), f(b)) D. [f(a), f(b)] ____9. Which of the following is NOT a notation for the derivative of 𝑓 if 𝑦 = 𝑓(𝑥)? 𝑑 𝑑𝑦 A. 𝑓 ′ (𝑥) B. 𝐷𝑦 [𝑓(𝑥)] C. [𝑓(𝑥)] D. 𝑑𝑥 𝑑𝑥 ____10. Which of the following statements is a correct? A. A function 𝑓 is said to be continuous everywhere if 𝑓 is continuous at every real number. B. A function 𝑓 is continuous at a number 𝑐 if one of the conditions of continuity is satisfied. C. A function 𝑓 is continuous at a number 𝑐 if two of the conditions of continuity is satisfied. D. A function 𝑓 is said to be discontinuous everywhere if 𝑓 is continuous at every real number. ____11. Which of the following is the constant multiple rule? A. 𝑓 ′ (𝑥) = 0 C. 𝑓 ′ (𝑥) = 𝑔′ (𝑥) + ℎ′ (𝑥) B. 𝑓 ′ (𝑥) = 𝑛𝑥 𝑛−1 D. 𝑓 ′ (𝑥) = 𝑘ℎ′ (𝑥) ____12. Extreme Value Theorem states that if a function 𝑓(𝑥) is continuous over a closed interval [a, b], then 𝑓(𝑥) is guaranteed to reach a maximum and minimum on [a, b]. What would be the first to be fulfilled in applying the theorem? A. The function to be used should be continuous over the interval (a, b). B. The function to be used should be continuous over the interval [a, b]. C. The function to be used should be continuous over the interval (f(a), f(b)). D. The function to be used should be continuous over the interval [f(a), f(b)]. ____13. What kind of rule can be used to solve the derivative of 𝑓(𝑥) = (4𝑥 − 1)4 easily? A. Constant Multiple B. Chain C. Product D. Quotient ____14. What kind of function is to be solved first in determining the derivative of 𝑗(𝑥) = sin 4 (2𝑥 + 1)? A. Exponential B. Logarithmic C. Polynomial D. Trigonometric ____15. Utilizing implicit differentiation, which of the following is the derivative of 𝑦 2 = 4𝑥? 1 2 A. 4x B. 8y C. D. 2𝑦 𝑦 ____16. For polynomial functions, lim 𝑥→𝑐 𝑓(𝑥) = 𝑓(𝑐). What is the limit of the polynomial function if 𝑓 (𝑐 ) = −12? A. –12 B. –1 C. 0 D. 12 ____17. What is the value of the expression lim (2𝑥 3 𝑥→0 + 4𝑥 2 − 1)? A. –12 B. –1 C. 0 D. 12 ____18. What is the value of the expression lim 1? 𝑥 𝑥→∞ A. 0 B. 1 C. 2 D. 3 ____19. After applying the third condition of continuity, what would be the correct statement about the continuity of 𝑓(𝑥) at 𝑥 = 0? A. 𝑓(𝑥) is continuous at 𝑥 = 0 since 𝑓(𝑐) exist. B. 𝑓(𝑥) is continuous at 𝑥 = 0 since 𝑓(𝑐) = lim 𝑓(𝑥). 𝑥→𝑐 C. 𝑓(𝑥) is discontinuous at 𝑥 = 0 since 𝑓(𝑐) ≠ lim 𝑓(𝑥). 𝑥→𝑐 D. 𝑓(𝑥) is discontinuous at 𝑥 = 0 since lim 𝑓(𝑥) does not exist. 𝑥→𝑐 ____20. To determine the slope of the tangent line, the formula to be used is 𝑚 = lim 𝑓(𝑥) −𝑓(𝑥0 ). What 𝑥→𝑥0 𝑥−𝑥0 is the slope of the tangent line of the graph of 𝑓(𝑥) = 𝑥 2 at point (2,4) where 𝑥0 = 2? A. –1 B. –2 C. 3 D. 4 ____21. What is the value of 𝑓 ′ (3) for the function 𝑓(𝑥) = 2𝑥 − 1? A. –1 B. 2 C. 3 D. –4 ____22. Which of the following is the derivative of 𝑔(𝑥) = 2𝑥(𝑥 + 1)? A. 4𝑥 + 2 B. 2𝑥 2 + 2𝑥 C. 𝑥 2 + 2 D. 2𝑥 + 1 ____23. What is the derivative of the function 𝑓(𝑥) = (4𝑥 − 1)4 ? A. 4(4𝑥 − 1)3 B. 8(4𝑥 − 1)3 C. 12(4𝑥 − 1)3 D. 16(4𝑥 − 1)3 ____24. Using the implicit differentiation, what is the derivative of 3𝑥 2 + 4𝑦 2 = 11? 3𝑥 4𝑥 3𝑦 4𝑦 A. − B. − C. − D.− 4𝑦 3𝑦 4𝑥 3𝑥 For items 25 to 26. An open-type rectangular box is to be made from a 24 cm by 9 cm cardboard by cutting out identical squares from the four corners and turning up the sides. ____25. What is the objective function? A. 𝑓(𝑥) = 4𝑠3 + 66𝑠2 + 216𝑠 C. 𝑓(𝑥) = 4𝑠 3 − 66𝑠2 + 216𝑠 B. 𝑓(𝑥) = 4𝑠3 + 66𝑠2 − 216𝑠 D. 𝑓(𝑥) = 4𝑠 3 − 66𝑠2 − 216𝑠 ____26. What is the volume of the open-type box? A. 2 cm3 B. 50 cm3 C. 100 cm3 D. 200 cm3 ____27. What is the resulting form of the function sin(cos(𝑥𝑦)) = 3 if u is integrated? A. sin 𝑢 = 3 B. sin 𝑢 = 0 C. cos 𝑢 = 3 D. cos 𝑢 = 0 ____28. Which of the following is the derivative of 𝑒 4𝑦 = 5𝑥 3 − 9𝑥? 3 4𝑥 2 +3 4𝑥 2 −3 5𝑥 2 +3 5𝑥 2 −3 A. 3 B. 3 C. 3 D. 3 5𝑦 2 𝑒 4𝑦 5𝑦 2 𝑒 4𝑦 4𝑦 2 𝑒 4𝑦 4𝑦 2 𝑒 4𝑦 For items 29 to 30. A water droplet falls onto a still pond and creates concentric circular ripples that propagate away from the center. Assuming that the area of a ripple is increasing at the rate of 2π cm2/s. ____29. Which of the following is the derivative of the area with respect to the time? 𝑑𝐴 𝑑𝑟 𝑑𝐴 𝑑𝑟 𝑑𝐴 𝑑𝑟 𝑑𝐴 𝑑𝑟 A. = 𝜋𝑟 B. = 2𝜋𝑟 C. = 𝜋𝑟 2 D. = 𝜋𝑟 4 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 ____30. What is the rate at which the radius is increasing at the instant when the radius is 10 cm? 1 1 1 1 A. 𝑐𝑚/𝑠 B. 𝑐𝑚/𝑠 C. 𝑐𝑚/𝑠 D. 𝑐𝑚/𝑠 10 20 30 40 Prepared by: ALVIN O. ABAN Subject Teacher