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# LONG TEST IN MATHEMATICS 9 **Directions:** Read and analyze the given statements below. Choose the correct answer and write the letter on the answer sheet. **1. Which of the following represent an inverse variation?** a. $y = kx$ b. $y = \frac{k}{x}$ c. $y = kxz$ d. $y = \frac{kx}{z}$ **2. Whic...

# LONG TEST IN MATHEMATICS 9 **Directions:** Read and analyze the given statements below. Choose the correct answer and write the letter on the answer sheet. **1. Which of the following represent an inverse variation?** a. $y = kx$ b. $y = \frac{k}{x}$ c. $y = kxz$ d. $y = \frac{kx}{z}$ **2. Which of the following describes that y is directly proportional to x?** a. Direct Variation b. Inverse Variation c. Joint Variation d. Combined Variation **3. What variation describes the situation of the amount of Rain and the Level of water (L) on Lamesa Dam?** a. Direct Variation b. Inverse Variation c. Joint Variation d. Combined Variation **4. Which of the following equation you will use to find the constant of a direct variation?** a. $k = xy$ b. $k = \frac{x}{y}$ c. $k = \frac{x}{y}$ d. $y = kx$ **5. What is the mathematical translation of "The volume (V) of a cylinder varies jointly as the square of radius (r) and height (h)"?** a. $V = krh$ b. $V = kr^2h$ c. $V = krh^2$ d. $V = k(rh)^2$ **6. If y varies directly as x, and y = 15 when x = 5, find y when x = 7.** a. 4 b. 15 c. 21 d. 30 **7. If y varies inversely as x, what is x, when y = 5 and k = 60?** a. 12 b. 300 c. $\frac{1}{12}$ d. $\frac{1}{300}$ **8. On a given planet, the weight (W) of an object varies directly with the mass (M) of the object, if the mass of a certain object is 4 kg when it's weight is 24 N. What is the mass of another object that weights 18 N?** a. 3 kg b. 6 kg c. 9 kg d. 12 kg **9. The number of hours constructing a deep well is inversely proportional as the number of men doing it. It takes 10 hours for 2 men to construction. How many men were needed to finish it in 4 hours?** a. 2 b. 4 c. 5 d. 10 **10. The area A of a triangle varies jointly as the base b and the height h, and A = 12 $m^{2}$ when b = 6 and h = 4m. The base of the triangle increased by 2m and the height increase by 4m, what is its new area?** a. 6 $m^{2}$ b. 12 $m^{2}$ c. 32 $m^{2}$ d. 56 $m^{2}$ **11. Which of the following laws of exponents described by the rule "add the exponents of the same base"?** a. Power of a power b. Quotient of a power c. Product of a power d. Power of a product **12. What is the simplest form of $x^{10}x^{5}$ ?** a. $x^{15}$ b. $x^{3}$ c. $x^{2}$ d. $x^{8}$ **13. What is the simplest form of $\frac{8a^{4}bc^{2}d^{5}}{4a^{2}c^{4}d^{3}e^{-3}}$?** a. $2a^{2}bc^{3}d^{2}$ b. $2a^{2}bcd^{2}e^{3}/c^{2}$ c. $\frac{2a^{2}bcd^{2}e^{3}}{c^{2}}$ d. $2a^{2}d^{2}e^{2}/c^{2}$ **14. What is the evaluated value of $(x^{5})(x^{1})^{3}$?** a. $x^{5}$ b. $x^{3}$ c. $x^{3}$ d. $x^{3}$ **15-16. and other questions:** (These are incomplete, and require the full image to answer correctly). **17. Which of the following is the equivalent radical expression of $2^{3/2}$?** a. $\sqrt{2^{2}}$ b. $\sqrt{8}$ c. $\sqrt{2^{2}}$ d. $\sqrt{8}$ **18. Which of the following is the equivalent radical expression of $(2x)^{5/3}$ ?** a. $3\sqrt{32x^{5}}$ b. $\sqrt{10x^{3}}$ c. $\sqrt{10}x^{3}$ d. $\sqrt{8}x^{3}$ **19. How will you transform $\sqrt{27a^{3}}$ to rational exponent?** a. $27a^{3}$ b. $27a^{\frac{1}{3}}$ c. $3a^{1}$ d. $(3a)^{7}$ **20. Which of the following is equivalent to $\sqrt{8a^3}$ ?** a. $2a^3$ b. $8a$ c. $2a^1$ d. $(3a)^{7}$