Mathematics 9 2ndQ Reviewer PDF

**MATHEMATICS 9** Janelle saw a problem in her Math test wherein one variable increases and the other decreases. What type of variation is represented in the problem? A. Combined Variation B. Direct Variation C. Joint Variation D. **Inverse Variation** The cost of a product M varies direct...

**MATHEMATICS 9** Janelle saw a problem in her Math test wherein one variable increases and the other decreases. What type of variation is represented in the problem? A. Combined Variation B. Direct Variation C. Joint Variation D. **Inverse Variation** The cost of a product M varies directly as the price of production N. Which of the following statements correctly represents the relationship of M and N? A. M increases as N is halved. B. **M increases as N increases.** C. M increases as N decreases. D. M increases as N is doubled. The profit of a company varies with the number of items sold and the selling price per item. The higher the price and the more items sold, the greater the profit. What type of variation is shown in this example? A. **Combined Variation** B. Direct Variation C. Joint Variation D. Inverse Variation 9-Hydrogen is learning about combined variation. Their teacher presented the formula [\$y = \\frac{\\text{kx}}{z}\$]{.math.inline} on the board and four students translated it into a mathematical statement. Who gave the correct answer? A. Peter: "y is inversely proportional to both x and z." B. Andrew: "y is directly proportional to both x and z" C. Paul: "y is directly proportional to z and inversely proportional to x" D. **Joseph: "y is directly proportional to x and inversely proportional to z"** Angela created a table of values for M and N. Jess is trying to figure out the relationship of the variables. Which of the following statements BEST describes the relationship of M and N? M 5 4 3 2 1 --- ---- ---- ---- ---- --- N 25 20 15 10 5 A. **N varies inversely as M with a constant of variation of 5** B. N varies directly as M with a constant of variation of 5 C. N varies inversely as M with a constant of variation of 1/5 D. N varies directly as M with a constant of variation of 1/5 For items 12 to 14, refer to this situation: A force F varies jointly with the mass of an object (m) and its acceleration (a). 12\. If a force of 150 N is required to move a 10 kg object with acceleration 3 m/s^2^, what is the mass of an object that can be moved with 225 N at acceleration 13\. If the force is doubled, given that the mass of the object did not change, what happens to the acceleration of the object? A. The acceleration is halved. B. **The acceleration is doubled.** C. The acceleration is quadrupled. D. The acceleration remains the same. 14\. In item number 12, if the force remains the same (225 N), but the acceleration is doubled (10 m/s^2^), what should be the mass of the object? How many hours would it take for 30 items to be produced at the same cost? Felix and Bangchan were arguing about an item on their math test. The item was to simplify this expression: \ [\$\$\\left( \\left( \\frac{4x\^{- 3}y\^{- 4}}{7x\^{- 5}y\^{0}} \\right)\^{0} \\right)\^{- 1}\$\$]{.math.display}\ Felix said that it was just 1, while Bangchan said it was impossible to get that answer. Who is incorrect and how will you explain the right answer to him? A. Felix is incorrect, and I will tell him that we just need to get the reciprocal since it is raised to -1 B. Felix is incorrect, and I will tell him that the whole expression is raised to another power that's why it can't be one. C. Bangchan is incorrect, and I will tell him that even if we raise it to another power, the whole expression is already just 1 because it was raised to -1. D. **Bangchan is incorrect, and I will tell him that according to the laws of exponents, if we have the power of a power, we just multiply the exponents, which makes the exponent just 0.** For items, refer to this situation. Yor walked from their home to the grocery store, which was 14 km south of their house, and then picked up Anya at her school, which was 8 km to the west of the grocery store. If we need to find how far Yor's house is to Anya's school, how would we find it? A. Create a quadratic equation and solve using factoring. B. **Use the Pythagorean theorem and the find the longest side.** C. Create an equation with a rational exponent and solve for x. D. Use the area of a triangle and solve for the missing leg of the triangle. How far is the house from Anya's school? 9-Oxygen is learning about zero and negative exponents. Their teacher asked four students to give statements regarding this topic. Which of the students' statements is true? A. **Beth: "Any number raised to zero is one."** B. Lizzy: "Any non-zero number raised to zero is equal to one." C. Jo: "Any non-zero number raised to a negative number becomes negative." D. KC: "Any number raised to a negative exponent turns into its negative reciprocal." For items 14-16, simplify the following expressions with rational exponents using the laws of exponents: 14\. [\$\\left( 64x\^{8} \\right)\^{\\frac{1}{6}}\$]{.math.inline} 15. [\$\\frac{a\^{\\frac{3}{2}}\*a\^{\\frac{5}{4}}}{a\^{\\frac{1}{4}}}\$]{.math.inline} 16\. [\$\\left( \\frac{16x\^{12}}{81y\^{4}} \\right)\^{\\frac{3}{4}}\$]{.math.inline} **A.** [\$\\frac{\\mathbf{8}\\mathbf{x}\^{\\mathbf{9}}}{\\mathbf{27}\\mathbf{y}\^{\\mathbf{3}}}\$]{.math.inline} C. [\$\\frac{8x\^{9}}{9y\^{3}}\$]{.math.inline} B. [\$\\frac{16x\^{9}}{27y\^{3}}\$]{.math.inline} D. [\$\\frac{16x\^{9}}{81y\^{3}}\$]{.math.inline} Keith is trying to simplify the expression [\$\\frac{3m\^{- 4}n\^{2}}{15m\^{- 3}n\^{- 2}}\$]{.math.inline}. Which of the following should be his final answer? A. B. If [\$\\sqrt\[3\]{40x\^{5}y\^{7}}\$]{.math.inline} was simplified, which expression would it become? Mary needs to simplify the expression [\$\\frac{\\sqrt{75x\^{4}}}{\\sqrt{3x}}\$]{.math.inline}. Which of the following is the MOST efficient method in solving this problem? A. **The expression should be placed under one root first and then simplified.** B. The numerator and denominator should be simplified first before dividing. C. Both solutions are efficient because they have the same number of steps and they end up with the same answer. D. Neither solutions are efficient because they contain too many steps and require too advanced skills to execute. Is the expression [\$\\sqrt{\\frac{8}{7}}\$]{.math.inline} simplified already? A. **Yes, because the fraction inside is in its simplest form.** B. Yes, because the numbers don't have perfect square factors anymore. C. No, because the 8 can be simplified. D. No, because the 8 can be simplified and the denominator rationalized. If [\$\\sqrt\[4\]{128a\^{12}b\^{17}}\$]{.math.inline} was simplified, which expression would it become? Jimin and Namjoon simplified [\$\\sqrt\[4\]{81x\^{12}y\^{8}}\$]{.math.inline}, but they did it differently. Jimin's approach: Rewrite [81*x*^12^*y*^8^]{.math.inline} as [(3^4^)(*x*^3^)^4^(*y*^2^)^4^]{.math.inline} and simplify directly. Namjoon's approach: Rewrite the expression with rational exponents then reduce each term individually. Which approach is more efficient and why? A. Neither is efficient because rewriting the expression is unnecessary. B. **Jimin's because grouping terms into fourth powers minimizes steps.** C. Namjoon's because using rational exponents is faster for larger powers. D. Both are equally efficient, as they yield the same result with the same number of steps. What becomes of the expression [\$\\sqrt{3}\\left( \\sqrt{27} - \\sqrt{3} \\right)\$]{.math.inline} when simplified? Nezuko is trying to simplify this expression: [\$\\sqrt{3}(\\sqrt{6} - 2\\sqrt{6})\$]{.math.inline}. What should be her first step? A. B. C. D. In simplifying the expression [\$\\frac{\\sqrt{98x\^{3}y\^{5}}}{\\sqrt{2x}} - 3\\sqrt{x\^{5}y}\$]{.math.inline}, Nicole listed the steps required to solve the problem. Which of the following is the correct order of the steps? A. Subtract the two terms together, and then simply the remaining term. B. **Simplify the first term and the second term, and then apply the operation.** C. Simplify the first term, subtract it with the second term, and then simplify the answer. D. Rationalize the first term, subtract it with the second term, and then rationalize the answer. What happens to the expression [\$- 3\\sqrt{18} + 3\\sqrt{8} - \\sqrt{24}\$]{.math.inline} when it is simplified? B. [\$3\\sqrt{2} - 2\\sqrt{6}\$]{.math.inline} D. [\$3\\sqrt{2} - 2\\sqrt{3}\$]{.math.inline} In order to simplify the expression [\$\\frac{\\sqrt{3} + 2}{\\sqrt{3} - 2}\$]{.math.inline}, Tanjiro multiplied both numerator and denominator by [\$\\sqrt{3} + 2\$]{.math.inline}. He ended up with [\$- 7 - 4\\sqrt{3}\$]{.math.inline}. Is he correct? A. Yes, Tanjiro did it correctly. B. **No, the answer should be positive.** C. No, he should have multiplied with [\$\\sqrt{3}\$]{.math.inline}. D. No, he should have multiplied both with [\$\\sqrt{3} - 2\$]{.math.inline}. Science High School will create a circular garden for Math and the architects need to calculate the area in square meters. The diameter of the garden is said to be [\$\\sqrt{50}\$]{.math.inline} meters. The head architect calculates the area by using [*πr*^2^]{.math.inline}, and given that [\$r = \\frac{5\\sqrt{2}}{2}\$]{.math.inline}, he gets [\$A = \\frac{25\\pi}{2}\$]{.math.inline}. Was the process of the architect correct or not? A. No, he used the wrong formula. B. No, he should have used [\$\\frac{\\sqrt{50}}{2}\$]{.math.inline} as the radius. C. **Yes, the architect's process was correct and concise.** D. Yes, but the architect's process contained too many steps. The Rotary Club is planning to create a square playground, which will be enclosed in a mesh net. If the area of the playground is 64 square meters, what is the logical first step to find the length of the mesh net required to enclose the playground? A. **Get the square root of 64.** B. Divide 64 by four and then get the square root. C. Write the formula for finding the area of a square. D. Write the representation and equation, and solve for the missing side. A teacher and a student were solving for the length of the side of a square room, which had an area of 75 square meters. The teacher got an approximate length of 8.66 meters, while the student rationalized [\$\\sqrt{75}\\ \$]{.math.inline}to get [\$5\\sqrt{3}\$]{.math.inline}. Which of the following correctly evaluates the teacher's and the student's methods? A. The teacher's method is the only correct way of solving this problem. B. The teacher's method is correct, but the student's method is faster and better. C. Both the student's and the teacher's method were wrong because the answer should have been [\$75\\sqrt{2}\$]{.math.inline}. D. **Both the student's and the teacher's method were correct. The student gave a more precise amount, while the teacher did approximation.**