Second Quarter Long Quiz MATHEMATICS'? S.Y. 2023-2024 Name: qquad Grade & Section: qquad Score: qquad Direction: Read and analyze each item carefully. Write the correct answer on the space provided for What happens to T when h is doubled in the equation T=4h ? qquad What type of variation is the statement " z varies directly as x and inversely as y" ? qquad 3. What is the mathematical statement of " z varies directly as x and inversely as y "? The number of hours h required to complete a certain job varies inversely as the number of machines m used to do the work. What equation describe the situation? qquad 5. The price of pencil is shown by the table below. # of Pencil (n) 2 4 6 Price in pesos (p) Price in pesos (p) 20 40 60 # of Pencil (n)246 "Price in pesos (p)"204060 What is the variation equation? 6. If A varies jointly as b and the square of c , Then what equation describes the relation among the three variables A,b , and c ? 7. What mathematical statement describes the graph below? qquad 8. If y varies directly as x and y=12 when x=4 , what is the value of y when x=12 ? qquad 9. If 3 men can do a portion of a job in 8 days, how many men can do the same job in 6 days? qquad 10. Rey's income varies directly as the number of days that he works. If he earns Php 8,000.00 in 20 days, how much will he earn if he worked 3 times as long? qquad 11. What is the simplified form of 4^(0)5^(-2)6^(-1)(1)/(2^(-1)) ? 12. What is 9^(1//2) equal to? qquad 13. What is the result after simplifying (-4)^((1)/(2)) ? qquad 14. What is the simplified form of (p^(21)q^(-15)r^(-3))^((1)/(3)) ? qquad 15. What is the radical form of 9x^(2//3) ? qquad 16. What is the equivalent of root(3)(4)+root(5)(2) using exponential notation? qquad 17. What is the radical form of (4v)^((2)/(5)) ? qquad 18. What is root(n)(a)*root(n)(b) equal to? qquad 19. Using the law of radicals root(n)(xy)=root(n)(x)root(n)(y) , what is the simplified form of root(4)(16x^(4)) ? qquad 20. What is the result after simplifying root(3)((3)/(4k)) ? 21. What is the sum of 2sqrt3,-5sqrt2,4sqrt3 , and 8sqrt2 ? 22. What is the result when we simplify (2+sqrt5)(5-sqrt7)? qquad 23. What is the simplified form of (sqrt3)/(root(4)(3)) ? qquad 24. What is the result when we simplify 2sqrt3+4sqrt3-5sqrt3 ? qquad 25. What is the result after simplifying (6-sqrt2)/(4-3sqrt2) ? qquad 26. What is the value of k which will make the equation root(3)(k+4)=root(3)(2k+3) true? qquad 27. The roots of the equation x-6= bar(sqrtx" are "4) and 9 . Which of these roots is/are extraneous root/s? qquad 28. The square root of four more than five times a number is 8 . What is the number? qquad 29. What is the area of a rectangular field having a length of 15sqrt6m and width of 10sqrt15m ? qquad 30. The length of the legs of a right triangle are 5cm and 12cm . What is the length of the hypotenuse? qquad
Answer
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Romeo RiveraProfessional · Tutor for 6 years
Answer
<p></p><br /><br /><p>1. Doubled<br />2. Combined/Joint/Both Variation<br />3. z = kx/y<br />4. hm = k (or 1/h = km where k is a constant)<br />5. p = 10n<br />6. A = kb*c^2<br />7. Cannot answer as graph not provided<br />8. y = 3kx (with k constant value of proportion.)<br />9. Employing work-force of 4 men get it done in 6 days.<br />10. Php 24,000<br />11. 4^3 = 64<br />12. The simplified form 9^(1/2)=3<br />13. The simplified form of (-4)^(1/2) is 2i<br />14. (p^7q^-5r^-1)<br />15. 9x<br />16. Cannot answer as equation not completable<br />17. 4^(4/5)v^(2/5)<br />18. n√(ab)<br />19. 4*4 = 16<br />20. Does not simplify<br />21. Addition not possible because square root terms need to be identical to add<br />22. Difference does not simplify due to difference in square roots<br />23. 1/4<br />24. 1√3<br />25. Does not simplify.<br />26. Solving equation offers k's potential value<br />27. Only x = 9 is a root. x = 4 causes x under the square root having a value of 0.04<br />28. The number is 36<br />29. The area = 150𝜋 m^2<br />30. 13 cm</p>
Explanation
<p></p><br /><br /><p>For question 1-3, its subject falls on algebra, which discusses the behavior of functions when variables change- direct variation and inverse variation.<br />Q1: As it's a direct ratio, when h is doubled, T will be doubled.<br />Q2: The variation type "a varies directly as x and inversely as y" is called Joint Variation.<br />Q3: Stringing this directly together, 'z is proportional to x/y' can also be written as z = kx/y, where k is a constant of variation.<br /><br />The subsequent questions 4,5 and 6 fall under ratio and proportion with touches of basic concept of functions.<br /><br />Questions 7 to 11 are involved in square roots, power rule, and exponential to radical conversion.<br /><br />Questions 12 asks what the equivalent addition expression in exponential form is.<br /><br />Remaining questions deal with subjects involving solving a quadratic equation, variation, calculation of area/configuration of geometric shapes, and several algebraic equations uses the rule of radicals.</p>
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