Grade 9 - Quarter 1 EXAMINATION_MATH.pptx

Math 9

1. Direction: Choose the letter that corresponds to the correct answer. Write your answer in the space provided before each number.

2. 1. In the quadratic equation (𝑦 + 5)(𝑦 – 5) = 4, what are the values of 𝑎, 𝑏, 𝑎𝑛𝑑 𝑐? A. a = 1, b = 5, c = -5 C. a = 1, b = 0, c = -29 B. a = 1, b = - 5, c = 5 D. a = 1, b = 0, c = 25

3. 2. Find the solutions of the following equation − 3𝑥 − 40 = 0. -5 and -8 C. -5 and 8 5 and -8 D. 5 and 8  

4. 3. Solve for x by extracting square roots, = 256 14 and -14 C. 16 and -16 B. 23 and -23 D. 18 and -18  

5. 4. In the equation − 12 = 0, the roots are? 2 and -2 C. 4 and - 4 B. 3 and -3 D. none of these  

6. 5 . In the equation + 7𝑥 − 120 = 0, the solutions are? 12 and -10 C. 15 and -8 B. - 20 and 6 D. 8 and -15  

7. 6.What is the nature of the roots of a quadratic equation where − 4𝑎𝑐 = 0? A. Real, rational and equal B. Real, irrational and not equal C. Real, rational and not equal D. No real roots  

8. 7. What are the values of the discriminants for the quadratic equations with real, irrational and not equal roots? A. – 4ac = 0 B. – 4ac < 0 C. – 4ac > 0 but not perfect square D. – 4ac > 0 and perfect square  

9. 8. What is the value of 𝑘 in 𝑘 − 3𝑥 − 10 = 0 if its discriminant is 89? A. -2 B. 0 C. 1 D. 2  

10. For # 9 – 11. Problem: Anna wants to make a wooden rectangular frame with an area of 450 and a perimeter of 90 in. What should be the dimension of the frame? 9. What equation represents the area of the frame in terms of its width? A. + 45𝑤 − 450 = 0 C. − 45𝑤 + 450 = 0 B. + 90𝑤 − 450 = 0 D. − 90𝑤 + 450 = 0  

11. For # 9 – 11. Problem: Anna wants to make a wooden rectangular frame with an area of 450 and a perimeter of 90 in. What should be the dimension of the frame? 10. What is the relationship of the sum of roots of the equation in #9 to the given perimeter? A. The sum of roots is half the perimeter. B. The sum of roots is twice the perimeter. C. The sum of roots and the perimeter are equal. D. The sum of roots is the negative of one half the perimeter  

12. For # 9 – 11. Problem: Anna wants to make a wooden rectangular frame with an area of 450 and a perimeter of 90 in. What should be the dimension of the frame? 11. What should be the dimension of the frame? A. 18 in by 25 in C. 5 in by 90 in B. 15 in by 30 in D. 6 in by 75 in  

13. 12. Which of the following rational algebraic equations is transformable to a quadratic equation?

14. 13. Given 𝑎, 𝑏, 𝑎𝑛𝑑 𝑐 are real numbers and 𝑎 ≠ 0, which of the following is the standard form of quadratic equation? + 𝑏𝑥 + 𝑐 = 0 C. 𝑎 = 𝑏𝑥 + 𝑐 B. 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0 D. + + 𝑐 = 0  

15. 14. Express (𝑤 + 7)(𝑤 − 2) = 0 in standard form A. + 5𝑤 + 14 = 0 C. + 5𝑤 − 14 = 0 B. − 5𝑤 − 14 = 0 D. − 5𝑤 + 14 = 0  

16. 15. Express in simplest form.  

17. 16. If a number is added to its square, the sum is 20. Find the number. A.3 B. 4 C. 5 D. 6

18. For question nos. 17– 19, refer to the problem below. Pedro is a well-known carpenter in Maragusan , Davao de Oro. He works in one of the hotels in the same place. One morning, he cut the 25𝑚 electric wire into two parts in such a way that the sum of their reciprocals is 17.Which of the following is the longest part of the electric wire? A. 5 B. 10 C. 15 D. 20  

19. For question nos. 17– 19, refer to the problem below. Pedro is a well-known carpenter in Maragusan , Davao de Oro. He works in one of the hotels in the same place. One morning, he cut the 25𝑚 electric wire into two parts in such a way that the sum of their reciprocals is 18. What are the measures of the two parts of the electric wire? A. 5 & 10 B.10 & 15 C. 15 & 20 D. 20 & 25  

20. For question nos. 17– 19, refer to the problem below. Pedro is a well-known carpenter in Maragusan , Davao de Oro. He works in one of the hotels in the same place. One morning, he cut the 25𝑚 electric wire into two parts in such a way that the sum of their reciprocals is 19. What quadratic equation can be derived from the given problem?  

21. 20. Which of the following coordinates of points belong to the solution set of the inequality y < + 3x − 5? (-2, 9) C. (-1, 5) B. (-3, 2) D. (1, 6)  

22. 21. The figure below shows the graph of y < − 4x − 1. Which of the following is true about the solution set of the inequality? I. The coordinates of all points along the parabola as shown by the broken line belong to the solution set of the inequality. II. The coordinates of all points on the shaded region belong to the solution set of the inequality. III. The coordinates of all points along the parabola as shown by the broken line do not belong to the solution set of the inequality. A. I and II B. I and III C. II and III D. I, II and III  

23. For items 22–23, read the problem carefully and choose the letter of the best answer. The longer leg of a right triangle is 1 inch more than the other leg. What are the possible lengths of the legs so that the hypotenuse is at most 5 inches? ___22. Which of the following mathematical sentences represents the hypotenuse? A. c ≥ 5 B. c ≤ 5 C. c > 5 D. c < 5

24. For items 22–23, read the problem carefully and choose the letter of the best answer. The longer leg of a right triangle is 1 inch more than the other leg. What are the possible lengths of the legs so that the hypotenuse is at most 5 inches? 23. Which of the following is the mathematical sentence of the given problem?

25. 24. Which graph represents a quadratic function?

26. 25. What direction does the parabola open if the quadratic term of the equation is positive? downward C. right side B. left side D. upward

27. 26. Which ordered pair represents the function 𝑓(𝑥) = – 3𝑥 + 2? A.(-5, 0) C.(-4, 0) B.(0, 3) D.( 0 ,2)  

28. 27. What is the vertex of the graph on the right? (2, 1) B. (3, - 2) C. (4, – 3) D. (5, – 2)

29. 28. In the equation − 6𝑥 − 7 = 0, what constant do you add to the trinomial in order to become a perfect square? A. −81 B. −9 C. 9 D. 81  

30. 29. What is 𝑘 of the quadratic function y = + 4x + 2 if h = − ? A. B. C. D.  

31. 30. What is the domain of the given quadratic function 𝑦 = ? all positive real numbers B. all real numbers C. all negative real numbers D. all non-real numbers  

32. 31. If the minimum point of the function 𝑦 = + 10𝑥 + 9 is (−5, −16), what is the equation of its axis of symmetry? 𝑦 = −5 C. 𝑥 = −5 B. 𝑦 = −16 D. 𝑥 = −16  

33. 32. Which of the following shows the graph of 𝑓(𝑥) = 2 – 3?  

34. 33. What is the domain of this quadratic function: f(x) =−2 − 5? A. The set of all Natural Numbers B. The set of all integers C. The set of all Whole Numbers D. The set of all Real Numbers  

35. For numbers 34 – 36, refer to the graph given below 34. What is the vertex of the parabola? (-1, 2) C. (2, -1) B. (1, -2) D. (-2, 1)

36. For numbers 34 – 36, refer to the graph given below 35. What are the x-intercepts of the graph? 0 and 1 C. 3 and 2 B. 3 and 0 D. 1 and 3

37. For numbers 34 – 36, refer to the graph given below 36. What is the range of the given graph? {y: y ≤ −1} C. {y: y ≤ 2} B. {y: y ≥ −1} D. {y: y ≥ 2}

38. 37. What is the quadratic function f(x) whose zeros are 2 and -7? 𝑓(𝑥) = + 5𝑥 − 14 B. 𝑓(𝑥) = − 5𝑥 + 14 C. 𝑓(𝑥) = − 5𝑥 − 14 D. 𝑓(𝑥) = + 5𝑥 + 14  

39. 38. An object is thrown vertically upward with a velocity of 80𝑚/𝑠𝑒𝑐. The distance 𝑆(𝑡) above the ground after 𝑡 seconds is given by the formula 𝑆(𝑡) = 80𝑡 − 5 . How long will it take the object to reach the ground? 4 seconds C. 7 seconds B. 5 seconds D. 8 seconds  

40. 39. What is the graph of a quadratic function? Circle B. Line C. Parabola D. V-Shape

41. 40. Which quadratic function opens upwards and has a vertex of (0,3)? 𝑦 = − B. 𝑦 = C. 𝑦 = + 3 D. 𝑦 = ( + 1) + 3