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MATH GRADE 9

Solve the following problems step by step.

1. The square root of 5 more than twice a number is 7. Find the number.

2. The square root of twice a certain number is subtracted from the number and the result is 4. Find the number.

3. The square root of 5 less than 6 times a certain number is divided by a number and the quotient is 2. Find the number.

4. If 4 is subracted from a number, the result is equal to the square root of 2 or more than the number. Find the number.

5. If the square root of 2 less than 6 times a number is divided by 2 less than the number, the quotient is 2. Find the number.

6. Find a number such that the square root of 1 less than the number is equal to the square root of less 3 than the number squared.

Define each them

1. Conjugate

2. Rationalizing denominator

3. Similar terms in radicals

4. Inverse variation

5. Joint variation

6. Direct variation

I. Write the letter that corresponds to your answer on the space provided. 1. What type of variation illustrated by the table? X 2 4 5 9 y 1 2 2.5 4.5 a. direct b. direct square c. inverse d. joint 2. A post 5 m high casts a shadow of 6 m. If the shadow of a nearby tree measured to be 24 m, how high is the tree? a. 144 m b. 30 m c. 120 m d. 20 m 3. The conjugate of a+bi is a. a+bi b. bi-a c. a-bi d. none of the choices 4. Which of the following are similar radicals? a. va and 2(az) b. V3 and V3 c. V3 and V3 d. V3 and V-3 5. The index of \\(xy)2 in simplified form is a. one b. two c. three d. four x -y 6. Simplify x-Vy a. Vx + Vy b. Vx - Vy C. Vx + VZ d. (x - y ) ( vx+ Vy) 7. The solution set of x2 + 3x + 2 2 0 is a. [-2, -1] b. (-00, - 2] U [-1, 00) C. (-2, -1) d. (-00, - 2) U (-1, 00) 8. The graph of y > -3x2 + 6x - 5 opens_ a. right b. left c. upward d. downward 9. The vertex of the graph, given in number 2 is the point a. (2, 5) b. (-1, 8 ) C. (1, -8) d. (-2, 5) 10. The table shows, what type of variation? X 4 5 9 2 2.5 4.5 a. direct b. inverse c. direct square d. joint 11. To obtain the value of the constant of this variation is by multiplying the value of the variables a. direct b. inverse c. direct square d. joint 12. Four less than one-half the square of a number is two. What is the number? a. 2 b. 3 V2 C. V12 d. 2V3dimensions? 13. A rectangle has an area of 10 square cm and perimeter of 14 cm. What are the a. 3 and 4 b. 4 and 10 c. -2 and -5 d. 2 and 5 14. If the height of a triangle is 15 cm and the base is half of its height. Find its area. 225 a. 3 b. 225 C. 275 d. 275 15. In the equation z = kx yn , y # 0, what varies inversely as z? a. k b . n C. X d. y 16. Express the statement "w varies directly as the cube of x but inversely as square of y" as an equation. a. W = = 2 3 kx 3 b. W = - K V X C. W = Z Vx 2/y 2 /y d. w = V 2 17. The distance travelled by a falling object varies directly as the square of the time it spends in falling. If a body falls 64 ft in 2 seconds, find the distance that will fall in 10 second. a. 40 ft b. 160 ft c. 1600 ft d. 4000 ft For 18-24 Identify the relationships described in each item. Refer to the choices below a. direct variation b. combined variation c. inverse variation d. joint variation 18. The speed of walking and the time it takes to travel 19. The number of copies produced by a copier and the number of hours that it is in operations 20. The number of concert tickets and the amount of revenue 21. The area of a circle and the lengths of its radius 22. The circumference of a circle and the length of its radius 23. The number of people working and the amount of time to finish the work 24. The number of people drinking from a pot of water and the number of days required to consume the contents of the pot 26. Evaluate V(-3x3)2 a. 9x3 b. 9x 6 C. 3x3 d. -3x3 27. Rationalize the denominator of - a 3V3x b 4v3x 3 x 3x2 C. 4V3x d. 4V3x2 28. Simplify 4Vx - 2 y + Vx+ 4Vy a. 4V x - 2Vy b. 3 Vx + 6 y C. 4V x + 4Jy d. 5Vx + 2 y29. Simplify V12 - V27 + V48. a. - 3V3 b. V3 C. 3V3 d. 5V3 30. Multiply (215) (3V10). a. 12V2 b. 30V2 C. 6V2 d. 150V2 31. Find the constant of variation when y varies inversely with x and y=1/4 when x=24. a. 3 b. 4 c. 5 d. 6 32. In number 31, what will be the value of y when x=2? a. 3 b. 4 C. 5 d. 6 33. Fifteen men can finish painting a wall in five days. How long will it take 3 men to finish the job? a. 10 days b. 15 days c. 20 days d. 25 days 34. The area of a triangle varies jointly with its base and height. If b=10 cm and h=16 cm, the area is 80 cm2. What is the constant of variation? a. 1/2 b. 1/3 C. 1/4 d. 1/5 35. Which of the following quantities are not related by the equation y=kx2 for some value of k? a. area and radius of a circle b. area and height of an equilateral triangle c. area and diagonal of a square d. area and height of a rectangle 36. The product of two positive numbers is 72. What is the bigger number? a. 12 b. 7 C. 8 d. 9 37. Four times the square of an integer less 10 times the integer is 50. Find the integer. a. -5/2 b. -5 C. 6 d. 5 38. A rectangle was formed by placing 2 equal squares side by side. The perimeter of the rectangle was 24 cm. What was the length of the side of the square. a. 3 cm b. 4 cm c. 5 cm d. 6 cm 39. In a farm, there are 600 coconut trees. The number of the trees in each row is 10 less than twice the number of rows. How many trees are there in each row. a. 20 trees b. 25 trees c. 30 trees d. 35 trees 40. A rectangular park 80 meters long and 60 meters wide is surrounded by a driveway of uniform width. How wide is the driveway if its area is 3/25 of the area of the park. a. 72 meters b. 7 meters c. 2 meters d. 3 meters 41. To do adding in radicals, it should be a. Similar index and radicand c. similar radicand only b. Similar index only d. different index and radicand42. It is the process of eliminating radicals in denominators. a. Rationalizing denominators c. finding rational numbers b. Removing radicals in the denominator d. extracting radicals 43. The conjugate of 4 - V5 is a. -4+ V5 b. 4- V5 C. -4- V5 d. 4 + V5 44. Simplify 12 25 a. 4V3 b. 6V/2 C. 2V3 5 5 d. V3 5 45. What is the product of (V16 ) (V12 )? a. 4V3 b. 5V/3 c. 2V/4 d. V28 46. Add V54 + V27 a. 6V/9+3 b. V81 C. V81 d. 312 + 3 47. Simplify a. 10V5 5 b. 10v5 c. 2V5 d. 5V5 48. In the expression 2i, i stands for? a. Integrated part c. imaginary b. Complex part d. none of these 49. Imaginary represents from the value, square root of? 1 b. - 1 C. 0 d. undefined 50. The value i4130 = a. b. - 1 C. 0 d. undefined