Review Questions In Mathematics
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REVIEW QUESTIONS IN MATHEMATICS
1. What is the absolute temperature of the freezing point of water in degree Rankine? a) 492 b) 0 c) 460 d) 273 2. A 10-liter pail is full of water. Neglecting the weight of the pail, how heavy is its water content? a) 5 kg b) 6.67 kg c) 10 kg d) 12.5 kg 3. If 16 is 4 more than 4x, find 5x – 1. a) 14 b) 3 c) 12 d) 5 4. Determine k so that the equation 4x² + kx + 1 = 0 a) 3 b) 4 c) 5 d) 6 5. Log (MN) is equal to: a) Log M-N b) Log M+N c) N Log M d) Log M + Log N 6. JJ is three times as old as Allen. Three years ago, JJ was four times as old as Allen. The sum of their ages is a) 20 b) 24 c) 28 d) 36 7. If A can do the work in “x” days and B in “y” days, how long will they finish the job working together? a) (x + y)/ xy b) (x +y)/ 2 c) xy/ (x +y)
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d) √xy Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35. a) 171 b) 182 c) 232 d) 216 Find the sum of 4 geometric means between 160 and 5. a) 130 b) 140 c) 150 d) 160 What is the number of permutations of the letters in the word BANANA? a) 36 b) 60 c) 52 d) 42 Roll two dice once. What is the probability that the sum is 7? a) 1/6 b) 1/8 c) 1/4 d) 1/7 Find each interior angle of a hexagon. a) 90⁰ b) 120⁰ c) 150⁰ d) 180⁰ Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum of the opposite angles is equal to 225⁰. a) 96 sq. cm b) 100 sq. cm c) 94 sq. cm d) 98 sq. cm
14. The sine of a certain angle is 0.6, calculate the cotangent of the angle. a) 4/3 b) 5/4 c) 4/5 d) 3/4 15. Two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26⁰. What is the third side? a) 197. 49 m b) 218.61 m c) 341.78 m d) 282.15 m 16. A spherical triangle ABC has ang angle C = 90⁰ and sides a = 50⁰ and c = 80⁰. Find the value of “b” in degrees. a) 73.22 b) 74.33 c) 75.44 d) 76.55 17. The distance from a point (1,3) to the line 4x + 3y + 12 = 0 is a) 4 units b) 5 units c) 6 units d) 7 units 18. Given three vertices of a triangle whose coordinates are A (1,1), B (3,-3) and (5,-3). Find the area of the triangle. a) 3 b) 4 c) 5 d) 6 19. Which of the following lines is parallel to the line 3x -2y + 6 = 0. a) 3x + 2y -12 = 0 b) 4x – 9y = 6 c) 12x + 18y = 15 d) 15x – 10y + 9 = 0 20. What is the radius of the circle x²+ y² - 6y = 0? a) 2 b) 3
c) 4 d) 5 21. Find the equation of the directrix of the parabola y² = 16x. a) X = 2 b) X =-2 c) X = 4 d) X= -4 22. The lengths of the major and minor axis of an ellipse are 10 m and 8 m, respectively. Find the distance between the foci. a) 3 b) 4 c) 5 d) 6 23. Evaluate: a) 1/5 b) 2/5 c) 3/5 d) 4/5 24. Find the slope of the tangent to the curve, y = 2x x² + x³ at (0,2). a) 1 b) 2 c) 3 d) 4 25. The sum of two positive numbers is 50. What are the numbers if their product is to be the largest possibile. a) 24 & 26 b) 28 & 22 c) 25 & 25 d) 20 & 30 26. A wall “h” meters high is 2m away from the building. The shortest ladder that can reach the building when one end resting on the ground outside the wall is 6m. how high is the wall in meters? a) 2.34 b) 2.24
c) 2.44 d) 2.14 27. What is the integral of sin³ x dx from 0 to . a) 0.667 b) 6.67 c) 66.70 d) 667 28. Evaluate the integral of sin^6 x dx from 0 to .
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a) b) c) 29.
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d) What is the area between y = 0, y = 3x², x = 0 and x = 2? a) 8 b) 21 c) 12 d) 6 Which of the following equations is an exact DE? a) (x² + 1) dx xy dy = 0 b) x dy + (3x – 2y) dx = 0 c) 2xy dx + (2 + x²) dy = 0 d) x²y dy – y dx = 0 The equation y² = cx is the general solution of a) y' = 2y/x b) y’ = 2x/y c) y’ = y/2x d) y’ = x/2y The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number of inhabitants. a) 100 yrs b) 116 yrs c) 120 yrs d) 98 yrs Find the equation of the family of orthogonal trajectories of the system of parabolas y² = 2x + C. a) y = Ce exp –x b) y = Ce exp 2x c) y = Ce exp x
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d) y = Ce exp -2x What is the polar form of the vector 3 + j4? a) 6 bar 53.1⁰ b) 10 bar 53.1⁰ c) 5 bar 53.1⁰ d) 8 bar 53.1⁰ Simplify (3 – i)² - 7(3 – i) + 10 a) -(3 +i) b) 3 + i c) 3 – i d) -(3 – i) The laplace transform of cos wt is a) s / [(s square + (w square)] b) w / [(s square) + (w square)] c) w / (s + w) d) s / (s + w) If the sum is 220 and the first term is 10, find the common difference if the last term is 30. a) 2 b) 5 c) 3 d) 2/3 Find the value of w in the following 3x – 2y + w = 11 x + 5y – 2w = -9 2x + y – 3w = -6 a) 3 b) 2 c) 1 d) 4 A jogger starts a course at a steady rate of 8kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take to catch the first jogger? a) 20 min b) 21 min c) 22 min d) 23 min If the first term of a geometric progression is 9 and the common ration is -2/3, find the fifth term. a) 8/5 b) 16/9
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c) 15/7 d) 13/4 If equal spheres are piled in the form of a complete pyramid with an equilateral triangle as a base, find the total number of spheres in the pile if each side of the base contains 4 spheres. a) 15 b) 20 c) 18 d) 21 The area of a regular hexagon inscribed in a circle of radius 1 is a) 1. 316 b) 2.768 c) 2.598 d) 3.729 An ellipse with an eccentricity of 0.65 and has one of his foci 2 units from the center. The length of the latus rectum is nearest to a) 3.5 units b) 3.8 units c) 4.2 units d) 3.2 units What is the derivative with respect to x of (x + 1) ² x³? a) 3x + 6 b) 3x – 3 c) 6x – 3 d) 6x + 3 A fencing is limited to 20 ft length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall? a) 120 b) 100 c) 140 d) 190 Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 cm³/ min. When the water is x cm deep, the water level is rising at the rate of 0.0149 cm/min. What is x? a) 3
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b) 2 c) 4 d) 5 Find the moment of inertia, with respect to x axis of the area bounded by the parabola y² = 4x and the line x = 1. a) 2.03 b) 2.13 c) 2.33 d) 2.53 Find the volume (in cubic meters) generated by rotating circle x² + y² + 6x + 4y + 12 = 0 about the yaxis. a) 39.48 b) 47.23 c) 59.22 d) 62.11 Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m. a) 5.533 b) 5.335 c) 33.55 d) 3.553 A train, an hour after starting, meets with an accident which detains in an hour, after which it proceeds at 3/5 of its former rate and arrives three hour after time; but had the accident happened in 50 miles farther on the line, it would have arrived one and a half hour sooner. Find the length of the journey. a) 910/9 miles b) 800/9 miles c) 920/9 miles d) 850/9 miles
ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.
A C A B D D C A C B A B B A C B B B D B D D B B C B A D A D C B A C D A A A A B B
42. 43. 44. 45. 46. 47. 48. 49. 50.
C A D B C B C A B
1. What is the absolute temperature of the freezing point of water in degree Rankine? a) 492 b) 0 c) 460 d) 273 2. A 10-liter pail is full of water. Neglecting the weight of the pail, how heavy is its water content? a) 5 kg b) 6.67 kg c) 10 kg d) 12.5 kg 3. If 16 is 4 more than 4x, find 5x – 1. a) 14 b) 3 c) 12 d) 5 4. Determine k so that the equation 4x² + kx + 1 = 0 a) 3 b) 4 c) 5 d) 6 5. Log (MN) is equal to: a) Log M-N b) Log M+N c) N Log M d) Log M + Log N 6. JJ is three times as old as Allen. Three years ago, JJ was four times as old as Allen. The sum of their ages is a) 20 b) 24 c) 28 d) 36 7. If A can do the work in “x” days and B in “y” days, how long will they finish the job working together? a) (x + y)/ xy b) (x +y)/ 2 c) xy/ (x +y)
8.
9.
10.
11.
12.
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d) √xy Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35. a) 171 b) 182 c) 232 d) 216 Find the sum of 4 geometric means between 160 and 5. a) 130 b) 140 c) 150 d) 160 What is the number of permutations of the letters in the word BANANA? a) 36 b) 60 c) 52 d) 42 Roll two dice once. What is the probability that the sum is 7? a) 1/6 b) 1/8 c) 1/4 d) 1/7 Find each interior angle of a hexagon. a) 90⁰ b) 120⁰ c) 150⁰ d) 180⁰ Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum of the opposite angles is equal to 225⁰. a) 96 sq. cm b) 100 sq. cm c) 94 sq. cm d) 98 sq. cm
14. The sine of a certain angle is 0.6, calculate the cotangent of the angle. a) 4/3 b) 5/4 c) 4/5 d) 3/4 15. Two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26⁰. What is the third side? a) 197. 49 m b) 218.61 m c) 341.78 m d) 282.15 m 16. A spherical triangle ABC has ang angle C = 90⁰ and sides a = 50⁰ and c = 80⁰. Find the value of “b” in degrees. a) 73.22 b) 74.33 c) 75.44 d) 76.55 17. The distance from a point (1,3) to the line 4x + 3y + 12 = 0 is a) 4 units b) 5 units c) 6 units d) 7 units 18. Given three vertices of a triangle whose coordinates are A (1,1), B (3,-3) and (5,-3). Find the area of the triangle. a) 3 b) 4 c) 5 d) 6 19. Which of the following lines is parallel to the line 3x -2y + 6 = 0. a) 3x + 2y -12 = 0 b) 4x – 9y = 6 c) 12x + 18y = 15 d) 15x – 10y + 9 = 0 20. What is the radius of the circle x²+ y² - 6y = 0? a) 2 b) 3
c) 4 d) 5 21. Find the equation of the directrix of the parabola y² = 16x. a) X = 2 b) X =-2 c) X = 4 d) X= -4 22. The lengths of the major and minor axis of an ellipse are 10 m and 8 m, respectively. Find the distance between the foci. a) 3 b) 4 c) 5 d) 6 23. Evaluate: a) 1/5 b) 2/5 c) 3/5 d) 4/5 24. Find the slope of the tangent to the curve, y = 2x x² + x³ at (0,2). a) 1 b) 2 c) 3 d) 4 25. The sum of two positive numbers is 50. What are the numbers if their product is to be the largest possibile. a) 24 & 26 b) 28 & 22 c) 25 & 25 d) 20 & 30 26. A wall “h” meters high is 2m away from the building. The shortest ladder that can reach the building when one end resting on the ground outside the wall is 6m. how high is the wall in meters? a) 2.34 b) 2.24
c) 2.44 d) 2.14 27. What is the integral of sin³ x dx from 0 to . a) 0.667 b) 6.67 c) 66.70 d) 667 28. Evaluate the integral of sin^6 x dx from 0 to .
34.
35.
a) b) c) 29.
30.
31.
32.
33.
d) What is the area between y = 0, y = 3x², x = 0 and x = 2? a) 8 b) 21 c) 12 d) 6 Which of the following equations is an exact DE? a) (x² + 1) dx xy dy = 0 b) x dy + (3x – 2y) dx = 0 c) 2xy dx + (2 + x²) dy = 0 d) x²y dy – y dx = 0 The equation y² = cx is the general solution of a) y' = 2y/x b) y’ = 2x/y c) y’ = y/2x d) y’ = x/2y The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number of inhabitants. a) 100 yrs b) 116 yrs c) 120 yrs d) 98 yrs Find the equation of the family of orthogonal trajectories of the system of parabolas y² = 2x + C. a) y = Ce exp –x b) y = Ce exp 2x c) y = Ce exp x
36.
37.
38.
39.
40.
d) y = Ce exp -2x What is the polar form of the vector 3 + j4? a) 6 bar 53.1⁰ b) 10 bar 53.1⁰ c) 5 bar 53.1⁰ d) 8 bar 53.1⁰ Simplify (3 – i)² - 7(3 – i) + 10 a) -(3 +i) b) 3 + i c) 3 – i d) -(3 – i) The laplace transform of cos wt is a) s / [(s square + (w square)] b) w / [(s square) + (w square)] c) w / (s + w) d) s / (s + w) If the sum is 220 and the first term is 10, find the common difference if the last term is 30. a) 2 b) 5 c) 3 d) 2/3 Find the value of w in the following 3x – 2y + w = 11 x + 5y – 2w = -9 2x + y – 3w = -6 a) 3 b) 2 c) 1 d) 4 A jogger starts a course at a steady rate of 8kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take to catch the first jogger? a) 20 min b) 21 min c) 22 min d) 23 min If the first term of a geometric progression is 9 and the common ration is -2/3, find the fifth term. a) 8/5 b) 16/9
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c) 15/7 d) 13/4 If equal spheres are piled in the form of a complete pyramid with an equilateral triangle as a base, find the total number of spheres in the pile if each side of the base contains 4 spheres. a) 15 b) 20 c) 18 d) 21 The area of a regular hexagon inscribed in a circle of radius 1 is a) 1. 316 b) 2.768 c) 2.598 d) 3.729 An ellipse with an eccentricity of 0.65 and has one of his foci 2 units from the center. The length of the latus rectum is nearest to a) 3.5 units b) 3.8 units c) 4.2 units d) 3.2 units What is the derivative with respect to x of (x + 1) ² x³? a) 3x + 6 b) 3x – 3 c) 6x – 3 d) 6x + 3 A fencing is limited to 20 ft length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall? a) 120 b) 100 c) 140 d) 190 Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 cm³/ min. When the water is x cm deep, the water level is rising at the rate of 0.0149 cm/min. What is x? a) 3
47.
48.
49.
50.
b) 2 c) 4 d) 5 Find the moment of inertia, with respect to x axis of the area bounded by the parabola y² = 4x and the line x = 1. a) 2.03 b) 2.13 c) 2.33 d) 2.53 Find the volume (in cubic meters) generated by rotating circle x² + y² + 6x + 4y + 12 = 0 about the yaxis. a) 39.48 b) 47.23 c) 59.22 d) 62.11 Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m. a) 5.533 b) 5.335 c) 33.55 d) 3.553 A train, an hour after starting, meets with an accident which detains in an hour, after which it proceeds at 3/5 of its former rate and arrives three hour after time; but had the accident happened in 50 miles farther on the line, it would have arrived one and a half hour sooner. Find the length of the journey. a) 910/9 miles b) 800/9 miles c) 920/9 miles d) 850/9 miles
ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.
A C A B D D C A C B A B B A C B B B D B D D B B C B A D A D C B A C D A A A A B B
42. 43. 44. 45. 46. 47. 48. 49. 50.
C A D B C B C A B
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