MATH Past Board Exam Questions 2019-2022 PDF

Past Board Exam Questions in Mathematics April 2019 1. Listed below are functions each denoted g(x) and each involving a real number x, constant c > 1. If f(x) = 2x, which of these functions yield the greatest value for f(g(x)), for all x > 1? A. g(x) = cx B. g(x) = c/x C. g(x) = c – x D. g(x) = x/c 2. Find the volume (in cubic units generated by rotating a circle x2 + y2 + 6x + 4y + 12 = 0 about the y-axis. A. 47.23 B. 59.22 C. 62.11 D. 39.48 3. The area enclosed by the ellipse 4x^2 + 9y^2 = 46 is revolved about the line x = 3, what is the volume generated? A. 370.3 B. 360.1 C. 355.3 D. 365.1 4. Calculate the volume of the solid formed by revolving the area bounded by the parabola y2 = 12x and the line x = 3 about the line x = 3. A. 131 B. 191 C. 181 D. 151 5. A conic section whose eccentricity is less than one (1) is known as: A. A parabola B. An ellipse C. A circle D. A hyperbola 6. If Rita can run around the block 5 times in 20 minutes, how many times can she run around the block in hour? A. 10 B. 50 C. 15 D. 100 7. Evaluate the double integral of 1/(x-y) dxdy with inner bounds 2y to 3y and outer bound of 0 to 2. A. ln 3 B. ln 4 C. ln 2 D. ln 8 8. Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. A. 2.5 mils B. 1 mil C. 4 mils D. 2.04 mils 9. A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8 cm/hr. If the icicle is currently 4 cm in radius and 20 cm long, is the volume of the icicle increasing or decreasing, and at what rate? A. Decreasing at 20 cu. cm/hr B. Increasing at 24 cu. cm/hr C. Decreasing at 24 cu. cm/hr D. Increasing at 20 cu. cm/hr Past Board Exam Questions in Mathematics 10.Lisa originally brought exact amount of money to buy 10 chocolates. She then discovers that the price of chocolate went up by 50 centavos each. She was able to buy 8 chocolates and have an extra of 2 pesos. How much did Lisa bring originally? A. 80 B. 40 C. 60 D. 30 11. Find the area of a triangle having vertices at -4 – i, 1 + 2i, 4 – 3i. A. 15 B. 16 C. 17 D. 18 12. There are four geometric mean between 3 and 720. Find the sum of the geometric progression. A. 1092 B. 1094 C. 1082 D. 1084 13. What percentage of the volume of cone is maximum right circular cylinder that can be inscribed in it? A. 24% B. 32% C. 44% D. 54% 14. A and B working together can do a job in 5 hrs. B and C together can do the same in 4 hrs and A and C in 2.5 hrs. In how many days can all of them finish the job working together? TROUBLESHOOT: 5 → 3 A. 1.07 hrs B. 2.80 hrs C. 2.03 hrs D. 3.10 hrs 15. The geometric mean and the arithmetic mean of numbers are 8 and 10 respectively. What is the harmonic mean? A. 7.5 B. 5.7 C. 6.4 D. 4.6 16. The centroid of the area bounded by the parabola y2 = 4ax and the line x = p coincides with the focus of the parabola. Find the value of p. A. 3/5 a B. 5/3 a C. 2/5 a D. 5/2 a 17. N engineers and N nurses, if two engineers are replaced by nurses, 51% of the engineers and nurses are nurses. Find N A. 100 B. 110 C. 50 D. 200 Past Board Exam Questions in Mathematics 18. Two stones are 1 mile apart and are at the same level as the foot of a hill. The angles of depression of the two stones viewed from the top of the hill are 5 degrees and 15 degrees respectively. Find the height of the hill. A. 109.01 m B. 209.01 m C. 309.01 m D. 409.01 m 19. Water is running out of a conical funnel at the rate of 1 cu. in/sec. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top. A. – 1/9pi in/sec B. -1/2pi in/sec C. 1/2pi in/sec D. 1/9pi in/sec 20. Find the radius of curvature of the parabola y2 = 4x at point P (4,4)? A. 22.36 B. 20.36 C. 25.36 D. 27.36 21. If Nannette cuts a length of ribbon that is 13.4 inches long into 4 equal pieces, how long will each piece be? A. 3.35 m B. 3.25 m C. 3.15 m D. 3.45 m 22. The equation y2 = cx is a general solution of A. y' = 2y/x B. y’ = 2x/y C. y’ = y/2x D. y’ = x/2y 23. Find the minimum distance from point P(4,2) to the parabola y2 = 8x. A. 3 sqrt. of 3 B. 2 sqrt. of 3 C. 3 sqrt. of 2 D. 2 sqrt. of 2 24. Find the general solution of y” + 8y’ + 41y = 0 A. y = e-5x(c1cos4x + c2sin4x) B. y = e5x(c1cos4x + c2sin4x) C. y = e-4x(c1cos5x + c2sin5x) D. y = e4x(c1cos5x + c2sin5x) 25. Find the general solution of y” + 10y’ + 41y = 0 A. y = e-5x(c1cos4x + c2sin4x) B. y = e5x(c1cos4x + c2sin4x) C. y = e-4x(c1cos5x + c2sin5x) D. y = e4x(c1cos5x + c2sin5x) 26. A transmitter with a height of 15m is located on top of a mountain which is 3.0 km high. What is the farthest distance on the surface of the earth that can be seen from the top of the mountain? Take the radius if the earth to be 6400 km. A. 225 km B. 152 km C. 196 km Past Board Exam Questions in Mathematics D. 205 km 27. Find all the values for z for which e4z = i. A. 1/6 pi i + 1/2 k pi i B. -1/6 pi i + 1/2 k pi i C. 1/8 pi i + 1/2 k pi i D. -1/8 pi i + 1/2 k pi i 28. 3 randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three student’s drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assume the possible combination is equally likely and knowing that 1 student gets a negative result, what is the probability that all 3 students get a negative result? A. 1/8 B. 1/7 C. 7/8 D. 1/4 29. Find the area under one arch of the cycloid x = a (theta – sin theta) and y = a (1- cos theta). A. 2pi a2/3 B. pi a2 C. 3pi a2 D. 2pi a2 30. Newton’s law of cooling states that the rate of change of the temperature of an object is directly proportional to its difference in temperature to the surrounding. If the air is at 30˚C and it takes 15 minutes to cool down an object from 100 ˚C to 70 ˚C, how long will it take to cool down from 100 ˚C to 50 ˚C? A. 33.59 min. B. 43.60 min. C. 35.39 min D. 45.30 min. 31. How many possible positive real roots are there in x4 – 4x3 + 7x2 – 6x – 18 = 0. A. 1 or 2 B. 3 or 1 C. 3 or 0 D. 1 or 0 32. Peter can finish in 2 hours while John can finish in 1.5 hours. How long will it take if they work together? A. 51.43 mins B. 52.10 mins C. 53.29 mins D. 54.72 mins 33. One end of a 32-meter ladder resting on a horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2 meters per minute. How fast is the top of the ladder rising when its foot is 10 meters from the wall? A. +0.568 m/min B. +0.658 m/min C. +0.896 m/min D. +0.986 m/min Past Board Exam Questions in Mathematics 34. A wall “h” meters high is 2 m away from the building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6 m. How high is the wall in meters? A. 2.34 B. 2.24 C. 2.44 D. 2.14 35. A container is in the form of a right circular cylinder with an altitude of 6 in and a radius of 2 in. If an asbestos of 1 in thick is inserted inside the container along its lateral surface, find the volume capacity of the container. A. 12.57 cu.in B. 12.75 cu.in C. 18.58 cu.in D. 18.85 cu.in 36. 60% of 390? A. 234 B. 190 C. 180 D. 134 37. Seven people are at the beach for a clambake. They have dug 12.6 pounds of clams. They eat the following amount of clams: 0.34 pounds, 1.6 pounds, 0.7 pounds, 1.265 pounds, 0.83 pounds, 1.43 pounds and 0.49 pounds. How many pounds of clams are left? A. 7.892 pounds B. 4.566 pounds C. 5.945 pounds D. 6.655 pounds 38. A game in a carnival consist of a player throwing a coin onto a table about 5 feet away. The table contains a grid of 1-inch squares and the coin is 3/4 inches in diameter. If the coin is entirely inside of a 1- inch square, the player gains wins their bet. Otherwise, the player loses. Given that the coin h=hits the table, what is the probability the player loses? A. 15/16 B. 12/13 C. 14/15 D. 11/12 39. The differential equation x(y-1)dx + (x+1)dy = 0 as values at x = 1, y = 2. Solve for the value of y at x = 2. A. 1.55 B. 1.23 C. 1.45 D. 1.35 40. Find the differential equation whose general solution is y = C1x + C2ex. A. (x - 1)y” – xy’ + y = 0 B. (x +1)y” – xy’ + y = 0 C. (x – 1)y” + xy’ + y = 0 D. (x + 1)y” + xy’ + y = 0 41. Which of the following differential equations describes a family of circles centered at the y-axis? A. xy" + (y’)3 + y’ = 0 B. xy” – (y’)3 + y’ = 0 C. xy” + (y’)3 – y’ = 0 D. xy” – (y’)3 – y’ = 0 Past Board Exam Questions in Mathematics 42. At what value of x is y = sin2x at maximum? A. pi/4 B. pi C. 3pi/2 D. 2pi 43. Solve for the limit A. 1 B. 0 C. pi D. 1 – i 44. Evaluate the integral of sin(x) raised to the 5th power and the limits from 0 to pi/2. A. 0.53 B. 0.43 C. 0.33 D. 0.23 45. Solve for the integral of cos(x) from pi/4 to pi/2 A. 0.293 B. 0.193 C. 0.393 D. 0.493 46. Solve for the value of |u x v| if |u| = 9, |v| = 3, and the angle between u and v is 85˚. A. 2.989 B. 31.897 C. 2.353 D. 26.897 47. The suspension cable of a bridge of length 400m takes form of a parabola. If the sag is 50m, what is the equation of the parabola if the lowest part is at the origin? A. x2 = 800y B. x2 = 1600y C. y2 = 800x D. y2 = 1600x 48. The suspension cable of a bridge of length 800m takes form of a parabola. If the sag is 100m, what is the equation of the parabola if the lowest part is at the origin? A. x = 1600y 2 B. x2 = 3200y C. y2 = 1600x D. y2 = 3200x 49. Find the number where 4 times added to 6 times added to 6 times its reciprocal is equal to -14. TROUBLESHOOT: 4x + 6/x = -14 (remove extra “6 times added to) A. -3, -1/2 B. -3, 1/2 C. 3. 1/2 D. 3, -1/2 50. What is the simplified expression of 3x2 multiplied to (2x3y)4? A. 6x9y4 B. 48x14y4 C. 6x14y4 D. 1296x16y4 51. A man on an observation sees a fire directly south of him. A boy on another tower 20 km east of the first tower observes the fire at bearing S40˚15’W. What is the distance of the first tower from the fire? Past Board Exam Questions in Mathematics A. 26.20 km B. 15.26 km C. 16. 93 km D. 23.62 km 52. Using area method, solve for the integral from x = -3 to x = 3 of sqrt(9 – x2). A. 4.5 pi B. 9 pi C. 3.5 pi D. 6 pi 53. What is b so that the points (-2, -1, -3), (-1, 0, -1) and (a, b, 3) lie on a straight line? A. 2 B. 4 C. 3 D. 1 54. If the equal spheres are piled in the form of a complete pyramid with a square base, find the total number of spheres in the pile if each side of the base contains 4 spheres. A. 18 B. 20 C. 30 D. 28 55. Joey is x years old y years from now. How is he/she now? A. x – y B. x + y C. y – x D. y + x 56. John, Noel, and Ryan working together is 6 hours more than John working alone and 1 hour more than Noel working alone, and twice that of Ryan working alone. How long will it take if they all work together? TROUBLESHOOT: John = 6 hrs alone, Noel = 1 hr alone, Ryan = 2x faster than John? = 3 hrs alone. A. 40 mins B. 42 mins C. 41 mins D. 43 mins 57. Solve for the limit A. 1 B. 0 C. pi D. infinity 58. n is directly proportional to z. If a, b, and c are constants, which of the following describe the relationship? A. n = cz B. n = az + b C. n = a + bz D. n = c/z 59. What is the polar form of 1 + i? A. sqrt.2(cos45˚ + isin45˚) B. sqrt.2(cos45˚ - isin45˚) C. -sqrt.2(cos45˚ - isin45˚) D. -sqrt.2(cos45˚ + isin45˚) 60. Find the area of the ellipse 4x2+ + 9y2 = 36? Past Board Exam Questions in Mathematics A. 15.71 B. 18.85 C. 12.57 D. 21.99 August 2019 1. Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane x + y + z = 10 and perpendicular to the line x = 3 + t, y = -18 - t, z = 5t. A. x = 6t – 1, y = 4t -7, z = -2t – 2 B. 4t + 1, y = -6t + 7, z = 2t + 2 C. x = 6t + 1, y = -4t + 7, z = -2t + 2 D. x = 4t + 1. y = -6t, z = 2t + 2 2. It represents the distance of a point from the y-axis. A. Ordinate B. Abscissa C. Coordinate D. Polar distance 3. The locus of a point which moves so that its distance from a fixed point and a fixed line is always equal is _______________. A. Ellipse B. Parabola C. Circle D. Hyperbola 4. Jerome ate 3 oz. of a 16-oz ice cream pack. What percentage of the pack did he eat? A. 18.75% B. 19.50% C. 17.25% D. 16.75% 5. Determine the equation that expresses the statement. F is directly proportional to y Symbols a, b, c, and d are constants. A. F = a B. F = a. y C. F = b D. F = cy^3 + a 6. If a quiz consists of four true-false questions, and a student guesses at each answer, what is the probability the student answer exactly half of the questions correctly? A. 0.5000 B. 0.2500 C. 0.1536 Past Board Exam Questions in Mathematics D. 0.7521 7. Evaluate A. 1 B. 0 C. i/2 D. –i/2 8. Find the equation of the circle with center at the origin and passes through (-3, 4). A. x2 + y2 = 36 B. x2 + y2 = 25 C. x2 + y2 = 9 D. x2 + y2 = 16 9. Find the area bounded by r = 2/(1 + cosθ) and cosθ = 0. A. 1/3 B. 2/3 C. 5/3 D. 8/3 10.The value of 5! Is equal to: A. 120 B. 1 C. 25 D. 5 11. If sinθ = a and cos2θ = b then what is the value of sin2θ – 2cosθ? I. a2 + 2 square root of b II. a2 – 2 square root of b III. b2 + 2 square root of a IV. b2 – 2 square root of a A. I only B. I and II only C. III and IV only D. III only 12. Find the equation of the parabola with vertex t (-1, -2) latus rectum 12, opens downward. A. x2 + 12x + 12y – 25 = 0 B. x2 + 12x2y + 22 = 0 C. x2 – 2x + y – 23 = 0 D. x2 + 2x + 12y – 25 = 0 13. A man is driving a car at the rate of 30 km/hour towards the foot of monument 6m high. At what rate is he approaching the top when he is 36m from the foot of the monument? A. -52.80 km/hr B. 10.55 km/hr C. -29.59 km/hr D. 12.52 km/hr 14. A cross-section of a trough is a semi-ellipse with width at the top 18 in. and depth 12 in. The trough is filled with water to a depth of 8 in. Find the width of the surface of the water. A. 6 square root of 5 in B. Square root of 5 in C. 6 in D. 5 square root of 6 in Past Board Exam Questions in Mathematics 15. A secondary school is contracting its alumni asking for dominations to help put up new computer laboratory. Past records show that 80% of the alumni will make a contribution of at least P50.00. A random sample of 20 alumni is selected. What is the probability that exactly 15 alumni will make a donation of at least P50.00? A. 0.576 B. 0.167 C. 0.174 D. 0.204 16. Determine the differential equation of the family of lines passing through (h, k) A. (y – h) + (y – k) = dy/dx B. (x – h)dx – (y – k)dy = 0 C. (x + h)dx – (y – k)dy = 0 D. (y – k)dx – (x – h)dy = 0 17. Find the complex numbers whose sum is 4 and whose product is 8. A. 1 ± 2i B. 2 ± i C. 1 ± i D. 2 ± 2i 18. If 3x2 is multiplied by the quantity 2x^3y raised to the 4th power, what would this expression simplify to? A. 6x^9y to the 4th power B. 48x^14y to the 4th power C. 6x^14y to the 4th power D. 1296x^16y to the 4th power 19.A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 in away from the center of the circle? A. 55/64 B. 5/8 C. 5/64 D. 12/45 20. In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a: A. Conjugate axis B. Latus rectum C. Focal width D. Minor axis 21. Find the position value of c such that the area of the region bounded by the parabola y = x2 – c2 and y = c2 – x2 is 576. A. 13 B. 5 C. 8 D. 6 22. Obtain L^-1 {1/(s^2 +1)^2} A. ½ (sint – tcost) B. – ½ (sint – tcost) C. ½ (sint + tcost) D. – ½ (sint + tcost) Past Board Exam Questions in Mathematics 23. If Jim and Jerry work together they can finish a job in 4 hours. If working alone takes Jim 10 hours to finish the job, how many hours would it take Jerry to do the job alone? A. 16 B. 6.0 C. 6.7 D. 5.6 24. A line through (0, 0) intersects y = x2 at a point (a, a2). The area of the upper region bounded above by the line and below the curve is 27. A. 2 cube root of 6 B. Cube root of 6 C. 3 cube root of 6 D. Cube root of 3 25. Simplify i^(39) A. –i B. i C. -1 D. 1 26. If a rock is dropped, its distance below the starting point at the end of t sec is given by s =16 t square, where s is in ft. Find the rate of change of distance after 1.5 minutes A. 288 ft/sec B. 281 ft/sec C. 2,880 ft/sec D. 800 ft/sec 27. Find the equation of the line with slope 3 and y-intercept -2. A. y = 2x +3 B. y = 2x -3 C. y = -3x + 2 D. y = 3x – 2 28.Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three students’ drug test evaluation as PPP, PPN, PNP. NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that all three students get positive results? A. ½ B. ¼ C. 3/4 D. 1/8 29. Find the area of the first octant part of the plane x/a + y/b + z/c = 1, where a, b, and c are positive. A. ½ square root of (a2b2 + b2c2 + a2c2) B. a + b + c C. square root of (a + b + c) D. square root of (a2 + b2 +c2) 30. Find the volume generated by revolving the area bounded by y2 = 12x and x = 3 about the line x = 3. A. 131 B. 191 Past Board Exam Questions in Mathematics C. 181 D. 151 31. Joey will be x years old y years from now. How old is she now? A. y – x B. x C. x – y D. y 32. A rectangle with sides parallel to the coordinate axes has one vertex at the origin, one of the positive x-axis and its fourth vertex in the first quadrant on the line with equation 2x + y = 100. What is the maximum possible area of rectangle? A. 3520 B. 1250 C. 1988 D. 2250 33. Find the volume generated by revolving the area bounded by y2 = 12x and x = 3 about the line x = 3. A. 191 B. 181 C. 151 D. 131 34. Find the equation of the line passing 3 units from the origin and parallel to 3x – 4y – 10 = 0. A. 3x + 4y – 5 = 0 B. 4x – 4y + 1 = 0 C. x – 3y + 15 = 0 D. 3x – 4y – 15 = 0 35. Patrick has a rectangular patio whose length is 5m less than the diagonal and a width that is 7m less than the diagonal. If the area of his patio is 195 m2, what is the length of the diagonal? A. 20 m B. 10 m C. 16 m D. 8 m 36. Find |u x v| correct to three decimal places where |u| = 9, |v| = 3, Lθ = 85 deg. Select the correct answer. A. 2.969 B. 31.897 C. 2.353 D. 26.897 37.If 1 is added to the difference when 10x is subtracted from -18x, the result is 57. What is the value of x? A. 7 B. 2 C. -2 D. -7 38. Joseph gave ¼ of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally? A. 20 B. 30 C. 40 D. 50 39. From the past experience, it is known 90% of one-year-old children can distinguish their mother voice of a similar sounding female. A random sample of 20 one year olds are given this voice recognition test. Let the random Past Board Exam Questions in Mathematics variable x denote the number of children who do not recognize their Mother’s voice. Find the mean of x. A. 20 B. 2 C. 4 D. 1 40. What percent of 50 is 12? A. 14% B. 4% C. 2% D. 24% 41. Find all values of z for which e^3z = 1 A. kπi B. 2kπ/3 C. 1/3 kπi D. 1/8 πi + ½ kπi 42. In the vicinity of a bonfire, the temperature T in deg C as distance of x meters from the center of the fire was given by: At what range of distances from the fire’s center was the temperature less than 500 deg C? A. More than 45 meters B. More than 30 meters C. More than 35 meters D. More than 20 meters 43. During his major league career, Hank Aaron hit 38 more home runs than Babe Ruth hit during his career, Together they hit 1,524 home runs. How many home runs did Babe Ruth hit? A. 781 home runs B. 800 home runs C. 743 home runs D. 762 home runs 44. If sinA = 4/5 and sinB = 7/25, what is sin(A +B) if A is in the 3rd quadrant and B is in the 2nd quadrant. A. -3/5 B. 3/5 C. 2/5 D. 4/5 45.Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three students’ drug test evaluation as PPP, PPN, PNP. NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability at least one student gets negative results? A. 4/8 B. 2/7 C. 7/8 D. 3/7 46. A bag contains 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability that the marble is blue? A. 3/8 B. 3/16 C. 3/5 D. 4/13 Past Board Exam Questions in Mathematics 47. z varies directly as x and inversely as y^2. If x = 1 and y = 2 then z = 2. Find z when x = 3 and y = 4. A. 1.5 B. 3.5 C. 2.5 D. 3 48. Which of these is equal to 6(x-3)? A. x^6 – 3^6 B. 6x + 3 C. 6x – 18 D. 6x – 3 49. If z = 6 e^πi/3 evaluate e^iz. A. e^3isq root of 3 B. e^-3sqroot of 3 C. e^sq root of 3 D. e^-sqroot of 3 50. after paying a commission of 7% of the sale price to his broker. Tess receives P103,00 for his car. How much was the car sold? A. P110,753 B. P110,000 C. P110,420 D. P95,790 51. What is the maximum rectangular area that can be fenced in 20 ft using two perpendicular corner sides of an existing wall? A. 310 ft2 B. 250 ft2 C. 100 ft2 D. 120 ft2 52. Find the area enclosed by the lemniscate of Bernoulli r2 = a2cos2θ. A. a2/2 B. a2/4 C. a2 D. a2/3 53. A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new products. The survey showed 40% of the consumers has seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. If a randomly selected consumer has seen an advertisement for the new soap, what is the probability that this consumer has tried the new soap? A. 72% B. 25% C. 40% D. 37.5% 54.Which of the following is equal to n-4.n4? A. 1 B. n C. -16n D. 0 55. Jason made 10 two-point baskets and 2 three-point baskets in Friday’s basketball game. He did not score any other points. How many points did he score? A. 22 B. 12 Past Board Exam Questions in Mathematics C. 26 D. 24 56. Evaluate ∫√(1 − cosx)dx A. 2√2 cos x + C B. -2√2 cos x/2 + C C. -2√2 cos x + C D. 2√2 cos x/2 + C 57. If the graph of y = f(x) is transformed into the graph of 2y – 6 = -4 f(x – 3), point (a, b) on the graph of y = f(x) becomes point (A, B) where A and B are expressed as: A. A = a + 4, B = 2b – 3 B. A = a + 6, B = 2b – 6 C. A = a + 3, B = -2b + 3 D. A. a – 2, B = 2b – 3 58. From the past experience, it is known 90% of one-year old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability that all 20 children recognize their mother’s voice. A. 0.222 B. 0.500 C. 1.000 D. 0.122 59. Find the radius of curvature of the parabola y2 – 4x = 0 at the point (4, 4). A. 22.36 B. 20.36 C. 35.36 D. 27.36 60. Find the differential equation of the family of lines passing through the origin. A. x dx + y dy = 0 B. x dy + ydx = 0 C. y dx + x dy = 0 D. y dx – x dy = 0 61. Find the point on the line 3x + y + 4 = 0 that is equidistant from the points (-5, 6) and (3, 2). A. (-2, 2) B. (-2, 3) C. (-2, -2) D. (2, 2) 62. Find all real solutions to the logarithmic equation ln(x^2 – 1) – ln(x – 1) = ln4 A. 0 B. 3 C. 5 D. ½ 63.Gabby cuts a piece of rope into three pieces. One piece is 5 inches long, one piece is 4 inches long, and one piece is 3 inches long. The longest piece of rope is approximately what percent of the original length before the rope was cut? A. 55% B. 42% C. 33% D. 50% 64. What is the result when 6ab + 3b is subtracted from -6ab – 3b? Past Board Exam Questions in Mathematics A. 12ab + 6b B. -12ab – 6b C. 18ab D. 0 65. Find 60% of 390 A. 134 B. 190 C. 180 D. 243 66. Find the area bounded by y = x^3, the x-axis and the lines x = -2 and x = 1. A. 0,43 B. 2.45 C. 1.25 D. 4.25 67. The table shows the number CD players sold in a small electronics store in the years 1989-1999 as follows: YEAR CD PLAYERS SOLD 1989 545 1990 675 1991 665 1992 665 1993 600 1994 550 1995 680 1996 560 1997 545 1998 560 1999 695 What was the average rate of change of sales between 1989 and 1999? A. 15 CD players/year B. 150 CD players/year C. 70 CD players/year D. 695 CD players/year 68. A man is driving a car at the rate of 30 km/hr towards the foot of a monument 6 m high. At what rate is he approaching the top when he is 36 m from the foot of the monument? A. 12.52 km/hr B. -52.80 km/hr C. 10.55 km/hr D. -29.59 km/hr 69. Find the vertex of the parabola x2 = 8y. A. (2, 4) B. (0, 8) C. (0, 0) D. (-2, 0) 70.A and B working together can do a job in 5 days. B and C together can do the same in 4 days and A and C in 2.5 days. In how many days can all of them finish the job working together? TROUBLESHOOT: 5 → 3 A. 1.07 B. 2.80 Past Board Exam Questions in Mathematics C. 2.03 D. 3.10 71. Which of the following is a disadvantage of using the sample range to measure of spread or dispersion? A. It produces very small spreads. B. The largest of the smallest observation (or both) may be a mistake or an outlier. C. The sample range is not measured in the same units as the data. D. It produces spreads that are too large. 72. Obtain L {t^n} A. n!/s^n-1 B. n!/s^n C. (n+1)/s^(n+1) D. n!/s^(n+1) 73. Jenny flipped a coin three times and got heads each time. What is the probability that she gets heads on the fourth flip? A. 1 B. 0 C. 1/16 D. 1/2 74. Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell? A. 45 B. 20 C. 25 D. 10 75. How many positive real roots are there in the polynomial x^4 – 4x^3 + 7x2 – 6x – 18 = 0 A. 1 or 2 B. 3 or 1 C. 3 or 0 D. 1 or 0 76. The square of a number added to 25 equals 10 times the number. What is the number? A. -5 B. -10 C. 5 D. 10 77. Evaluate lim (1 + 2x)^(1 +2x)/x x →0 A. 1 B. e C. 0 D. e2 78. A man on a wharf 3.60 m above sea level is pulling a rope tied to a raft at the rate of 0.60 m/sec. How fast is the raft approaching the wharf when there are 6m of rope out? A. -0.22 m/sec B. -1.75 m/sec C. -0.12 m/sec D. -0.75 m/sec 79.From a stationary point directly in from of the center of the bull’s eye. Kim aims two arrows at the bull’s eye. The first arrow nicks one point on the edge of the bull’s eye; the second strikes the center of the bull’s eye. Kim knows the second arrow traveled 20 meters since she knows how far she is from the target. If the bull’s eye is 4 meters wide, how far did the first arrow travel? Past Board Exam Questions in Mathematics Assume the arrows traveled in straight – line paths and the bull’s eye is circular. A. 19.9 m B. 24.0 m C. 20.1 m D. 22.5 m 80. A voltage v = 150 + j180 is applied across an impedance and the current flowing is found to be I = 5 – j4. Determine the resistance. TROUBLESHOOT: R = 0.73 ohms. Choose the nearest answer A. 0.75 ohms B. 0.77 ohms C. 0.78 ohms D. 0.76 ohms 81. Determine the equation that expresses that G is proportional to k and inversely proportional to C and z. Symbols a, b and c are constants. A. G = ck/zC B. G = bc/zk C. G = a/bc D. G = ck/GG 82. Determine the equation of the line passing through the points (1, 17) and (13, 4). A. 13x – 12y – 217 = 0 B. 13x – 12y + 217 = 0 C. 13x + 12y – 217 = 0 D. 13x + 12y + 217 = 0 83. Describe the locus represented by | z – i | = 2. A. Hyperbola B. Circle C. Parabola D. Ellipse 84. Two hundred single-sport athletes were cross-classified according to gender as follows: Swimmer Runner Cyclist Male 25 60 25 Female 20 50 20 What is the probability that the athlete is male or a swimmer or both? A. 0.550 B. 0.450 C. 0.230 D. 0.005 85. Solve the equation (x2y – 2) + (x + 2xy – 5) i = 0 A. x = 1, y = 2 B. x = 3, y = 4 C. x = ½, y = 3 D. x = 4, y = - ½ 86. Find the two numbers whose sum is 50 and with the largest possible product. A. 25, 25 B. 23, 25 C. 22, D. 20,30 87. If dy = x2 dx; what is the equation of y in terms of x if the curve passes through (1, 1)? A. x^(3) + 3y2 + 2 = 0 B. x^(3) – 3y + 2 = 0 C. x2 – 3y + 3 = 0 D. 2y + x3 – 2 = 0 Past Board Exam Questions in Mathematics 88.A car rental company offers two plans for renting a car: Plan A: $ 30 / day and $ 0.20 / mile Plan B: $ 55 / day with free unlimited mileage For what range of miles will Plan B save a customer’s money? A. More than 125 miles B. Less than 250 miles C. More than 170 miles D. Less than 170 miles 89. Find the value of x for which f(x) = x2 + 5x – 2 is maximum. A. 5/2 B. 2 C. -2 D. -5/2 90. In order to pass a certain exam, candidates must answer correctly 70% of the test questions. If there are 70 questions on the exam, how many questions must be answered correctly in order to pass? A. 52 B. 60 C. 56 D. 49 91. A group consists of n engineers and n nurses. If two of the engineers are replaced by other nurses, then 51% of the group members will be nurses. Find the value of n. A. 100 B. 110 C. 80 D. 55 92. While bowling in a tournament, Jake and his friends had the following scores: Jake 189 Charles and Max each scored 120 Terry 95 What was the total score fore Jake and his friends at the tournament? A. 524 B. 526 C. 404 D. 504 93. Find the height of a tree if the angle of elevation of its top changes from 20˚ to 40˚ as the observer advances 23 meters toward the base. A. 16.78 m B. 14.78 m C. 13.78 m D. 15.78 m 94. A normal to a given plane is _______ A. Oblique to the given plane B. Parallel to the plane C. Perpendicular to the plane D. Lying in the plane 95. Find the equation of the normal x2 + y2 = 1 at the point (2, 1) A. x + y = 1 B. x = 2y C. y = 2x D. x – y = 0 96. Evaluate ∫ x dx / square root of (x2 – 8x). TROUBLESHOOT: It should be Square root of (x2 – 8x) + 4 ln(... A. Square root of (x2 – 4x + 4) ln (x – 4 + sq root of (x2 + 8x) + C B. Square root of (x2 – 4x + 2) ln (x – 4 + sq root of (x2 - 8x) + C Past Board Exam Questions in Mathematics C. Square root of (x2 – 8x + 4) ln (x – 4 + sq root of (x2 - 8x) + C D.. Square root of (x2 – 2x) + 4 ln (x – 4 + sq root of (x2 - 2x) + C E. 97.The plane rectangular coordinate system is divided into four parts which are known as ______. A. Octants B. Quadrants C. Coordinates D. Axis 98. What curve is described by the equation 4x2 – y2 + 8x + 4y = 15? A. Hyperbola B. Circle C. Parabola D. Ellipse 99. From a recent study, 90% of one-year old children can distinguish their mother’s voice from that of a similar sounding female. A random sample of 20 one-year-olds are given this voice recognition test. Find the probability that all he 20 one-year-olds recognize their mother’s voice. A. 0.122 B. 0.001 C. 0.522 D. 1.000 100. What is the length of the latus rectum of the parabola y = 4px 2? TROUBLESHOOT: The given equation should be y^2 = 4px. A. p B. -4p C. 2p D. 4p Past Board Exam Questions in Mathematics September 2021 1. At the city part, 32% of the trees are oaks, if there are 400 trees in the park, how many trees are NOT oak. A. 278 B. 312 C. 272 D. 128 2. It is estimated that the annual cost of driving a certain new car is given by the formula: C = 0.25 m + 1,600 Where m represents the number of miles driven per year and C is the cost in dollars. Jane purchases such a car and determines between $5,350 and $5,600 for next year’s driving cost. What is the corresponding range of miles that she can drive her new car? A. Between 13,000 mi and 18,000 mi B. More than 16,000 mi C. Between 15,000 and 16,000 mi D. Between 13,000 mi and 16,000 3. At exactly what time after 5 o’clock will the hour hand and the minute hand be perpendicular for the first time? A. 5:15 and 25 seconds B. 5:10 and 54 seconds C. 5:20 and 14 seconds D. 5:05 and 34 seconds 4. Find the equation of the line passing through the intersection of x – y = 0 and 3x – 2y = 2 cutting from the first quadrant a triangle whose area is 9. A. x + y + 1 = 0 B. 2x + y – 2 = 0 C. 3x + y – 3 = 0 D. x + 2y – 6 = 0 5. A ball bounces 2/3 of the altitude from which it falls is dropped from a height of 18 ft., how far will it travel before coming to rest? A. 99 ft B. 90 ft C. 19 ft D. 9 ft 6. Determine the correct equation for the line with a slope of 7 and y-intercept of -4. A. y = -1/7x – 4 B. y = 7x – 4 C. y = 7x + 4 D. y = -7x + 4 7. Evaluate lim (z – 1 – i)” ------------------ z --> 1 + I z” – 2z + 2 TROUBLESHOOT: (z” – 2z + 2)^2; z“ = z^2 ; I = i A. -1/4 B. -12 + 6i C. -4/3 – 4i D. Square root of 2 (1 + i)/2 8. Find the area of the region enclosed by the triangle with vertices (1, 1), ( 3, 2) and (2, -4). Past Board Exam Questions in Mathematics TROUBLESHOOT: (2, 4) A. 7/2 B. 5/2 C. 1/2 D. 3/2 9. Find the area of the polygon with vertices at: 2 + 3i, 3 + I, -2 -4i, -4 – I, -1 + 2i. A. 47 B. 35/2 C. 25 D. 47/2 10. If the general equation of the conic is Ax” + Bxy + Cy” + Dx + Ey + F = 0 and B2 – 4AC > 0, then the conic is ______. x“ = x^2; y“ = y^2 A. Ellipse B. Circle C. Hyperbola D. Parabola 11. If one inch equals 2.54 centimeters, how many inches are there in 20.32 centimeters? A. 7.2 B. 10.2 C. 9 D. 8 12. If the side of a square can be expressed as a^2bcube, what is the area of the square in simplified form? A. a^2b to the 6th power B. a^4b to the 6th power C. a^4b to the 5th power D. a^2b to the 5th power 13. Find the area bounded by y” = 4x and x” = 4y, of the square in simplified form? x“ = x^2; y“ = y^2 A. 5.33 B. 0.33 C. 8.33 D. 2.33 14. Hotels, like airlines, often overbook, counting on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservations will not be used if four reservations are made, what is the chance fewer than two will cancel? A. 0.3825 B. 0.7241 C. 0.5211 D. 0.8192 15. A chord of a circle of a diameter 10 ft is decreasing in length 1 ft/min. Find the rate of change of the smaller arc subtended by the chord when the chord is 8 ft. long. A. 3/5 ft/min B. 5/3 ft/min C. 3 ft/min D. 5 ft/min 16. Evaluate ∫lnx dx from 1 to e A. 0 B. 1 C. 2 D. 3 Past Board Exam Questions in Mathematics 17. Parcel charges of a courier company are follows: P40 for the first 2 kilograms P15 for each of the succeeding kilogram weight of parcels. With these rates, what amount would be charged on a parcel weighing 30 kg? A. P660 B. P450 C. P460 D. P650 18.A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function? A. Even quarter-wave B. Odd C. Odd quarter-wave D. Even 19. What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis? TROUBLESHOOT: 2xdy – ydx = 0; choose C A. 2ydx == xdy = 0 B. xdy + ydx = 0 C. 2xdx – ydy = 0 D. dy/dx – x = 0 20. Liza thought she had the exact money to buy 10 chocolate bars. However, the price per bar had increased by 50 centavos. Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have? A. 80 B. 40 C. 60 D. 30 21. Fred walks 0.75 miles to school; Raffy walks in 1.3 miles; Fely walks 2.8 miles; and Beth walks 0.54 miles. What is the total distance the four walk to school? A. 4.13 miles B. 5.39 miles C. 4.78 miles D. 5.63 miles 22. 42% of 997 = A. 499.44 B. 418.74 C. 450.24 D. 990.24 23. A 20 ft light post casts a shadow 25 ft long. At the same time, a building nearby casts a shadow 50 ft long. How tall is the building? A. 62 ft B. 94 ft C. 40 ft D. 10 ft 24. Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft high if the height is increasing at 2 in/min. TROUBLESHOOT: It should be in3/min A. 100,132.88 in/min B. 53,288.13 in/min Past Board Exam Questions in Mathematics C. 30.288.13 in/min D. 130,288.13 in/min 25. What type of conic is x” – 4y + 3x + 5 = 0? x“ = x^2 A. Hyperbola B. Parabola C. Circle D. Ellipse 26. The tangent of an angle of a right triangle is 0.75. What is the cosecant of the angle? A. 1.333 B. 1.414 C. 1.732 D. 1.667 27.The line passing through the focus and perpendicular to the directrix of a parabola is called ________. A. Latus rectum B. Axis C. Secant line D. Tangent line 28. Find the volume generated by revolving the circle x” + y” + 6x + 47 + 12 = 0 about the y-axis. x“ = x^2; y“ = y^2 A. 22.58 B. 55.28 C. 65.55 D. 59.22 29. The temperature at 6 PM 31 ½F. By midnight it had dropped 400F. What was the temperature at midnight? TROUBLESHOOT: ½ F = ˚F ; 400F = 40 ˚F A. -9½F B. 0½F C. -11½F D. 2½F 30. A shirt that regularly costs Php 340 is marked down 15%. What is the sale price of the shirt? A. Php 289.00 B. Php 338.50 C. Php 295.00 D. Php 190 31. The dimensions of a rectangular prism can be expressed as x + 1, x -2 and x + 4. In terms of x, what is the volume of the prism? x” = x2 A. x^3 + 5x” – 2x + 8 B. x^3 + 3x” – 6x – 8 C. x^3 + 3x” + 6x – 8 D. x^3 – 5x” + 2x + 8 32. The product of the sines of the angles of a triangle is maximum. What is the ratio of its sides? A. 1:2:2 B. 1:1:1 C. 1:2:1 D. 1:1:3 33. Compute log(3 – 2i) Past Board Exam Questions in Mathematics A. 0.5570 – 0.2554i B. 1.6575 + 0.8554i C. 0.2575 – 0.3545i D. 0.7580 + 0.7580i 34. The square of a number added to 25 equals 10 times the number. What is the number? A. -5 B. 5 C. -10 D. 10 35. Find the maximum value of 3^sin3x. š = ∞ A. 1/3 B. š C. 1 D. 3 36. What is the ratio of the sides of a triangle if the product of the sines of its angles is a maximum? A. 1:2:2 B. 1:1:2 C. 1:1:1 D. 1:3:3 37.After the price of gasoline went up by 10%, a consumer reduced his consumption by the same percent. By what percent would his gasoline bill be unchanged? A. 1% B. 10% C. 11% D. 0.1% 38. Larry finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower? A. 73.61 m B. 53.61 m C. 83.61 m D. 63.61 m 39. If y = 2x + sin2x, find x when y’ = 0. Ð = π A. 3Ð/2 B. 2Ð/3 C. Ð/2 D. Ð/3 40. When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. What is the radius of the ball bearing? A. 2.2 cm B. 0.6 cm C. 1.8 cm D. 1.2 cm 41. Evaluate lim x ---------------- x -->š sq root (1 + x) š = ∞ A. 0 B. 1 C. None D. Infinity 42. Which of the following equations is an exact differential equation? x“ = x^2 A. xdx + (3x – 2y)dy = 0 Past Board Exam Questions in Mathematics B. (2xy + x)dx + (x” + y)dy = 0 C. y"dx + (2x – 3y)dy = 0 D. (x” + 1)dx – xydy = 0 43. What is the conic section where eccentricity is less than 1? A. Circle B. Ellipse C. Parabola D. Line 44. Manuelita had 35 stuffed animals. Her grandmother gave fifteen of them to her. What percentage of the stuffed animals did her grandmother give her? TROUBLESHOOT: Manuelita had 75 stuffed animals… A. 15% B. 20% C. 10% D. 25% 45. A high school band teacher has a record of each student’s attendance. The result is listed below in days each student has been absent. 3, 4, 7, 2, 2, 1, 0, 0, 1, 0, 3, 3, 2, 1, 6, 0, 1, 0, 1, 1, 1, 5, 3, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, 4, What proportion of students have been absent less than 5 days? A. 0.06 B. 0.60 C. 0.90 D. 0.09 46.If log2=a, log3=b, log5=c, then log(7.5)=______. A. c/(a+b) B. ab/c C. c/ab D. b+c-a 47. Each of the question on a quiz is a five-part multiple choice question with exactly one correct answer. A student totally unprepared for the quiz, guesses on each 15 questions. How many questions should the student expect to answer correctly? A. 2 B. 13 C. 5 D. 3 48. Which of the following is not a multiple of 11? TROUBLESHOOT: C. 122 should be 121 A. 221 B. 759 C. 122 D. 1111 49. From the base of a building, the angle of elevation to the top of a 4.0 m vertical pole a distance away is 18 deg. 50 min. from the top of the building, the angle of depression of the base of the pole is 48 deg. 10 min. Find the height of the building. TROUBLESHOOT: D. 21.0 m should be 13.10 m A. 9.1 m B. 8.1 m C. 11.2 m D. 21.0 m 50. What is the maximum rectangular area that can be fenced in 20 ft. using two perpendicular corner sides of an existing wall? Past Board Exam Questions in Mathematics A. 310 square feet B. 120 square feet C. 100 square feet D. 250 square feet 51. From a sample size of 100, the following descriptive measures were calculated: median = 23; mean = 20; standard deviation = 5; range = 35. Seventy five sample values are between 5 and 35. If you knew the sample mean, median, and standard deviation were correct, which of the following conclusions might you draw? A. The number of sample values between 10 and 30 was miscounted B. The range must have been calculated incorrectly because it should not be seven times the standard deviation’s value C. The number of sample values between 5 and 35 have been miscounted because all 100 values must be in this interval. D. The distribution is skewed to the right because the median exceeds the mean. 52. Four is added to the quantity two minus the sum of negative seven and six. This answer is then multiplied by three. What is the result? A. 57 B. -21 C. 15 D. 21 53. Solve [y – square root of (x” + y”)] + xdy = 0 TROUBLESHOOT: The equation should be [y – square root of (x” + y”)] – xdy = 0 x" = x^2 and y” = y^2 A. Square root of (x” + y” + y) = C B. Square root of (x” + y”) + y = C C. Square root of (x” – y”) + y = C D. Square root of (x + y) + y = C 54.The value of a computer is depreciated over 5 years for tax purposes. That is, at end of 5 years, the computer is worth 0. If a business paid P21,000 for a computer, how much will it have depreciated after 2 years? A. P4,200 B. P8,400 C. P10,500 D. P8,200 56. If 1 cm = 0.39 in, about how many cm are there in 0.75 in? A. 0.52 B. 1.75 C. 0.29 D. 1.92 57. Find the area of the square whose side is a^2 b^3. A. a^2 b^3 B. a^2 b^6 C. a^4 b^3 D. a^4 b^6 58. Evaluate sin [Arccos (-2/3))] A. Square root of 3 B. Square root of 5 C. (1/3)square root of 5 D. (1/5)square root of 3 59. Find the volume generated when the area bounded by y = 2x + 3 and y = x>> is revolved about the x-axis. x>> = x^2 Past Board Exam Questions in Mathematics A. 422 B. 300 C. 308 D. 228 60. Evaluate lim (2 – x)^tan Ðx/2 x--> 1 Ð = π A. Infinity B. e^2/Ð C. e^2Ð D. e 61. Daniel has one more Algebra exam to take before computing the average of his grades. His Algebra scores so far are 93, 54, 94, 36, 97. What must be his score on this last exam so he can maintain his present average? TROUBLESHOOT: 54 → 94; 36 → 96. His scores should be 93, 94, 94, 96, 97 A. 94 B. 95 C. 92 D. 97 62. When two lines are parallel, the slope of one is A. The negative of the other B. Equal to the other C. The negative reciprocal of the other D. The reciprocal of the other 63. For the 2 functions, f(x) and g(x), tables of values are shown below. What is the value of g[f(2)]? TROUBLESHOOT: It should be g[f(3)] x º f(x) x º g(x) -------- -------- -5 º 7 -2 º 3 -1 º -5 1 º -3 1 º 3 2 º -3 3 º 2 3 º -5 A. -1 B. -5 C. -3 D. 2 63.The difference between six times the quantity 6x + 1 and three times the quantity x – 1 is 108. What is the value of x? A. 35/11 B. 3 C. 12 D. 12/11 64. Michael walks to school. He leaves each morning at 7:32 A.M. and arrives at school 15 minutes later. If he travels at steady rate of 4.5 miles/hr, what is the distance between his home and school? A. 1.8 miles B. 1.5 miles C. 1.9 miles D. 1.1 miles 65. What percentage of 18000 is 234? A. 1.3% B. 1 300% C. 130% Past Board Exam Questions in Mathematics D. 13% 66. Jun rows his banca across a river at 4 kph. How long will it take Jun to cross the river? TROUBLESHOOT: The choices are in minutes. A. 34.25 B. 0.25 C. 43.22 D. 3.75 67. Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft high if the height is increasing at 2 in/min. TROUBLESHOOT: It should be in3/min A. 100,132.88 in/min B. 53,288.13 in/min C. 30.288.13 in/min D. 130,288.13 in/min 68. Jonas is 5ft 11 in tall and Pedro is 6ft 5 in tall. How much taller is Pedro than Jonas? A. 1 ft B. 6 in C. 7 in D. 1 ft 7 in 69. A man is running around a circular track, 200 m in circumference. An observer uses a stopwatch to time each lap, obtaining the data as follows: Time (sec) Distance (m) 30 200 68 400 114 600 168 800 230 1000 300 1200 378 1400 What is the man’s average speed between 68 sec and 168 sec? A. 3 m/s B. 8 m/s C. 1.82 m/s D. 4 m/s 70. The time a student spends learning a computer software package is normally distributed with a mean of 8 hours and standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends less than 6 hours learning a software package? A. 1 B. 0.15 C. 0.21 D. 0.09 71.Sam scored 96% on his first Calculus quiz, 74% on his second and 85% on his third. What is his quiz average? A. 85% B. 75% C. 96% D. 95% 72. A line segment is a size of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle? A. 2:1 B. 4:1 C. 1:1 Past Board Exam Questions in Mathematics D. 3:2 73. The position vectors of points A and B are: 2 + i and 3 – 2i, respectively. Find an equation for line AB. A. x – 3y = -4 B. –x + 4y = 5 C. 3x – y = 2 D. 3x + y = 7 74. From the top of a building 100 m high, the angles of depression of two cars due east of the observer are 32 degrees 25’ and 58 degrees 33’ respectively. Find the distance between the cars. A. 106.00 m B. 96.30 m C. 9.63 m D. 63.91 m 75. Find the centroid of a semi-circular region of radius a. Ð = π A. a/2Ð B. 4a/3Ð C. 3a/4Ð D. a/Ð 76. Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486. A. 540 B. 748 C. 984 D. 844 77. Given: sin A = -4/5, A in Quadrant III cot B = 4.5 B in Quadrant III Evaluate sin (A + B) TROUBLESHOOT: It should be cot B = 4.0 A. 5/19square root of 17 B. 19/5square root of 17 C. Square root of 17 D. -1/square root of 17 78. Evaluate f(-3) if f(x) = x” – 2x + 1. A. 16 B. 8 C. 48 D. 32 79. What conic section is described by the equation 4x” – “y” +8x + 4y = 15 x“ = x^2; y“ = y^2 A. Ellipse B. Hyperbola C. Parabola D. Circle 80. What is 20% of 96? A. 19.20 B. 0.09 C. 0.92 D. 1.92 81.A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least P50. A random sample of 20 alumni is selected. What is the probability that less than 17 alumni will make a contribution of at least P50? A. 0.589 B. 0.301 C. 0.200 Past Board Exam Questions in Mathematics D. 0.421 82. At exactly what time after 5 o’clock will the hour hand and the minute hand be perpendicular for the first time? A. 5:10 and 54 sec. B. 5:15 and 25 sec. C. 5:05 and 34 sec. D. 5:20 and 14 sec. 83. Find the equation of the normal line to x” + y” = 1 at the point (2, 1). A. y = 2x B. x – y = 0 C. x = 2y D. x + y = 1 84. Mon and Mila can restock an aisle at the supermarket in 1 hour working together. Working alone, Mon can restock and aisle in 1.5 hours and Mila in 2 hours. If they work together in 2 hours, how many aisles will they have completed? A. 5.11 B. 4.33 C. 4.50 D. 3.50 85. Solve the differential equation y'’ – 4 y’ + 3y = sinx A. y(x) = C1 e^3x + C2 e^x + 1/5 cos x + 1/10 sin x B. y(x) = C1 e^3x + C2 e^x sin x C. y(x) = C1 sin 3x + C2 x + cos 3x D. y(x) = C1 sin x + C2 x + 1/10 sin x 86. Find solution to the system of equations x – 2y = 5 and 2x + 5y = 1. A. (3, -1) B. (-1, -3) C. (3, 1) D. (1, 3) 87. What is the smallest positive value of x where y = sin2x reaches maximum? A. Ð/4 B. Ð C. 3Ð/2 D. 2Ð 88. A movie is scheduled for 2 hours. The theater advertisements are 3.8 long. There are two previous ones: 4.6 min and 2.9 min long. The rest of the time is devoted to the feature. How long is the feature film? A. 94.3 min B. 97.5 min C. 108.7 min D. 118.9 min 89. Find the vertex of the parabola x^2 = 4y. A. (4, 0) B. (0, 0) C. (0, 4) D. (-4, 0) 90.If the coefficient ao of a Fourier series of a periodic function of zero, it means that the function has A. Odd-quarter wave symmetry Past Board Exam Questions in Mathematics B. Even-quarter wave symmetry C. Odd symmetry D. Odd symmetry or even-quarter wave symmetry or odd-quarter wave symmetry 91. The towns are located near the straight shore of the lake. Their nearest distances to the point in the shore are 1 km and 2 km respectively, and these points on the shore are 6 km apart. Where should be the finish port be located to maximize the total amount of paving necessary to build a straight road from each town to the pier. A. 12 km from the point on the shore nearest the first town B. 12 km from the point on the shore nearest the other town C. 2 km from the point on the shore nearest the first town D. 2 km from the point on the shore nearest the other town 92. When the energy/hour required in driving a boat varies as the cube of the velocity, find the most economical rate/hour when going against rest current of 4 kph. A. 5 kph B. 12 kph C. 8 kph D. 6 kph 93. The sum of the distances from the two foci to any point in what curve is constant? A. Hyperbola B. Parabola C. Any conic D. Ellipse 94. The equation x” + Bx + y” + Cy + D = 0 is: x“ = x^2; y“ = y^2 A. Hyperbola B. Ellipse C. Circle D. Parabola 95. Solve the equation 5z” + 2z + 10 = 0 A. 1 – i, 1 – 2i B. 1 + i, 1 – 2i C. 1 + i, 1 – 2i D. (-1 ± 7i)/5 96. A normal to a given plane is A. Perpendicular to the plane B. Parallel to the plane C. Lying in the plane D. Oblique to the plane 97. The area of a square whose sides measures 4 units is added to the difference of 11 and 9 divided by 2. What is the total value? A. 5 B. 9 C. 16 D. 17 98. The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find the width of the rectangle. A. 14.5 inches B. 37.5 inches C. 13.5 inches D. 15 inches Past Board Exam Questions in Mathematics 99.The current I following in an RL circuit is given by I = (E/R)(1 – e^Rt/L), where E is the voltage applied to the circuit, R is the resistance and L is the inductance, Express I in terms of E and R when t = L/R. TROUBLESHOOT: I = (E/R)(1 – e^-Rt/L) A. 0.632 (E/R) B. 0.435 (E/R) C. 0.548 (E/R) D. 0.388 (E/R) 100. If a person throws away 3.5 lbs of trash daily, how much trash will the person throw away in one week? A. 24.0 lbs B. 24.5 lbs C. 40.2 lbs D. 31.5 lbs Past Board Exam Questions in Mathematics April 2022 1. A conic section whose eccentricity is less than one (1) is known as: A. A parabola B. An ellipse C. A circle D. A hyperbola 2. Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. A. 2.5 mils B. 1 mil C. 4 mils D. 2.04 mils 3. The geometric mean and the arithmetic mean of numbers are 8 and 10 respectively. What is the harmonic mean? A. 7.5 B. 5.7 C. 6.4 D. 4.6 4. The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the focus of the parabola. Find the value of p. A. 3/5 a B. 5/3 a C. 2/5 a D. 5/2 a 5. Find the minimum distance from the point P (4,2) to the parabola y^2 = 8x. A. 3 sqrt. of 3 B. 2 sqrt. Of 3 C. 3 sqrt. of 2 D. 2 sqrt. of 2 6. Find all the values for z for which e^4z = i. A. 1/6 pi i + 1/2 k pi i B. -1/6 pi i + 1/2 k pi i C. 1/8 pi i + 1/2 k pi i D. -1/8 pi i + 1/2 k pi i 7. Three circles of radii 3, 4, and 5 inches, respectively are tangent to each other externally. Find the largest angle of a triangle formed by joining the centers. A. 72.6º B. 75.1º C. 73.4º D. 73.3º 8. Find the length of the vector (2,4,4). A. 6 B. 7 C. 8 D. 9 9. Find the domain of the function f(x) = 3x, -6≤x≤8? A. (-6, 8) B. [-18, 24] C. (-18, 24) D. [-6, 8] 10. Ten liters of 25% salt solution and 15 liters of 25% salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration of salt in the mixture? A. 16.82% Past Board Exam Questions in Mathematics B. 28.15% C. 21.52% D. 19.55% 11.Listed below are functions each denoted g(x) and each involving a real number x, constant c > 1. If f(x) = 2x, which of these functions yield the greatest value for f(g(x)), for all x > 1? A. g(x) = cx B. g(x) = c/x C. g(x) = c – x D. g(x) = x/c 13. From the past experience, it is known 90% of one-year-old children can distinguish their mother voice of a similar sounding female. A random sample of 20 one year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their Mother’s voice. Find the mean of x. A. 20 B. 2 C. 4 D. 1 14. A tangent to a conic is a line which A. Passes inside a conic B. Touches the conic at only one point C. Is parallel to the normal D. Touches the normal 15. A certain two-digit number is equal to five times the sum of its digit. If 9 were added to the number, its digits would be reversed. Find the number. A. 8 B. 7 C. 9 D. 6 16. Find the sum of the first 100 positive odd numbers. A. 10,000 B. 5,000 C. 9,899 D. 8,910 17. The locus of a point which moves so that its distance from a fixed point and a fixed line is always equal is. A. Hyperbola B. Circle C. Parabola D. Ellipse 18. It represents the distance of a point from the x-axis. A. Ordinate B. Coordinate C. Abscissa D. Polar distance 19. A contractor has 50 men of the same capacity at work on a job in 30days, the working day being 8 hours, but the contract expires in 20 days. How many workers should he add? A. 30 B. 25 C. 15 D. 20 20. What is the graph of the equation Ax^2 + Cy^2 + Dx + Ey + F = 0? A. Ellipse Past Board Exam Questions in Mathematics B. Hyperbola C. Parabola D. Circle 21. What is the shape of the graph of the polar equation r = a + bcosθ? A. Limacon B. Cardioid C. Lemniscate D. Circle 21.From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice similar sounding female. A random sample of 20 one year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the variance. A. 2 B. 1.8 C. 4.2 D. 1.5 22. Find the area of the polygon with vertices at 2 + 3i, 3 + i, -2 - 4i, -4 – i, -1 + 2i. A. 47/5 B. 47/2 C. 45/2 D. 45/4 23. What is the differential equation of the family of circles with center at the y-axis? A. xy" + (y’)3 + y’ = 0 B. xy” – (y’)3 + y’ = 0 C. xy” + (y’)3 – y’ = 0 D. xy” – (y’)3 – y’ = 0 24. Find the area bounded by the line x – 2y + 10 = 0, the x-axis, the y-axis and x = 10. A. 75 sq. units B. 50 sq. units C. 100 sq. units D. 25 sq. units. 25. What is the Laplace of F(x) = 2, from 0 ≤ x ≤ 3 and F(x) = x, where x ≥ 3. A. 2/s + e^-3s (1/s + 1/s^2) B. 1/s + e^-3s (1/s + 1/s^2) C. 1/s - e^-3s (1/s) D. 2/s + 1/s^2 26. If the roots of an equation are zero, then they are classified as. A. Trivial solution B. Hyperbolic solution C. Zeros of solution D. Extraneous roots 27. Which of the following is true? A. sin(-θ)=sin(θ) B. tan(-θ)=tan(θ) C. cos(-θ)=cos(θ) D. csc(-θ)=csc(θ) 28. A frequency curve which is composed of a series of rectangle constructed with the steps as the base and the frequency as the height. A. Histogram B. Ogive C. Frequency distribution Past Board Exam Questions in Mathematics D. Bar graph 29. The angular distance of a point on the terrestrial sphere from the North Pole is called. A. Co-latitude B. Altitude C. Latitude D. Co-decination 30. It is a sequence of numbers such that successive terms differ by a constant. A. Arithmetic progression B. Geometric progression C. Infinite progression D. Harmonic progression 31.If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is. A. A paraboloid B. A sinusoid C. A cissoids D. An exponential 32. Each of the faces of a regular hexahedron is a. A. Triangle B. Square C. Rectangle D. Hexagon 33. The integral of any quotient whose numerator is the differential of the denominator is A. Product B. Derivative C. Cologarithm D. Logarithm 34. If a=b, then b=a. This illustrate which axiom in algebra? A. Replacement axiom B. Transitive axiom C. Symmetric axiom D. Reflexive axiom 35. It is the measure of relationship between two variables. A. Correlation B. Function C. Equation D. Relation 36. It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms. A. Cube B. Pyramid C. Prism D. Parallelepiped 37. Find the coordinates of the centroid of the plane are bounded by the parabola y=4-x^2 and the x-axis. A. (0,1) B. (0,1.6) C. (0,2) D. (1,0) 38. Find the moment of inertia of the area bounded by the parabola y^2 = 4x and the line x=1, with respect to the x-axis. A. 2.133 B. 1.333 Past Board Exam Questions in Mathematics C. 3.333 D. 4.133 39. A survey of 500 television viewers produced the following result: 285 watch football games; 195 watch Hockey games; 115 watch basketball games; 45 watch football and basketball games; 70 watch football and hockey games; 50 watch hockey and basketball games; 50 do not watch any of the three games. How many watch basketball games ONLY? A. 30 B. 40 C. 60 D. 50 40. Find the equation of the normal to x^2 + y^2 = 1 at the point (2, 1). A. x – y = 0 B. x = 2y C. y = 2x D. x + y = 1 41.A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8 cm/hr. If the icicle is currently 4 cm in radius and 20 cm long, is the volume of the icicle increasing or decreasing, and at what rate? A. Decreasing at 20 cu. cm/hr B. Increasing at 24 cu. cm/hr C. Decreasing at 24 cu. cm/hr D. Increasing at 20 cu. cm/hr 42. The drivers at F and M trucking must report the mileage on their vehicle each week. The mileage reading of Ed’s vehicle was 20, 907 at the beginning of one week, 21, 053 at the end of the same week. What is the total number of miles driven by Ed that week? A. 145 miles B. 1046 miles C. 146 miles D. 46 miles 43. Marvin helps his teachers plan a field trip. There are 125 persons to the field trip and each school bus holds 48 persons. What is the minimum number of school buses is needed to reserve for the trip? A. 5 B. 4 C. 3 D. 2 44. A point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing is known as A. Inflection point B. Minimal point C. Maximum point D. Point of tangency 45. How many ancestors does a set of triplets have in the eleven generations before them? Assume there are no duplicates. A. 4085 B. 4005 C. 4009 D. 4095 46. Approximately how many liters of water will a 10-gallon container hold? A. 42 B. 42 C. 9 D. 38 Past Board Exam Questions in Mathematics 47. In an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms? A. 3, 36 1/3, 70 B. 3, 10, 17 C. 3, 23, 43 D. 3, 69 1/2, 136 48. Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally? A. 30 B. 20 C. 50 D. 40 49. Find the equation of the circle tangent to 4x – 3y + 12 = 0 at (-3, 0) and tangent also is 3x + 4y – 16 = 0 at (4, 1) A. x^2 + y^2 + 4x – 3y + 6 = 0 B. x^2 + y^2 + x 0 2y + 3 = 0 C. x^2 + y^2 + x – y + 5 = 0 D. x^2 + y^2 – 2x + 6y – 15 = 0 50.A steel girder 8 m long is moved on rollers along a walkway 4 m wide and into a corridor perpendicular to the walkway. How wide must the corridor be to successfully move the girder? A. 1.8 m B. 18 m C. 10 m D. 8 m 51. On a particular morning, the temperature went up 1 degree every 2 hours. If the temperature was 53 degrees at 5 A. M. at what time was it 57 degrees? A. 12 P.M. B. 1 P.M. C. 8 A.M. D. 7 A.M 52. What do you call a radical expressing an irrational number? A. Surd B. Radix C. Complex number D. Index 53. In two intersecting lines, the angles opposite to each other are termed as______. A. Opposite angles B. Vertical angles C. Horizontal angles D. Inscribed angles 54. What do you call the integral divided by the difference of the abscissa? A. Average value B. Mean value C. Abscissa value D. Integral value 55. When the ellipse is rotated about its longer axis, the ellipsoid is ______. A. Spheroid B. Oblate C. Prolate D. Paraboloid Past Board Exam Questions in Mathematics 56. In polar coordinate system, the distance from a point to the pole is known as____. A. Polar angle B. Radius vector C. X-coordinate D. Y-coordinate 57. The axis of the hyperbola through its foci is known as _____. A. Conjugate axis B. Traverse axis C. Major axis D. Minor axis 58. The axis of the hyperbola which is parallel to its directrices is known as ______. A. Conjugate axis B. Traverse axis C. Minor axis D. Major axis 59. The symbol “/” used in division is called _______. A. Solidus B. Modulus C. Minus D. Obelus 60.A point of the curve where the second derivative of a function is equal to zero is called____. A. Maxima B. Minima C. Point of inflection D. Point of intersection 61. To compute for the value of the factorial, in symbolic form (n!) where n is a large number, we use a formula called. A. Matheson formula B. Stirlings approximation formula C. Diophantine formula D. Richardson-Duchman formula 62. When two planes intersect with each other, the amount of divergence between the two planes is expressed by the measure of. A. Polyhedral B. Dihedral C. Reflex angle D. Plane angle 63. The median of a triangle is the line connecting a vertex and the midpoint of the opposite side. For a given triangle, the medians intersects at a point which is called. A. Circumcenter B. Incenter C. Orthocenter D. Centroid 64. A five pointed star is also known as. A. Pentagon B. Quintagon C. Pentatron D. Pentagram Past Board Exam Questions in Mathematics 65. Give one indicated root of (-16i)^1/2. TROUBLESHOOT: (-16i)^1/4 A. 2cis330deg B. 2cis165deg C. 2cis167.5deg D. 2cis67.5deg 66. A snack machine accepts only 5-centavo coins. Chocolate bars cost 25cent each, packages of peanuts cost 75cent each and a can of cola costs 50 cent. How many 5-centavo coins are needed to buy 2 chocolates bars, one pack of peanuts and a can of soda? A. 30 B. 32 C. 35 D. 6 67. If a derivative of a function is constant, the function is_____. A. 1st degree B. Exponential C. Logarithmic D. Sinusoidal 68. During an examination, the following scores are collected: 0 8 9 11 12 13 18 18 20. If there was an error in encoding where “18” should be “16”, which of the following is affected? A. Mean B. Standard deviation C. Mean and standard deviation D. Median 69.A transmitter with a height of 15 m is located on the top of a mountain which is 3 km high. What is the farthest distance on the surface of the earth that can be seen from the top of the mountain? Take the radius of the earth to be 6400 km. A. 205 km B. 152 km C. 225 km D. 196 km 70. A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lbs of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank the mixture at 2 gpm. Find the amount of salt in the tank at the end of 30 minutes. A. 171.24 lbs B. 124.11 lbs C. 143.25 lbs D. 105.12 lbs Past Board Exam Questions in Mathematics September 2022 1. An epidemic spread at a rate jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 5000 inhabitants, 160 people have the disease at the beginning of the week and 1200 have it at the end of the week. How many days does it take for 80% of the population to become infected? A. 15 days B. 18 days C. 20 days D. 23 days 2. Given is an 8 cm square. If the second square is made by connecting the midpoints of the sides of the first square and the third square is made by connecting the midpoints of the sides of the second square and this process continuous indefinitely, find the sum of the perimeters of the squares. A. 102.95 B. 109.25 C. 1.09 D. 105.92 3. The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is A. (11, -24) B. (-11, -20) C. (11, -18) D. (11, -20) 4. In the curve 2+12x-x^3, find the critical points. A. (2, 18) & (-2, -14) B. (2, 18) & (2, -14) C. (-2, 18) & (-2, 14) D. (-2, 18) & (2, -14) 5. A statue 3 m high is standing on a base of 4m high. If an observers eye is 1.5 m above the ground how far should he stand from the base in order that the angle subtended by the statue is a maximum? A. 3.41 B. 3.51 C. 3.71 D. 4.41 6. Two engineers facing each other with a distance of 5km from each other, the angles of elevation of the balloon from the two engineers are 56 degrees and 58 degrees, respectively. What is the distance of the balloon from the two engineers? A. 4.45 km, 4.54 km B. 4.54 km, 4.45 km C. 4.64 km, 4.54 km D. 4.46 km, 4.45 km 7. A tangent to a conic is a line A. Which is parallel to the normal B. Which touches the conic at only one point C. Which passes inside the conic D. All of the above 8. The area enclosed by the ellipse 4x^2 + 9y^2= 36 is revolved about the line x = 3, what is the volume generated? A. 370.3 B. 360.1 C. 355.3 D. 365.1 Past Board Exam Questions in Mathematics 9. A conic section whose eccentricity is less than one (1) is known as: A. A parabola B. An ellipse C. A circle D. A hyperbola 10.Evaluate the double integral of 1/ (x-y) dxdy with inner bounds of 2y to 3y and outer bounds of 0 to 2. A. ln3 B. ln4 C. ln2 D. ln8 11. The centroid of the area bounded by the parabola y^2 = 4ax and the lin x = p coincides with the focus of the parabola. Find the value of p. A. 3/5 a B. 5/3 a C. 2/5 a D. 5/2 a 12. Find the area of the polygon with vertices at: 2+3i, 3+i, -2-4i, -4-i, -1+2i A. 47 B. 35/2 C. 25 D. 47/2 13. Evaluate ∫lnxdx from 1 to e A. 0 B. 1 C. 2 D. 3 14. The dimensions of a rectangular prism can be expressed as x+1, x-2, and x+4. In terms of x, what is the volume of the prism? A. x^3 + 5x” – 2x + 8 B. x^3 + 3x” – 6x + 8 C. x^3 + 3x” + 6x – 8 D. x^3 – 5x” + 2x + 8 15. Melissa is 4 times as old as Jim. Pat is 5 years older than Melissa. If Jim is y, how old is Pat? A. 4y + 5 B. y + 5 C. 5y + 4 D. 4 + 5y 16. Solve for the limit lim |x + 2| x-->-2 A. 0 B. 1 C. Pi D. Infinity 17. From the top of a building the angle of depression of the foot of a pole is 48 deg 10 min. From the foot of a building the angle of elevation of the top of a pole is 18 deg 50 min. Both building the pole are on a level ground. If the height of a pole is 4 m, how high is the building? A. 13.10 m B. 12.10 m C. 10.90 m D. 11.60 m 18. Carmela and Marian got summer jobs at the ice cream shop and were supposed to work 15 hours per week each for 8 weeks. During that time, Marian was ill for one week and Carmela took her shifts. How many hours did Carmela work during the 8 weeks? Past Board Exam Questions in Mathematics A. 120 B. 135 C. 150 D. 185 19.Find the moment of inertia of the area bounded by the parabola y^2 = 4x and the line x = 1, with respect to x-axis. A. 2.133 B. 1.333 C. 3.333 D. 4.133 20. A political scientist asked the group of people how they felt about the policy statements. Each person was to respond A (agree), N neutral or D disagree to each NN, ND, NA, DD, DA, AA, AD, and AN. Assuming each response combination is equally likely, what is the probability that the person being interviewed agrees with exactly one of the two policy statements? A. 1/9 B. 2/9 C. 2/5 D. 4/9 21. There are a set of triplets. If there are 11 generations, how many ancestors do they have if duplication is not allowed? A. 4095 B. 59,049 C. 4085 D. 4064 22. Solve the equation y’ = y/2x. A. y^2 = cx^3 B. y = cx^2 C. y^2 = cx D. y = cx 23. A ball is dropped from a height of 18m. On each rebound it rises 2/3 of the height form which it last fell. What distance has it traveled at the instant it strikes the ground for the 5th time? A. 37.89 m B. 75.78 m C. 73.89 m D. 57.78 m 24. A cylindrical container open at the top with minimum surface area at a given volume. What is the relationship of its radius to height? A. Radius = height B. Radius = 2height C. Radius = height/2 D. Radius = 3 height 25. Solve (x + y)dy = (x – y)dx A. x^2 + y^2 = C B. x^2 – 2xy – y^2 = C C. x^2 + 2xy + y^2 = C D. x^2 – 2xy + y^2 = C 26. Solve Re[(1 i)^(1 + i)] A. B. C. D. Past Board Exam Questions in Mathematics 27. A cylindrical can is to have volume 1000 cubic centimeters. Determine the height which will minimize the amount of material to be used. A. 11.84 cm B. 10.84 cm C. 12.84 cm D. 10.64 cm 28.A cylindrical can is to have volume 1000 cubic centimeters. Determine the radius which will minimize the amount of material to be used. A. 5.42 cm B. 7.24 cm C. 6.42 cm D. 4.25 cm 29. A container is in the form of a right circular cylinder with an altitude of 6 in and a radius of 2 in. If an asbestos of 1 in thick is inserted inside the container along its lateral surface, find the volume capacity of the container. A. 12.57 cu.in B. 12.75 cu.in C. 18.58 cu.in D. 18.85 cu.in 30. Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft high if the height is increasing at 2 in/min. TROUBLESHOOT: It should be in3/min A. 100,132.88 in/min B. 53,288.13 in/min C. 30.288.13 in/min D. 130,288.13 in/min 31. Find the area bounded by the parabola x^2 + 2x + 2y + 5 0 and x^2 – x + y + 1 = 0. A. 14 B. 14/3 C. 16 D. 16/3 32. Simplify the following: cosA + cosB + sinA + sinB ----------- --------- --- sinA – sinB cosA – cosB A. 0 B. sinA C. 1 D. cosA 33. A 6 foot pine tree is planted 15 feet from a lightened streetlight whose lamp is 18 feet above the ground. How many feet long is the shadow of the tree? A. 5.0 B. 7.5 C. 7.8 D. 9.6 34. Chona the golden retriever gained 5.1 pounds in one month. She weighs 65.1 pounds now. What is the percentage weight gain of Chona in one month? A. 7.3% B. 8.5% C. 6% D. 9.1% 35. A stone is thrown into still water and causes concentric circular ripples. The radius of the ripples increases at the rate of 12 in/s. At what rate does the area of the ripple increases in sq. in/s when its radius is 3 inches? Past Board Exam Questions in Mathematics A. 402.55 B. 226.19 C. 275.60 D. 390.50 36. The coefficient ao of a Fourier series of a periodic function is zero, it means that the function has A. Odd-quarter wave symmetry B. Even-quarter wave symmetry C. Odd symmetry D. Odd symmetry or even-quarter wave symmetry or odd-quarter wave symmetry 37.Donations were made by alumni for a school to fund a new computer room. Data shows that 80% of alumni give at least P50. If the administration contacts 20 alumni, what is the probability that less than 17 of them will give at least P50. A. 0.589 B. 0.746 C. 0.164 D. 0.761 38. A code is composed of 2 letters, the first being a vowel and three digits. In how many ways can be it made without repetition? A. 18,000 B. 20,000 C. 90,000 D. 70,000 39. A group of five friends went out to lunch. The total bill for the lunch was $53.75. Their meals all cost about the same, so they wanted to split the bill evenly. Without considering tip, how much should each friend pay? A. $11.25 B. $10.75 C. $12.85 D. $11.50 40. Susan starts work at 4:00 and Dee starts at 5:00. They both finish at the same time. If Susan works x hours, how many hours does Dee work? A. x + 1 B. x C. x – 1 D. 2x 41. The distance from the sun to the earth is approximately 9.3 x 10^-7 miles. What is the distance expressed ins standard notation? A. 930,000,000 B. 0.00000093 C. 93,700,000 D. 93,000,000 42. Peter can paint a room in an hour and a half and Joe can paint the same room in 2 hours. How many minutes will it take to paint the room if they do it together? Round answer to nearest minute. A. 51 B. 30 C. 64 D. 210 43. What is the greatest common factor of 24 and 64? A. 8 B. 12 C. 4 D. 16 Past Board Exam Questions in Mathematics 44. A machine on a production line produces parts that are not acceptable by company standards four percent time. If the machine produces 500 parts, how many will be defective? A. 8 B. 16 C. 10 D. 20 45. Lisa originally brought exact amount of money to buy 10 chocolates. She then discovers that the price of chocolate went up by 50 centavos each. She was able to buy 8 chocolates and have an extra of 2 pesos. How much did Lisa bring originally? A. 80 B. 40 C. 60 D. 30 46.If is a conic section with B^2 – 4AC greater than zero is A. Circle B. Ellipse C. Parabola D. Hyperbola 47. A chord of a circle of a diameter 10 ft is decreasing in length 1 ft/min. Find the rate of change of the smaller arc subtended by the chord when the chord is 8 ft long. A. 3/5 ft/min B. 5/3 ft/min C. 3 ft/min D. 5 ft/min 48. A normal to a given plane is A. Oblique to the plane B. Parallel to the plane C. Perpendicular to the plane D. Lying in the plane 49. Melinda and Joaquin can restock and aisle at the supermarket in one hour working together. Melinda can restock an aisle in 1.5 hours working alone, and it takes Joaquin two hours to restock an aisle. If they work together for two hours, and then work separately for another two hours, how many aisles will they have completed? A. 5 B. 4.33 C. 4.5 D. 3.5 50. Evaluate TROUBLESHOOT: The given should be (1+sinx)/(1-sinx) – (1-sinx)/(1+sinx) 1 + six 1 - sinx ------- + -------- 1 – sinx 1 + sinx A. -4tan(x)csc(x) B. 4tan(x)csc(x) C. 4tan(x)sec(x) D. -4tan(x)sec(x) 51. The temperature of the room at 6:00 PM is 31 1/2F. At midnight the temperature drops by 400 1/2F. What was the temperature at midnight? A. 9 1/2F B. -9 1/2F C. 11 1/2F Past Board Exam Questions in Mathematics D. -11 1/2F 52. A transmitter with a height of 15 m is located on the top of a mountain which is 3 km high. What is the farthest distance on the surface of the earth that can be seen the top of the mountain? Take the radius of the earth to be 6400 km. A. 205 km B. 152 km C. 225 km D. 196 km 53. Three circles of radii 3, 4, and 5 inches respectively, are tangent to each other externally. Find the largest angle of the triangle formed by joining the centers. A. 72.6º B. 73.4º C. 75.1º D. 73.3º 54.An air balloon flying vertically upward at constant speed is situated 150 m horizontally from an observer. After one minute, it is found that the angle of elevation from the observer is 28 deg 59 min. what will be the angle of elevation after 3 minutes from its initial position? A. 48º B. 61º C. 59º D. 50º 55. Find the equation x = y = z that is equidistant from (3,0,5) amd (1,-1,4) A. (1,1,1) B. (3,3,3) C. (2,2,2) D. (4,4,4) 56. A steel girder 8 m long is moved on rollers along a passage 4 m wide and into a corridor at right angles to the passageway. Neglecting the width of the girder, how wide must the corridor be? A. 2.0 m B. 1.8 m C. 2.4 m D. 3.6 m 57. What is the length of the shortest line that can be drawn tangent to the ellipse b2x2 + a2y2 = a2b2 and meeting the coordinate axes? A. a2 + b2 B. a + b C. sqrt(a2 + b2) D. ½ sqrt(a2 + b2) 58. One end of a 32-meter ladder resting on a horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2 meters per minute. How fast is the top of the ladder rising when its foot is 10 meters from the wall? A. +0.568 m/min B. +0.658 m/min C. +0.896 m/min D. +0.986 m/min 59. Identify the curve described by |z – 3i| - |z + 3i| = 4 A. Ellipse B. Line C. Circle Past Board Exam Questions in Mathematics D. Hyperbola 60. From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice similar sounding female. A random sample of 20 one year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the variance. A. 2 B. 1.8 C. 4.2 D. 1.5 61. Emilio is 1 year and 7 months old and Brooke is 2 years 8 months old. How much older is Brooke than Emilio? A. 1 year and 1 month B. 1 month C. 2 years D. 1 year and 2 months 62. Observer A and B are 53 km from each other. At an instant an airplane passed by, if the angle of elevation of A and B are 56’18” and 48’26” respectively, what is the distance of the plane from the ground? A. 33.41 km B. 31.15 km C. 34.11 km D. 35.41 km 63.Find the orthogonal trajectories of the family of parabolas y^2 = 2x + C. A. y = Ce^6 B. y = Ce^(-x) C. y = Ce^(2x) D. y = Ce^(-2x) 64. Manuelita had 75 stuffed animals. Her grandmother gave fifteen of them to her. What percentage of the stuffed animals did her mother give her? A. 20% B. 25% C. 15% D. 10% 65. A cardboard 20 in x 20 in is to be formed into a box cutting four equal squares and folding the edges. Find the volume of the largest box. A. 592 cu.in. B. 698 cu.in. C. 529 cu.in. D. 689 cu.in. 66. What percentage of the volume of a cone is the maximum volume right cylinder that can be inscribed in? A. 24% B. 44% C. 34% D. 54% -engrKang☺

MATH Past Board Exam Questions 2019-2022 PDF

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