MESL

• A woman bought three times as many cans of peaches and two times as many cans of tuna as cans of peaches. She purchased a total of 24 cans. How many cans did she buy?

  • She bought 4 cans of peaches, 8 cans of tuna, and a total of 12 cans (Option C)
• A man makes a business trip from his house to Batangas in 2 hours. One hour later, he returns home in traffic at a rate of 20kph less than his going rate. If he is gone a total of 6 hours, how fast did he travel going back home?

  • He traveled at 40kph going back home (Option C)
• A trapezoid has its two bases in a ratio of 4:5 with a height of 20 meters. If the trapezoid has an area of 360, find the two bases.

  • The two bases are 20 meters and 16 meters (Option A)
• Which of the following is the nth term of the set of numbers 8, 4, 0, -4?

  • The nth term is 12-4n (Option A)
• A spring with a normal length of 10 inches and a modulus of 12 pounds per inch. How much work is done in stretching this spring from a length of 12 inches to a total length of 15 inches?

  • The work done is 126 in-lb (Option A)
• A right circular tank of depth 12 feet and radius of 4 feet is half full of oil weighing 60 pounds per cubic foot. Find the work done in pumping the oil to a height 6 feet above the tank.

  • The work done is 136 ft-tons (Option A)
• Hooke’s law states that within the limits of elasticity, the displacement produced in a body is proportional to the force applied. If the modulus of a spring is 20 pounds per inch, the work required to stretch or compress the spring a distance of 6 inches is:

  • The work required is 30 in-lb (Option A)
• What is the value of square root -7 times square root of -10?

  • The answer is the negative square root of 70 (Option B)
• The points A(1,0), B(9,2), and C(3,6) are vertices of a triangle. Which of the following is an equation of one of the medians?

  • The equation of one of the medians is x + 7y = 23 (Option A)
• Find the area of the triangle which the line 4x - 6y + 12 = 0 forms with the coordinate axes.

  • The area of the triangle is 3 square units (Option A)
• A particle's position along the axis after 1 second of travel is given by the equation x = 24t^2 - 3t^3 + 10. What is the particle’s average velocity, in in/sec during the first 3 seconds?

  • The average velocity is 45 in/sec (Option B)
• Find the area of the region bounded by y = x^3 - 3x^2 + 2x + 1, the axis, and vertical lines x = 0 and x = 2.

  • The area is 2 square units (Option B)
• Find the rate of change of the area of a square with respect to its side when x = 5.

  • The rate of change is 10 (Option C)
• A spherical snowball melting in such a way that its surface area decreases at a rate of 1 cm^3/min. How fast is its radius shrinking when it is 3 cm?

  • The radius is shrinking at -1/2π cm/min (Option A)
• Two cities 270 km apart lie on the same meridian. Find their difference in latitude if the Earth’s radius is 3960 km.

  • The difference in latitude is 3/55 radians (Option A)
• Find the maximum area of a rectangle circumscribed about a fixed rectangle of length 6 cm and width of 4 cm.

  • The maximum area is 24 square units (Option A)
• The perimeter of an isosceles right triangle is 10.2426. Compute the area of the triangle in square units.

  • The area of the triangle is 4.5 square units (Option C)
• A piece of wire is shaped to enclose a rectangle with a length of 15 cm and an area of 150 sq. cm. It is then reshaped to enclose a square. Find the area of the square in cm^2.

  • The area of the square is 156.25 cm^2 (Option A)
• Find the area of the region bounded by the parabola x = y^2 and the line y = x - 2.

  • The area is 8/2 square units (Option A)
• Five horses are in a race. A woman picks two of the horses at random and bets on one of them. Find the probability that a person picked the winner.

  • The probability is 1/10 (Option A)
• The probability that A hits the target is 1/3 and the probability that B hits the target is 1/5. They both fire at the target. Find the probability that one of them hits the target.

  • The probability is 2/5 (Option A)
• What is (1+i) raised to the power of 10?

  • The answer is 32i (Option A)
• What is the maximum area of the rectangle whose base is on the x-axis and whose upper two vertices lie on the parabola y = 12 - x^2?

  • The maximum area is 32 square units (Option A)
• Find the equation of a line through point A(4,1) perpendicular to the line 2x - 3y + 4 = 0.

  • The equation is 3x + 2y = 14 (Option A)
• Find the particular solution of the differential dx/dt = x - 1; x(0) = 1.

  • The particular solution is x(t) = 1 (Option A)
• Find the volume of the solid of revolution formed by rotating the region bounded by the parabola y = x^2 and the line y = 0 and x = 2 about the x-axis.

  • The volume is 2π/5 (Option A)
• Find the slope of the curve defined by the equation yx^2 - 4 = 0 at the point (4,4).

  • The slope is -2 (Option A)
• A function y has the set of positive integers N as the domain. For each n in N, y(n) = 12 + cos(nπ) + sin[(2n-1)π/2]. What are the values of y corresponding to any odd positive integer?

  • The values of y corresponding to any odd positive integer are 12 (Option A)
• Find the volume obtained if the region bounded by y = x^2 and y - 2x = 0 is rotated about the x-axis.

  • The volume is 64π/15 (Option A)
• Question 29:

  • Find the volume obtained if the region bounded by y = x^2 and y - 2x = 0 is rotated about the x-axis
  • Answer: A. 64π/15
• Question 30:

  • Which of the following are the solutions to the differential equation y”’ – 3y” + y = 0?
  • Options:

  I. e^x

  II. x(e^x)

  III. e^-x

  • Answer: C. I and II only
• Question 31:

  • Find all integers n such that (2n-6) is greater than 1 but less than 14
  • Answer: A. 4, 5, 6, 7, 8, 9
• Question 32:

  • Write the equation of the line with x-intercept a = 4/5 and y-intercept b = 1/2
  • Answer: A. 5x + 8y = 4
• Question 33:

  • Find all the values of m for which y = e^(mx) is a solution of 6y” – y’ – y = 0 on (-∞, +∞)
  • Answer: D. m = -1/3, 1/2
• Question 34:

  • If the columns (or rows) of a determinant are identical, what is the value of the determinant?
  • Answer: C. Zero
• Question 35:

  • What is I raised to the power of 96?
  • Answer: D. m = -1/3, 1/2
• Question 36:

  • The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show given that his wife does is 0.70. Find the probability that at least 1 person of the married couple will watch the show.
  • Answer: D. 0.55
• Question 37:

  • A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, what is the probability of getting 2 tails and 1 head?
  • Answer: A. 2/9
• Question 38:

  • The probability that a doctor correctly diagnoses a particular illness is 0.70. Given that the doctor makes an incorrect diagnosis, what is the probability that the doctor makes an incorrect diagnosis and the patient sues?
  • Answer: A. 0.27
• Question 39:

  • In the curve y = 3cos(1/2)x, what is the amplitude and period?
  • Answer: B. 3, 4π