Reviewer in Chemistry 1. Rank the following gas according to increasing effusion rates relative to O2 (reference). MM F2 = 38, MM CH4 = 16, MM CO2 = 44, MM O2 = 32
2. What is the vapor pressure of 1000.0 g of a water solution at 250C that contains 124.0g of the nonvolatile solute ethylene glycol, C2H6O2? The vapor pressure of pure water at this temperature is 23.76 torr. Assume an ideal solution.
3. The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is 4.5 x 109 years. In a particular rock sample, the ratio of the numbers of Pb-206 to U- 238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock?
4. The diameter of a spherical mothball is observed to halve in 200 days. Approximately, how long will it take for its remaining volume to become half of its volume at 200 days. 5. A 350mL sample of 0.276 M HNO3 is partially neutralized by 125mL of 0.0120 M Ca(OH)2. Find the concentration of nitric acid in the resulting solution.
6. A commonly occurring isotope of tin-118, while most oxygen occurs in nature as oxygen-16. A molecule of tin(IV) oxide formed from these isotopes contains how many neutrons?
7. A method of removing CO2 from a spacecraft is to allow the CO2 to react with sodium hydroxide. (The products of the reaction are sodium carbonate and water). What volume of carbon dioxide at 25oC and 749 mmHg can be removed per kilogram of sodium hydroxide that reacts?
8. The solubility of constant of stronyium sulfate, SrSO4 is 2.8 x 10 -7. How many grams of SrSO4 must be dissolved in water to produce 1L saturated solution.
9. The mineral manganosite is a compound of manganese-55 and oxygen-16. If 77% of the mass manganosite is due to manganese, what is the empirical formula of
manganosite?
10. The first step in the Otswald process for producing nitric acid is 4NH3(g) + 5O2(g) ? 4NO(g) + 6H2O(g). If the reaction of 150 g of ammonia with 150 g of oxygen gas yields 87 g of nitric oxide (NO), what is the percent yield of this reaction?
================================================== =================================== Reviewer in Physics 1. A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision?
2. A parallel-plate air capacitor is made from two plates 0.070 m square, spaced 6.3 mm apart. What must the potential difference between the plates be to produce an energy density of 0.037 J/m3? 3. A single force (not shown) is applied at point B in the y-direction, in line with points A and B. What should this force being order for the frame to be in equilibrium in that direction?
4. Determine the force in member AG for the pin-connected truss shown.
5. The two cables shown carry a 100 N vertical load. What is the tension in Cable AB?
6. What are the x- and y- coordinates of the centroid of the perimeter line?
7. A particle starting from rest experienced an acceleration of 3 m/s2 for 2 s. The particle then returned to rest in a distance of 8 m. Assuming all accelerations were uniform, what was the total time elapsed for the particles motion?
8. The location of a particle moving in the –y plane is given by the parametric equations x= t2 + 4t and y=(1/4)t4- 60t where x and y are in meters and t is in seconds. What is the particles velocity at t=4s?
9. Two blocks are connected over a pulley. The mass of block A is 10 kg and the coefficient of kinetic friction between A and the incline is 0.20. of the incline is 30o. Block A slides down the incline at constant speed. What is the mass of Block B?
10. A motorist is travelling at 70km/h when he sees a traffic light in an intersection 250 m ahead turn red. The light’s red cycle is 15 s. The motorist wants to enter the intersection without stopping his vehicle, just as the light turns green. What uniform deceleration of the vehicle will just put the motorist in the intersection when the
light turns greens?
Algebra 1. The polynomial x3 + 4x2 – 3x + 8 is divided by x-5, then the remainder is.
2. In certain Board Examination, 119 examinees too the Shop Machinery subjected, 104 examinees took thye Power Plant Machinery subject and 115 examinees took the Industrial Plant Machinery subject. Seventy-eight (78) conditioned examinees took only Shop Machinery and Power Machinery subjects. Seventy-one (71) conditioned examinees took only the Power Plant Machinery and Industrial Plant Machinery subjects. Eighty-five (85) conditioned examinees took only Industrial Plant Machinery and Shop Machinery subjects. Fifty-four took all the three subjects.
How many examinees took the Certified Plant Mechanic board examination?
3. A certain manufactured part can be defective because it has one or more out of the three possible defects: insufficient tensile strength, a burr, or a diameter outside of tolerance limit. In a lot of 500 pieces: 19 have a tensile strength defects, 17 have a burr, 11 have an unacceptable diameter, 12 have tensile strength and burr defects, 7 have tensile strength and diameter defects, 5 have burr and diameter defects and 2 have all three defects. Determine: How many of the pieces have no defects? How many pieces have only burr defects? How many pieces have exactly 2 defects?
4. A certain company manufactures two products, X and Y, and each of these products must be processed on two different machines. Product X requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product Y requires two minutes of work time per unit on machine 1 and 3 minutes of work time per unit on machine 2. Each day, 100 minutes are available on machine 1 and 200 minutes are available on machine 2. To satisfy certain customers, the company must produce at least 6 units per day of product X and at least 12 units of product Y. If the profit of each unit of product X is P50 and the profit of each unit of product Y is P60, how many of each product should be produced in order to maximize the company's profit?
Trigonometry 1. Triangle ABC is a right triangle with the right angle at C. CD is perpendicular to AB. BC = 4, and CD = 1. Find the area of the triangle ABC.
2. A ladder 5 m long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with the ground. How high of the wall does it reach?
3. If 3x = 9y and 27y = 81 z, find x/z.
4. A corner lot of land is 35 m on one street and 25 m on the other street, the angle between the two lines of the street being 85o24’. The other of the lot are
respectively perpendicular to the lines of the streets. What is the worth of the lot at P 180 per sq m?
Solid Mensuration and Analytic Geometry 1. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. Find the altitudes if the areas of the triangles differ by 21 units 2.
2. One of the diagonals of a rhombus is 25 units and its area is 75 units 2. Determine the length of the side.
3. It is desired that the volume of the sphere be tripled. By how many times will the radius be increased?
4. The area of a circle is 89.42 in2. What is the length of the side of a regular hexagon inscribed in a circle?
5. Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units, the locus of the third vertex is______.
6. Determine B such that 3x + 2y -7 = 0 is perpendicular to 2x - By + 2= 0.
7. The center of a circle is at (1, 1) and one point on its circumference is (-1, -3). Find the other end of the diameter through ( -1, -3).
8. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.
Calculus 1. Water is running out in a conical funnel at the rate of 1 cu. In. per second. If the radius of the base of the funnel is 4 inches and the altitude in 8 inches, find the rate at which the water level is dropping when it is 2 inches from top.
2. What is the area of the largest rectangle that can be inscribed in a semi-circle of radius 10?
3. Three sides of a trapezoid are each 8 cm. long. How long is the fourth side when the area of the trapezoid has the greatest value?
4. The volume of the sphere is increasing at the rate of 6 cm3 / hr. At what rate is its surface area increasing (in cn2/hr) when the radius is 50cm?
Differential Equation and Advanced Mathematics
1. A tank initialy contains 400 liters of water. Salt solution, containing 1/8 kg of salt per liter of solution flows into the tank at the rate of 8 li/min and the solution, kept well-stirred, flows out of the tank at the rate of 4 li/min. Find the amount of salt in the tank after 100 minutes.
2. A body whose temperature is 180degrees is immersed in a liquid which is kept at a constant temperature of 60 degrees. In 10 minutes the temperature of the immersed body decreased to 120 degrees. How long will it take for the body's temperature to decrease to 90o?
3. A 10-ohm resistor and a 5-henry inductor are connected in series with a 50-volt source at time t = 0. Express the current I as a function of time.
4. What is the general solution of (D3 -3D2 - 4D + 12)y = 0
5. Solve the differential equation: x(y-1)dx + (x+1)dy = 0. If y = 2 when x = 1,
determine y when x = 2.
6. Find the principal 5th root of 50(cos 150° + j sin 150°). 7. The indicial equation of the differential equation x 2 y"+xy'+(x 2 -4)y = 0 is 8. The Fourier cosine transform of f(x) = e -2x
7. The indicial equation of the differential equation x 2 y"+xy'+(x 2 -4)y = 0 is
8. The Fourier cosine transform of f(x) = e
-2x
