UNIVERSITY OF RIZAL SYSTEM Morong Campus COLLEGE OF ENGINEERING EE PROFESSIONAL PROFICIENCY COURSE ELECTRICAL ENGINEERING DEPARTMENT PRE-BOARD EXAM # 2: MATHEMATICS NAME: ______________________________ SECTION: _5-EE_ SCORE: ________ *Show your complete solutions for the problems. SHADE THE LETTER OF YOUR ANSWERS ON THE 2ND PAGE . No erasures.* 1.] If (x+3) is a factor of x3+3x2+4x+k, find k. A. 12 B. -12 C. 14 D. -14 2.] Solve for the value of x: x3logx = 100x A. 10 B. 100 C. 1000 D. 10000 3.] When you divide x to the 10 plus 1 by the quantity x minus square root of 2, the remainder is: A. 13 B. 33 C. 34 D. 43 4.] A man is 41 years old and his son is 9. In how many years will the father be three times as old as the son? A. 5 B. 6 C. 7 D. 8 5.] A tank can be filled by three pipes separately in 20, 30 and 40 minutes respectively. If only the first two pipes will be opened, how long will it take to fill up the tank? A. 20 mins B. 12 mins C 115 mins D. 31 mins 6.] Admissions ticket to Marlon’s concert were P400 for adults and P125 for children. Receipts for the day showed that 2700 persons attended (wow!) and P887500 was collected. How many children attended that day? A. 500 B. 700 C. 140 D. 1800 7.] Boy Pagpag has 1000 invested part at 5% and the remainder at 3% simple interest. The total income per year from these investments is 44. How much he has invested at higher rate? A. 200 B. 700 C. 500 D. 120 8.] Tito Roy sold 9 dozen plain eggs for P942. The following day he sold at the same price, 12 dozen plain eggs and 15 dozen salted eggs for P990. Find the price per piece of his salted eggs. A. P1.50 B. P3.00 C. P3.50 D. P2.75 9.] The sum of the digits of a certain two digit number is 12. If the digits are reversed, the resulting number is 6 more than half the original number. Find the difference between the digits. A. 4 B. 3 C. 2 D. 5 10.] When each side of a given square is increased by three inches the area is increased by 27 square inches. Determine the dimensions of the original square. A. 2 B. 4 C. 3 D. 9 11.] In the expansion of (x+2y)10, the numerical coefficient of the 5th term is: A. 5040 B. 210 C. 3340 D. 3360 12.] In the expansion of [x2 – (1/x3)]30, find the term free of x. A. 86493225 B. 68493225 C. 86943225 D. 86493252 13.] The first term of an arithmetic progression is -2 and the sum of the first 11 tems is 88. The common difference is: A. 4 B. 3 C. 2 D. 1 14.] The sum of a geometric series is as follows: S = 1.0+1.1+1.21+1.331+… up to 50th term. Determine the sum S. A. 2123.51 B. 2654.34 C. 1163.91 D. 1255.82 15.] In how many ways can you express 47 as a sum of two primes? A. 0 B. 1 C. 2 D. 3 16.] How many 3 digit numbers may be formed from the digits 0 to 5 if no digit may be repeated in a given number? A. 100 B. 120 C. 130 D. 180 17.] A number between 1 and 10000 (inclusive) is randomly selected. What is the probability that it will be divisible both by 4 and 5? (EE April 1999) A. 0.20 B. 0.25 C. 0.05 D. 0.10 18.] A drawer contains 10 white balls and 6 black balls. What is the probability of randomly drawing a white and a black ball? A. 0.300 B. 0.250 C. 0.360 D. 0.208 19.] What are your chances of winning the 6/42 lotto draw? (assuming tumaya ka) A. 2546725 B. 5245786 C. 10127420 D. 8437224 20.] If you sunk 50% of your shots in basketball, find the probability that you will make exactly 3 of your next 10 shots. A. 0.1172 B. 0.1111 C. 0.2350 D. 0.0214 21.] What is the area in sq.cm of the circle circumscribed about an equilateral triangle with sides 10 cm? A. 124.7 B. 114.7 C. 134.7 D. 104.7 22.] The perimeter of an isosceles right triangle is 6.8284. Compute the area of the triangle (sq. units). A. 2 B. 1 C. 0.5 D. 4 23.] The sum of the interior angle of the polygon is 540˚. Find the number of sides. A. 5 B. 6 C. 8 D. 11 24.] Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. A. 1 B. 2 C. 4 D. 2.5 25.] A piece of wire is shaped to enclose a square whose area is 169 sq.cm. It is then reshaped to enclose a rectangle whose length is 15 cm. The area of the rectangle is: A. 165 B. 175 C. 170 D. 156 26.] Which of the following is perpendicular to the line x/3 + y/4 = 1? A. x – 4y – 8 = 0 B. 4x – 3y – 6 = 0 C. 3x – 4y – 5 = 0 D. 4x + 3y – 11 = 0 27.] If the points (-3, -5), (x, y) and (3, 4) lie on a straight line, which of the following is correct? A. 3x + 2y – 1 = 0 B. 2x + 3y + 1 = 0 C. 2x + 3y – 1 = 0 D. 3x – 2y – 1 = 0 28.] The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is: A. 2x – 3y = 12 B. 3x + 2y = 12 C. 3x – 2y = 12 D. 2x – 37 = 12 29.] How far from the y-axis is the center of the curve 2x2 + 2y2 + 10x – 6y – 55 = 0? A. -3.0 B. 2.75 C. -3.25 D. 2.5 30.] Find the area of the circle whose center is at (2, -5) and tangent to the line 4x + 3y – 8 = 0. A. 6 π B. 9 π C. 3 π D. 12 π 31.] Find the shortest distance from the point (1, 2) to a point on the circumference of the circle defined by the equation x2 + y2 + 10x + 6y + 30 = 0. A. 5.61 B. 5.71 C. 5.81 D. 5.91 32.] Find the value of k for which the equation x2 + y2 + 4x - 2y - k = 0 represents a point circle. A. 5 B. -5 C. 6 D. -6 33.] The length of the latus rectum of the curve (x – 2)2 / 4 + (y + 4)2 / 25 = 1 is: A. 1.6 B. 2.3 C. 0.80 D. 1.52 34.] Find the area bounded by the curves x2 + 8y + 16 = 0, x – 4 = 0, the x-axis and the y-axis. A. 10.67 B. 10.33 C. 9.67 D. 8 35.] The eccentricity of the ellipse (x2 / 4) + (y2 / 16) = 1 is: A. 0.725 B. 0.256 C. 0.689 D. 0.866 36.] Find the ratio of the major axis to the minor axis of the ellipse x2 + 4y2 – 24y – 72x – 144 = 0. A. 0.67 B. 1.8 C. 1.5 D. 0.75 37.] The chords of the ellipse 64x2 + 25y2 = 1600 having equal slopes of 1/5 are bisected by its diameter. Determine the equation of the diameter of the ellipse. A. 5x – 64y = 0 B. 64x – 5y = 0 C. 5x + 64 y = 0 D. 64x + 5y = 0 38.] 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 (in miles). A. 94,550,000 B. 94,335.000 C. 91,450,000 D. 93,000,000 39.] The polar form of the equation 3x + 4y – 2 = 0 is: A. 3r sin θ + 4r cos θ = 2 C. 3r cos θ + 4r sin θ = 2 B. 3r cos θ + 4r sin θ = -2 D. 3r sin θ + 4r tan θ = -2 40.] The polar form of the equation 3x2 + 2y2 = 8 is: A. r2 = 8 B. r = 8 /cos2 θ + 2 C. r = 8 D. r2 = 8 /cos2 θ + 2 GOD BLESS URS-M 2015! ANSWERS in MATH2: NAME: “BeliEEve in the Lord Jesus…” Prepared by: Dr. Marlon A. Bautista SCORE: