TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES QUEZON CITY
CIVIL ENGINEERING ALGEBRA 1. The terms of a sum may be grouped in any manner without affecting the result. This law is known as: A. Associative Law C. Reflexive Law B. Commutative Law D. Distributive Law 2. The expression (x – 3)3 is identical to: A. x3 – 27 C. (x + 3) (x2 – 6x + 9) 2 B. (x – 3) (x – 3x + 9) D. x3 – 9x2 + 27x – 27 3. Solve for x if 8x = 2(y+2) and 16(3x-y) = 4y. A. 1 C. 3 B. 2 D. 4 4. The simplest form of [(n+1)!]2 / [(n!)(n-1)!] is A. n(n+1) C. n2 B. n+1 D. n(n+1)2 5. Terms that differ only in numeric coefficients are known as: A. unlike terms C. equal terms B. unequal terms D. like terms 6. When the given function f(x) = cx3 - 3x2 + dx – 4 is divided by (x+2), the remainder is -34. When divided by (x-2), the remainder is 2. What is the value of d? A. 1 C. 3 B. 2 D. 4 7. Find the value of constant “h” in the 2x2 – hx2 + 4x + 5h = 0 so that the sum of the roots is 2. A. 4 C. 6 B. 12 D. 18 8. The average of 2013 numbers is 2014. If a number is neglected, the new average becomes 2013. What was the number neglected? A. 2013 C. 2012 B. 4026 D. 4024 9. There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers? A. 16, 37 C. 18, 35 B. 20, 33 D. 24, 29 10. Find the term independent of y in the expansion of (2y2 – 3y-1)9. A. 217,728 C. -734,832 B. -326,592 D. 489,888 11. Find the sum of the coefficients in the expansion of (2x3y+1)35. A. -1 C. 1 B. -2 D. 2 12. If (5x – 3), (x + 2), and (3x – 11) form an arithmetic progression, find the fifteenth term. A. – 86 C. – 81 B. – 79 D. – 84 13. Find the common ratio of a geometric progression whose first term is 1 and for which the sum of the first 6 terms is 28 times the sum of the first 3 terms. A. 4 C. 5 B. 3 D. 2 14. A rubber ball is dropped from a height of 15 meters. On each rebound, it rises 2/3 of the height from which it last fell. Find the distance traversed by the fall before it comes to rest. The geometric progression occurs after the first rebound.
A. 96 m B. 85 m
C. 100 m D. 75 m
15. Find the tenth term in the sequence 1, 1, ½, 1/6, 1/24… A. 1/322560 C. 1/362880 B. 1/317520 D. 1/352800 16. A club of 40 executive, 33 likes to smoke Marlboro, and 20 likes to smoke Philip Morris. How many like both? A. 13 C. 11 B. 10 D. 12 17. When William was as old as Mae is now, the sum of their ages was 51. When Mae will be as old as William is now, the sum of their ages will be 103. How many years older is William than Mae? A. 25 C. 19 B. 13 D. 32 18. At what time between 2:00 and 3:00 will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark? A. 2:21 3/11 C. 2:23 7/13 B. 2:18 6/13 D. 2:19 7/13 19. A boat can go 12 kph in still water. Going full speed, it goes 25 km upstream in the same time it takes to go 35 km downstream. What is the rate of the current? A. 3 kph C. 4 kph B. 1 kph D. 2 kph 20. Ana can finish her differential equations homework in 30 minutes while Annie can do the same homework for 26 minutes. If Ana did the homework for 12 minutes until Annie helped her, after how many minutes will they finish the homework? A. 12.36 C. 7.64 B. 8.36 D. 10.72 21. If 20 bakers can bake 40 cakes in 8 hrs, how many bakers can bake 10 cakes in 2 hours? A. 20 C. 10 B. 30 D. 40 22. The ratio or product of two expressions in direct or inverse relation with each other is called: A. ratio and proportion C. means B. extremes D. constant of variation 23. How much of a 7% solution should be mixed with appropriate amount of 12% solution to get 5 liters of a 10% solution? A. 2 L C. 3 L B. 2.5 L D. 4 L 24. An investor has ₱ 1, 100 income from bonds bearing 4% and 5% if the amount at 4% and 5% were interchanged he would earn ₱ 50 more per year. Find the total sum invested. A. ₱ 20, 000 C. ₱ 25, 000 B. ₱ 30, 000 D. ₱ 35, 000 25. Equal volumes of different liquids evaporate at different but constant rates. If the first is totally evaporated in 6 week and the second is 5 weeks, when will the second be ½ the volume of the first? A. 27/7 C. 33/7 B. 30/7 D. 29/7
TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES QUEZON CITY
CIVIL ENGINEERING SUPPLEMENTARY PROBLEMS 26. Which of the following is the value of xy if x-y=2, x2 + 2xy + y2 = 3? A. -1/4 C. 1/4 B. -4 D. Not in the choices 27. Consider the sequence: 1, -2, 3, -4, 5, -6, … , whose nth term is (-1)n+1(n). What is the average of the first 200 terms of the sequence? A. -1 C. 0 B. -0.5 D. 1 28. A figure is 30 cm high is reduced by 19% in a copier. The height of the figure in the resulting copy will be A. 5.7 cm C. 24.3 cm B. 27 cm D. 13.08 cm 29. Yoyet reads the clock differently such that he recognizes the hour hand as the minute hand and the minute hand as hour hand. How many minutes after 5 o’clock will he read the time correctly? A. 26.55 C. 28.92 B. 27.27 D. 28.66 30. A cask containing 20 gallons of wine was emptied on one-fifth of its content and then is filled with water. If this is done 6 times, how many gallons of wine remain in the cask? A. 5.121 C. 5.010 B. 5.243 D. 5.343 31. A man wishes to buy a piece of land worth 15 million pesos. If it were possible for him to save one peso for the first day, two pesos on the second day, 4 pesos on the third day and so on. In how many days would he save enough money to buy the land? A. 20 C. 24 B. 23 D. 27 32. What part of 90% alcohol solution must be replaced by an equal amount of pure alcohol to make a 95% alcohol solution? A. 50% C. 25% B. 45% D. 5% 33. Pure tin and pure iron was added to a 50 kg of an alloy containing 10% tin and 20 % iron. The process produced a new alloy containing 20% tin and 50% iron. What is the weight of the new alloy? A. 66.67 kg C. 116.67 kg B. 86.25 kg D. 153.33 kg 34. 9 liters of wine are taken from a container full of wine. It is then filled with water. Then 9 liters of the mixture are taken and the container is again filled with water. If the ratio of the quantity of the wine now in the container to the quantity of the water in it is 16/9, what is the capacity of the container? A. 60 L C. 45 L B. 54 L D. 36 L 35. A can do a job in 4 days, B can do the job in 6 days and C can do the job in 8 days. How long will it take to do the job if A and B work for 1 day then B and C finish the job? A. 1 C. 4 B. 2 D. 3
36. A project activity can be done by 25 men in 60 days. At the end of the 5th day, 6 men were laid off. At the start of the 33rd day, 12 more men were hired to finish the job. How many days is the project advanced/ delayed? A. 0.81 advanced C. 0.19 advanced B. 0.81 delayed D. 0.19 delayed 37. A survey was conducted by SWS to find out which of the three presidentiables they liked best. The results indicated that 500 liked Noynoy, 470 liked Villar, and 430 liked Estrada. But of these, 180 liked both Noynoy and Estrada, 140 liked both Noynoy and Villar, and 210 liked both Estrada and Villar. Only 60 liked all the presidentiables. How many persons responded to the survey? A. 910 C. 960 B. 980 D. 930 38. La Immaculada High School has 85 seniors, each of whom plays on at least one of the school’s three varsity sports teams: football, baseball, and basketball. It so happen that 74 are on the football team; 26 are on the baseball team; 17 are on both the football and basketball teams; 18 are on both the baseball and football teams; and 13 are on both the baseball and basketball teams. Determine the number of seniors playing all three sports given that twice this number is members of the basketball team. A. 10 C. 22 B. 11 D. 20 39. The sum of the digits of a 2-digit number is 10. If the number is divided by the units’ digit, the quotient is 3 remainder is 4. Find the number. A. 37 C. 46 B. 28 D. 19 40. A number is less than 100 and its tens’ digit is 2 more than its units’ digit. If the number with the digits reversed is subtracted from the original number, the remainder is 3 times the sum of the digits. Find the number. A. 42 C. 75 B. 53 D. 64
