MODULE EXAM 1 Alegebra and Trigo

 

MODULE EXAM 1

 ALGEBRA AND TRIGONOMETRY TRIGONOMETRY 1.

Tanya  produced three lanterns on her first hour of work. Her boss told her, “DO IT FAST”. This made  her work even slower making only two lanterns per hour for the next two hours. When her  friend Michelle told her “YOU CAN DO IT, it motivated her to make 5 lanterns on the fourth hour. What is the average production speed in lanterns per hour? SITUATION 1

Fro From a  buil ild din ing g acro cross, th the e angle of depres ressio sion of th the e base of the fro ron nt edif ific ice e is 23.5° and the angle of elevation of its top is 52.78°. The height of observation is 14m. 2. What is the height of the edifice in meters? 3. How far is the building from the said edifice in meters? 4. What is the angle of elevation of the top of the edifice from the foot of the building in degrees? 5.   Eight  men

can dig 150 ft of trench in 7hours. Three men can backfill 100 ft of trench in 4 hours. How long will it take 6 men to dig and fill 200 ft of trench, in hours? SITUATION 2

Given the sinusoidal function f(t) = 3 sin 2t. Determiner the following: 6. The amplitude of the curve. 7. The period of the curve. 8. The frequency of the curve. SITUATION 3

Two trains  A & B are moving on parallel tracks in the same direction and at different speeds. Train B,  180m long, is moving at 120 kph. Train A, 120 long, is behind train B and moving at 180 kph. At a certain time, the clear distance between the trains is 550m. 9. Find  the distance travelled by the train B when the front end of train A caught up with its tail end? 10. Find the distance travelled by train A when its front caught up with the tail end of Train B? 11. How long will it take for train A to completely overtake train B? 12.   The  side

of the mountain slopes upward at an angle of 21° 14’. At a point on the mountain sid side a  min ine e tun tunnel is con const stru ruct cte ed at an angle of 15 15°° 27’ downw wnward fro rom m th the e hori rizo zon ntal. Fi Fin nd the the vertical distance to the surface of the mountain from a point 250m down the tunnel? 13.   The  average

of 12 numbers is 11. If one number is removed, the new average is 9. What number was removed? 14.   The  top

of the tower at “B”, 2000 m away from “A” where the transit is set, has a vertical angle of  3˚30’. The height of the mast is 12 m and the height of the instrument at “A” is 1.10 m. If the the  ele lev vatio tion of the the base of the the ins instr tru ument is 133 33..3 m, determ termin ine e the the ele leva vattio ion n of the the base of  the tower.

 

  15.   John  Wick

on a bicycle coasts downhill covers the 4 feet the first second, 12 feet the 2nd sec second, and  in general, ral, 8 feet more each sec eco ond th tha an the pre revi vio ous secon cond. If she re rea aches the the bottom at the end of 14 seconds, how far did she coasts?    A  truck 16.  A

travels from point M northward for 30 min. Then eastward for one hour, then shifted N 30° W. If the constant speed is 40 kph, how far directly from M, in km. will be it after 2 hours. 17. An

examination examin ation has has two types types of questions questions as follows: Type A: 10 points at 3 minutes each Type B: 15 points at 6 minutes each There are  16 questions in the exam for a total time of 60 minutes. Determine the maximum score of this exam? SITUATION 4

Point A  and B on opposite sides of a building are 124m apart. The angles of depression from the top of the building to A and B are 54.3° and 68.5, respectively. Determine the following: 18. The height of the building. 19. Distance of point A from the building 20. Distance of point B from the building. 21.

The  ele lect ctri rica call res resis isttance of a cable vari varie es dire irect ctly ly as it its s le len ngth and in inve vers rse ely as the square of its  diameter. If a cable 600 meters long and 25 mm in diameter has a resistance of 0.1 ohm, find the length (m) of the cable 75 mm in diameter with resistance of 1/6 ohm. 22.

A  manufac facturi turin ng firm firm main mainttains ins one prod roduct asse ssemb mbly ly li lin ne to pro rod duce sig ign nal genera rato tors rs.. Wee We ekly demand  for for the gen ene erat rators is 35 unit its. s. The lin line opera rate tes s for for 7 ho hou urs per day, 5 days per  week we ek.. Dete Determ rmin ine e the the maxi maximu mum m prod produc ucti tion on time time per per un unit it in ho hour urs s re requ quir ired ed fo forr th the e li line ne to meet meet th the e demand? 23.

A  clock has a dial face 12 inches in radius. The minute hand is 9 inches long while the hour  hand is  6 inches long. The plane of rotation of the minute hand is 2 inches above the plane of  rota rotattion ion of  the hour hand. Det Determin rmine e the dis ista tan nce betwe tween (i (in nch) ch) the tip ips s of th the e hands at 5:40 am 24.  A    A  hill

slopes at an angle of 33° with the horizontal. A path leads up it, making an angle of  48.30’ with the line of steepest slope; find the inclination of the path with the horizontal.

   A  company 25.  A

has N machines of equal capacity that produces a total of 180 pieces each work day. If  two machines break down, the workload of the remaining machines is increased by 3 pieces each per day to maintain production. Find N.