2022 Civil Engineering Free Refresher Course 1
Subject coverage in the 2022 Civil Engineering Refresher Course 1 are Algebra and Trigonometry. It consists of 100 problem sets. Results and scores will be shown at the end of the quiz.
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SITUATION 2: You are given the trigonometric function y = - 2sin(πt/4 + π/2) , Calculate the time required for one cycle.
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SITUATION 2: You are given the trigonometric function y = - 2sin(πt/4 + π/2) , Find the maximum displacement.
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A grocer bought a number of items for P 1440. Later the price increased by P 2.00 per item and as a result he received 24 fewer items for the same amount. Find the number of items bought first.
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Which of the following is a palindromic number?
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Compute the value of A.
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The following are the zeros of this equation x3 – 3x2 – 10x + 24 EXCEPT:
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Compute the value of C
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Find the remainder of 3x^3 – x^2 – 8x + 5 when divided by x + 2
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SITUATION 6: Given the cosine function equal to 60/61 , Find csc θ
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SITUATION 8: Using the law of tangents, find to the nearest degree, the measure of the other two angles of a triangle in which a = 14 , b = 11 , C = 56°.Find angle A.
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An engineering component has a mass of 400 g. If each of its dimensions are reduced by 30% , determine the new mass.
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Factor the following: ax + ay – bx – by
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Compute the distance between the directrices of the curve 9x^2 – 25y^2 – 54x – 250y + 481 = 0.
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Every student at a particular technological institute is required to take preboard exams. A student who passes it will take Design and the other one who fails will take Hydraulics. In a batch of 1240 students there are more students took Hydraulics than Design. However if there are 30 more students who passed the preboard, each subject would have the same enrolment. How many students took Hydraulics?
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Find the value of x in (3 )^5 (9 )^6 = 3^2x
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SITUATION 2: You are given the trigonometric function y = - 2sin(πt/4 + π/2) , If tan B = x/ √(1-x^2), what is cos B ?
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SITUATION 8: Using the law of tangents, find to the nearest degree, the measure of the other two angles of a triangle in which a = 14 , b = 11 , C = 56°.Find angle B.
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Find the summation of (5K – 3) from K = 1 to K = 16.
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SITUATION 6: Given the cosine function equal to 60/61 , Find sin θ.
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SITUATION 4: Two sides of the triangle are 50 and 60. The angle included is 30° .If cot 2A = tan 3A , find the value of A in degrees.
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Which of the following is NOT a perfect number?
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SITUATION 3: Answer the following by converting from degrees to radians. 12° 12’ 20”
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SITUATION 1: The sides of the triangle are a = 23.9 m , b = 36.3 m. The angle opposite b is 102.7° Calculate the angle A.
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The diameter of a tumor D in mm , t in days after diagnosis is given by D(t) = 10e^0.0277t How long until the diameter is doubled?
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A ship P sails at a steady speed of 45 kph in a W 32° N from a point. At the same time, another ship Q leaves the port at a steady speed of 35 kph in a direction N 15° E. Determine their distance apart after 4 hours.
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SITUATION 5: Identify the quadrants of the following: sec A 0
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A is 8% taller than B , while B is 9% taller than C. By how much percent is A taller than C?
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It is usually defined as the angle made by the ray drawn and it can be read from north or south.
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What is the sum of the roots of the equation 3x^2 – 4x + 6 = 0?
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SITUATION 3: Answer the following by converting from degrees to radians. 112° 40’
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Solve for x: |x - 2| + 1 = x
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The sum of the sides of the triangle ABC is equal to 400 m. A = 38°, B = 58°. Find the side AC in meters.
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The Father of Trigonometry.
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These are angles whose sum is 360°
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There is a fixed circle having a radius of 5 with center at (4,8). Find the equation of the curve connecting the centers of all circles that are tangent to this fixed circle and the x-axis.
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SITUATION 3: Answer the following by converting from degrees to radians. 25°
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Find the locus of a point the sum of the squares of whose distances from (2,3) and (-1,-2) is 34.
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A river flows due south at 125 ft/min. A motorboat, moving at 475 ft/min in still water, is headed due east across the river. Find the direction in which the boat moves and its speed.
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SITUATION 5: Identify the quadrants of the following: sin A > 0 and cot A > 0
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SITUATION 5: Identify the quadrants of the following: sin A 0
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What kind of symmetry, if any, does the graph of y = x^2 – 16 have?
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How many triangles can be formed given a = 31.5 , b = 51.8 , and A = 33° 40’.
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Solve for x: cos 2x – 3sinx + 1 = 0 I. π/6 II. 5π/6 III. 0
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Find the value of k so that the equation 4x^2 + kx + 9 = 0 has one root equal to -3
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Solve for x and y:
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SITUATION 7: Solve the right spherical triangle given c = 112° 48’ and A = 56° 11’ 56”.Find the angle B.
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Divide 60 into two parts with the ratio of 2:3.
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Evaluate: 1/2 * 2/3 * … 2016/2017
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Rewrite as a single function of an angle: tan 37° + tan 68° / 1 – tan 37°tan 68°
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SITUATION 4: Two sides of the triangle are 50 and 60. The angle included is 30° .Find the third side
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If d = 1000 – 200q and c = 4000 + 20d , find c as a function of q.
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The perimeter of triangle ABC is 300 m , A = 36° , B = 58° and C = 86° . Determine the side opposite the biggest angle.
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The power is required to operate a turbine varies directly as the cube of the speed. If ½ horsepower will operate at a speed of 100 rev/min, how fast will 4 horsepower operate it?
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The value of e that is 2.71828… is called:
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Find the 2017th digit in the decimal equivalent of 2017/9999.
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Find the number of terms 5 ,8 , 11 … of which sum is 1025.
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One liter of a 25% solution is mixed with 3 liters of a 40% solution. What is the percentage of sugar in the new mixture?
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An equilateral triangle has an altitude of 5√3 cm long. Find the area of the triangle.
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The geometric mean of two numbers is 6 while the arithmetic mean is 4. Find the product of geometric and harmonic means.
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Klay Thompson left from Warriors game at past 3:00 pm as indicated in his watch. Between two to three hours later, he returned at Oracle Arena and he noticed that the hands of the watch interchanged. At what time did he left his home?
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For a given function f(t) = f(-t). What type of symmetry does f(t) have?
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Find the constant term of the third term in the expansion of (2x + y)^6.
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Eleven men can finish the job in 15 days. Five men were working at the start and after six days four men were added. How many days will it take to finish the job?
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The angles of elevation of the top of the tower at two points 30 m and 80 from the foot of the tower, on a horizontal line, are complimentary. What is the height of the tower?
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Solve for x: 7x = 4x + 12
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Calculate the following sum:
ctto
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Simplify: (a-x)(b-x)…(z-x)
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SITUATION 2: You are given the trigonometric function y = - 2sin(πt/4 + π/2) , Calculate the phase shift of the function.
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A ship sailing due east when a light is observed bearing N 62° 10’ E. After the ship has travelled 2250 m, the light bears N 48° 25’ E. If the course is continued, how close will the ship approach the light?
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Find the trigonometric function asked of certain angles in standard position of the given points are onthe terminal side of the angles. The tangent function at (0,4).
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Compute the value of B.
ccto
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The Greenwich mean time of Manila is +8. What is the GMT of Tokyo?
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The length of a triangle exceeds twice its width by 3 inches. If the area of the rectangle is 10 , calculate the measure of the width.
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SITUATION 8: Using the law of tangents, find to the nearest degree, the measure of the other two angles of a triangle in which a = 14 , b = 11 , C = 56°.Find side c.
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Simplify: (-54s)(-4/9)
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The principal value of the equation sin x = cos x is:
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SITUATION 7: Solve the right spherical triangle given c = 112° 48’ and A = 56° 11’ 56”.Find the side a.
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Solve for x: 10x + 10x+1 = 5x + 5x+1 + 5x+2
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A car travels northward from point D for one hour, then northward for 30 mins., then shifted N 30° E. the bus constant speed is 64.7 km. directly away from D. how long in hours has it travelled?
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Solve this trigonometric equation: 2cos x + sec x = 3.
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Solve for x:
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What is the equivalent value of 630 degrees in centesimal system.
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SITUATION 1: The sides of the triangle are a = 23.9 m , b = 36.3 m. The angle opposite b is 102.7° Calculate the angle C.
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The A-frame cabin is below 35 feet wide. The roof of the cabin makes a 55° angle with the cabin’s base. Find the length of one side of the roof from its ground level.
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A hyperbola has the equation x^2 – 8x – 4y^2 + 64y = 256, find the center of hyperbola.
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At what time after 12 noon will the minute hand and hour hand of a clock be on a straight line for the first time?
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SITUATION 1: The sides of the triangle are a = 23.9 m , b = 36.3 m. The angle opposite b is 102.7° Find the period of the function y = 3 cot 1/2 t.
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Find the 5th term of the expansion (2 – x)^ 6?
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Simplify this radical:
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An isosceles triangle has an area of 46 m2. One side of the equal interior angle is 65.5° What is the perimeter of the triangle in meters?
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SITUATION 1: The sides of the triangle are a = 23.9 m , b = 36.3 m. The angle opposite b is 102.7° In triangle DEF , DE = 18 , EF = 6 . The length FD must be:
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The sum of the ages of the two brothers is 20. In five years, one is twice the another. Find the present ages of the two brothers.
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The perimeter of a triangle is 84 m while its area is 102 m2. Determine the diameter of the circle that may be inscribed in this triangle.
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Find the nth term of the series 1, 4 ,7 , 10 , 13…
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SITUATION 1: The sides of the triangle are a = 23.9 m , b = 36.3 m. The angle opposite b is 102.7° Find the length of the side 6 in meters
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Twelve workmen employed on a building site earn between them, a total of P 2415 per week. Laborers are paid P 175 per week and craftsmen earn P 220 per week. How many craftsmen are employed?
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SITUATION 7: Solve the right spherical triangle given c = 112° 48’ and A = 56° 11’ 56”.Find the side b.
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Two lines are represented by the equations -1/2 y = 6x + 10 and y = mx. Find the value of m such that the lines will be parallel.
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One number is more than the another and the sum is 71. Find the larger number.
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SITUATION 6: Given the cosine function equal to 60/61 , Find tan θ.
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CE 2022 1
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