# Civil Engineering Board Exam Problems

This is a repository of solved problems similar to past CE board exam in the Philippines given by the Professional Regulation Commission. We don't have the exact problems from the actual board examinations but problems here are carefully crafted so that it will be as close as possible to the actual board examinations.

Title
Which curve has a constant first derivative?
Find $x$ from $xy = 12$, $yz = 20$, and $zx = 15$
Value of t for a germ population to double its original value
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?
Comparing alternatives: Buy a truck vs rent a truck
Largest box that can be made from rectangular cardboard
Investment of P250,000.00 per year
Angle turned by train in 1 minute
Equivalent Cartesian Equation of Parametric Equations
Equation of the sphere of radius 3 and tangent to coordinate-planes
Equivalent land area of 600 mm^2 map-area with given map-scale
Evaluate the integral of (x dx) / (x^2 + 2) with lower limit of 0 and upper limit of 1
Determine the radius of curvature of the curve x = y^3 at point (1, 1)
Calculate the area enclosed by the curve x^2 + y^2 - 10x + 4y - 196 = 0.
Sum of the first ten terms of a Geometric Progression
Calculation of true distance of a line measuring 160.42 m using a tape that is 0.02m too long
A circle has an equation of x^2 + y^2 + 2cy = 0. Find the value of c when the length of the tangent from (5, 4) to the circle is equal to one.
Calculate the acute angle between 2x - 4y - z = -5 and 3x + 4y + 5z = -6
If arcsin (3x - 4y) = 1.571 and arccos (x - y) = 1.047, what is the value of x?
The digits of a three-digit number are in arithmetic progression, find the sum of all the digits
There are 7 arithmetic means between 3 and 35. What is the sum of all the terms?
A boat going upstream takes 1.5 times longer than going the same distance downstream. If the water current in the river is 8 kph, calculate the speed of the boat in still water.
What is the equation of the normal to the curve x^2 + y^2 = 25 at (4, 3)?
What is the radius of the circle x^2 + y^2 - 6x = 0?
When the polynomial x^4 + bx^3 + 5x^2 + dx + 6 is divided by x - 2 the remainder is 16. When it is divided by x + 1 the remainder is 10. Find the value of constant d.
Gas is escaping from a spherical balloon at a constant rate of 2 fˆ3/min. How fast is the outer surface area shrinking?
Determine the percentage uncertainty in the area of a square that is 6.08 (+/-) 0.01 m on a side.
In still water, your small boat average 8 miles per hour. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. What is the rate of water's current?
BCR of $180,000 investment yielding$60,000 annual benefits at 7% annually
Which pizza is a better buy: large with 16-inch-diameter for $15 or medium with 8-inch-diameter for$7.50?
Given the following equations: ab = 1/8, ac = 3, bc = 6. Find the value of a + b + c.
Which of the following is the derivative with respect to x of (x + 1)^3 - x^3?
How many terms from the progression 3, 5, 7, 9, ... must be taken in order that their sum will be 2600?
How many men paid for a total amount of \$262,143.75 if the first person to arrive only paid 25 cents?
Find the equation of the curve passing through the point (3, 2) and having s slope 5x^2 - x + 1 at every point (x, y)
A coin is so unbalanced that you are likely to get two heads in two successive throws as you are to get tails in one
What is the Coefficient of the 8th Term of the Expansion of (2x - 1/x)^10?
How Far An Object Has Fallen If Its Velocity Is 80 Feet Per Second
How Long Would it Take to Fly From Earth to Jupiter?
Volume of Inflating Spherical Balloon as a Function of Time
Smallest Triangular Portion From A Square Lot
Dimensions of the Lot for a Given Cost of Fencing
Amount of Sales Needed to Receive the Desired Monthly Income
The Tide in Bay of Fundy: The Depths of High and Low Tides
Longest Day of the Year: Summer Solstice
What is the Chance of Rain: Local vs Federal Forecasts
Number of days the project delayed
Probability That Exactly 1 is Defective in Getting 2 Cell Phones
Angle Correction for Repeated Measurement
Expected Profit for the Acceptance of Estimate of an Engineering Company