Mathematics 1

Module 1

CE Department – College of Engineering

Compiled
Compiled
by: by:
Engr.
Engr.
Marbel
Marbel
Perez
Perez Engineering Correlation
Bulacan State University
CE Department – College of Engineering Compiled by: Engr. Marbel Perez

Chapter 1 Mathematics

1.1 Algebra

1.2 Geometry and Solid Geometry

1.3 Trigonometry

Duration: 36 hours

Introduction

This module will serve as a reviewer for the Civil Engineering Licensure

Examination. It contains a compilation of useful formulas for the subjects of

Algebra, Geometry (along with Solid Mensuration) and Trigonometry. It is worth

noting that this module will only contain a summarized style of presentation as

this subject, CE Correlation, contains all the topic discussed in the whole Civil

Engineering course, therefore the sheer amount of topics will make this

unnecessarily long.

Objectives

1. To be able solve problems in the Civil Engineering Licensure Examination in the

subjects of;

2. Algebra,

3. Geometry and Solid mensuration;

4. Trigonometry

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Pre-Test

1. A is 8% taller than B , while B is 9% taller than C. By how much percent is A

taller than C? a. 12.22% b.13.86% c.17.72% d. 19.04%

2. What is the sum of the roots of the equation 3x^2 – 4x + 6 = 0?

a. -4 b. 4 c. 4/3 d. -4/3

3. Find the 5th term of the expansion (2 – x)^ 6?

a. 60x5 b. 12x4 c. 60x4 d. 12x5

4. 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.

a. 30 feet b. 35 c. 50 d. 60

5. Solve this trigonometric equation: 2cos x + sec x = 3.

a. π/2 b. 3π/2 c. π/3 d. 5π/4

6. 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.

a. N 75° 20’ E b. N 75° 20’ W c. S 75° 20’ E d. S 75° 20’ W

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1.1 Algebra

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1.2 Geometry and Solid Geometry

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1.3 Trigonometry

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Post Test

Algebra

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?

a. 13.75% b. 36.25% c. 23.55% d. 44.35%

A is 8% taller than B , while B is 9% taller than C. By how much percent is A taller than

C?

a. 12.22% b.13.86% c.17.72% d. 19.04%

What is the sum of the roots of the equation 3x^2 – 4x + 6 = 0?

a. -4 b. 4 c. 4/3 d. -4/3

Find the 5th term of the expansion (2 – x)^ 6?

a. 60x5 b. 12x4 c. 60x4 d. 12x5

Calculate the following sum:

a. 76 b. 85 c. 90 d. 80

Find the nth term of the series 1, 4 ,7 , 10 , 13…

a. 3n – 2 b. 3n + 2 c. 2n + 2 d. n + 2

Solve for x: 7x = 4x + 12

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a. 3 b. 4 c. 7 d. 10

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.

a. 2.4 b. 2.1 c. 1.6 d. 1.3

One number is more than the another and the sum is 71. Find the larger number.

a. 36 b. 31 c. 34 d. 38

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.

a. 5,15 b. 14,24 c. 8,18 d. 11,21

Simplify this radical:

a. 4x b. 2√x c. 2x d. 4√x

Given that x < y < 0 < w < z, what is the sign of xyz/w?

a. Negative b. Positive c. Imaginary d. Cannot determine

Solve for x and y:

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a. x = 3/4, y = 1/5 b. x = -3/4, y = 1/5 c. x = 3/4, y = -1/5 d. x = -3/4 , y = -1/5

The following are the zeros of this equation x3 – 3x2 – 10x + 24 EXCEPT:

a. 2 b. 4 c. 3 d. -3

Solve for x:

a. 5 b. -5 c. 1/5 d. -1/5

Divide 60 into two parts with the ratio of 2:3.

a. 30,30 b. 36,24 c. 15,45 d. 10,50

Find the value of x in (35)(96) = 32x

a. 8.5 b. 9 c. 9.5 d. 8

Find the 2017th digit in the decimal equivalent of 2017/9999.

a. 2 b. 0 c. 1 d. 7

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If d = 1000 – 200q and c = 4000 + 20d , find c as a function of q.

a. 24000 + 4000q b. 24000 – 4000q c. -24000 + 4000q d. -24000 – 4000q

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?

a. 30 days b. 25 c. 21 d. 17

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.

a. 150 b. 135 c. 162 d. 144

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?

a.700 b. 650 c. 600 d. 550

Log M + log N is equal to:

a. log MN b. same c, log M/N d. logMN

Evaluate: 1/2 * 2/3 * … 2016/2017

a. 1 b. 0 c. 1/2017 d. 2017

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Find the value of k so that the equation 4x^2 + kx + 9 = 0 has one root equal to -3

a. k = 12 b. k = 15 c. k = 20 d. k = 24

Find the constant term of the third term in the expansion of (2x + y)^6.

a. 180 b. 225 c. 240 d. 300

Factor the following: ax + ay – bx – by

a. (a+b)(x-y) b. (a-b)(x+y) c. (b-a)(x+y) d. (y-x)(a+b)

Which of the following is a palindromic number?

a. 2017 b. 2002 c. 2010 d. 2000

Solve for x: 10x + 10x+1 = 5x + 5x+1 + 5x+2

a. 1.2169 b. 1.3185 c. 1.4468 d. 1.4947

For a given function f(t) = f(-t). What type of symmetry does f(t) have?

a. odd b. even c. rotational d. quarter-wave

Simplify: (-54s)(-4/9)

a. 3s/2 b. 24s c. 168s d. 9s/4

Solve for x: |x - 2| + 1 = x

a. 1/4 b. 2/5 c. 3/2 d. 4/7

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. 30 days b. 27 c. 25 d. 21

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?

a. 3:25.9 b. 3:27.6 c. 3:28.2 d. 3:31.5

SITUATION 1: Resolve into partial fraction of the following:

Compute the value of B.

a. 5 b. 3 c. 2 d. 0

Compute the value of A.

a. 5 b. 3 c. 2 d. 0

Compute the value of C.

a. 5 b. 3 c. 2 d. 0

Find the remainder of 3x^3 – x^2 – 8x + 5 when divided by x + 2

a. 3 b. 6 c.7 d. -7

Find the summation of (5K – 3) from K = 1 to K = 16.

a. 632 b. 705 c. 790 d. 847

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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?

a. 125 rpm b. 200 c. 300 d. 450

Trigonometry

The sum of the sides of the triangle ABC is equal to 400 m. A = 38°, B = 58°. Find the

side AC in meters.

a. 150 b. 123 c. 113 d. 138

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.

a. 193 km b. 205 c. 235 d. 176

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. a. 32.55°
b. 35.96° c. 41.05° d. 44.74°
Find the angle C. a.

37.34°
b. 38.71° c. 33.19° d. 35.19°
Find the length of the side 6 in meters.

a. 22.6 b. 37.5 c. 28.1 d. 30.2

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Find the period of the function y = 3 cot 1/2 t.

a. π b. 1/2 π c. 2π d. 0

In triangle DEF , DE = 18 , EF = 6 . The length FD must be:

a. 12 b. 24 c. 13 d. None

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.

a. 7.49 m b. 8.66 c. 4.86 d. 5.21

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?

a. 30 mins b. 60 c. 120 d. 180

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?

a. 49 m b. 60 c. 55 d. 32

The perimeter of triangle ABC is 300 m , A = 36° , B = 58° and C = 86° . Determine the

side opposite the biggest angle.

a. 115 b. 107 c. 112 d. 123

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.

a. 30 feet b. 35 c. 50 d. 60

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Solve this trigonometric equation: 2cos x + sec x = 3.

a. π/2 b. 3π/2 c. π/3 d. 5π/4

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.

a. N 75° 20’ E b. N 75° 20’ W c. S 75° 20’ E d. S 75° 20’ W

It is usually defined as the angle made by the ray drawn and it can be read from north or

south.

a. Depression b. Elevation c. Bearing d. None of these

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?

a. 2945 m b. 2943 c. 2950 d. 2934

The Father of Trigonometry.

a. Archimedes b. Hipparchus c. Pythagoras d. Napier

Geometry and Solid Mensuration

Find the distance of the vertex curve (x-2)^2 = 4y to the line 2x – 3y – 8 = 0.

a. 1.10 b. 1.35 c. 1.60 d. 1.95

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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.

a. x^2 + 8x – 26y = 55 c. x^2 – 8x – 26y = 55

b. x^2 + 8x + 26y = 55 d. x^2 – 8x + 26y = 55

What kind of symmetry, if any, does the graph of y = x^2 – 16 have?

a. It is symmetrical with respect to x-axis.

b. It does not have any symmetry.

c. It is symmetrical with respect to y-axis

d. It is symmetrical with respect to both axes.

The surface area of an open cylinder tank is 68 sq m. If the diameter is 2/3 of its height,

compute the height of the tank.

a. 5.58 m b. 5.28 c. 5.15 d. 4.97

Find the volume of a cone to be constructed from a sector having a diameter of 72 cm

and a central angle of 210°

a. 11450 b. 13500 c. 15510 d. 12270

A 4.2 by 4.2 square pyramid with a lateral edge of 15 cm. What is the volume?

a. 86.44 sq cm b. 87.17 c. 90.64 d. 93.78

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A sphere has a volume of 2000 cu m. There exist a small circle of the sphere, the plane

of which is 6.5 m from the center. Calculate the area of the small circle in m sq.

a. 52 b. 59 c. 63 d. 68

A man cycles 24 km due south and then 20 km due east. Another man, standing at the

same time as the first man cycles 32 km due east and 7 km due south. Find the

distance between the two men.

a. 20.81 km b. 25.12 c. 22.12 d. 16.57

One edge of regular hexahedron is 24 cm long. Find the ratio of its volume to its surface

area.

a. 0.5 b. 4 c. 0.125 d. 2

Find the volume of the regular polyhedron with an edge of 3 m.

a. 5.74 m3 b. 6.18 c. 3.18 d. 7.33

Star shaped figures are known as :

a. Polygon b. Polyhedron c. Stars d. Polygrams

A piece of thin card board in the form of a sector of a circle of radius 36 cm is rolled into

a cone. Find the volume of the cone if the angle of the sector is 45°.

a. 780.45 b. 764.19 c. 757.50 d. 742.13

A right circular cone has a base radius of x and altitude of 3x, what is the slant height?

a. 3.16x b. 2.57x c. 6.19x d. 4.89x

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A spherical ball with a radius of 14 cm was dropped on a cone with a depth of 20 cm.

Find the height from the base of the cone to the point of tangency of the ball and the

cone.

a. 16.31 cm b. 15.74 c. 14.55 d. 13.84

SITUATION 1: Imagine a cube to measure 5 units per edge and to have its total surface

area painted yellow.

How many times you must cut completely through the cube to make cubes which

measure 1 unit on an edge?

a. 15 b. 25 c. 12 d. 125

How many cubes have one yellow face?

a. 8 b. 36 c. 54 d. 27

How many cube are in all?

a. 125 b. 75 c. 25 d. 100

A light is placed 5 m from the center of a giant globe 3 m in diameter, what will be the

length of the wire?

a. 9 m b. 10 c. 12 d. 15

An angle included by a tangent and a chord drawn from the point of contact is

measured by the intercepted arc?

a. doubled b. same d. third d. half

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A place hillside is inclined at an angle of 28° with the horizontal. A man wearing skis can

climb hillside by following a straight path inclined at an angle of 12° to the horizontal, but

one without skis must follow a path inclined with the horizontal. Find the angle between

the directions of the two paths.

a. 19° 48’ b. 11° 16’ c. 15° 35’ d. 17° 46’

A large steel buoy consists of a spherical segment and a cone having a common base

of 3 m. The altitude of the segment is 2 m and that of the cone is 6 m. Find the total

surface of the buoy.

a. 114.91 sq m b. 104.06 sq m c. 115.71 sq m d. 100.32 sq m

What is the area of the decagon inscribed in a circle that has an area of 412 sq m. a.

385.4 sq m b. 406.12 sq m c. 371.18 sq m d. 421.15 sq m

A pyramid 20 cm high is divided into three parts by two planes parallel to the base.

These planes are at distances 4 and 12 cm from the vertex. Determine the ratio of the

smallest part to the largest part.

a. 0.102 b. 0.265 c. 0.038 d. 0.037

The areas of the faces of the rectangular box are 8, 12 , and 16. Determine the volume.

a. 42.12 b. 39.19 c. 16.72 d. 54.33

In 2014, Ms Sisippi bought two lots at P9.6 million each. One lot contains 40 sq m more

than the other but costs P 12,000 per sq m. Find the area of the smaller lot.

a. 140 b. 160 c. 180 d. 200

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CE Department – College of Engineering Compiled by: Engr. Marbel Perez

SUGGESTED READINGS AND WEBSITES

Svirin, A. (2004). 1300 Math Formulas. A.Svirin.

Tiongson, J. R., & Rojas, R. A., Jr. (2006). 1001 Solved Problems in Engineering
Mathematics (Second ed.). Cebu City: First Benchmark Publisher,Inc.

Padilla, P. B., Jr. (2001). Board Exam Guide in Engineering Mathematics. Manila:
Padilla Civil Engineering Review School and Publishing.

Google. (n.d.). Retrieved from https://www.dictionary.com/browse/google

References

Svirin, A. (2004). 1300 Math Formulas. A.Svirin.

Tiongson, J. R., & Rojas, R. A., Jr. (2006). 1001 Solved Problems in Engineering
Mathematics (Second ed.). Cebu City: First Benchmark Publisher,Inc.

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CE Department – College of Engineering Compiled by: Engr. Marbel Perez

Padilla, P. B., Jr. (2001). Board Exam Guide in Engineering Mathematics. Manila:
Padilla Civil Engineering Review School and Publishing.

Google. (n.d.). Retrieved from https://www.dictionary.com/browse/google

Various Engineers. (2019). Civil Engineering Board Exam Review Group. Retrieved

2020, from https://www.facebook.com/CEBoardExamPH/.

Answer Key (Post Test)

Answer will be provided later, the post test part of this module will serve as your Plate

no. 1, to be submitted to an agreed upon date. The plate shall contain the full solution

to the problems given in the Post Test. For more information kindly contact Engr Marbel

Perez.

Email: marbel.perez@bulsu.edu.ph

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