ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
1. The ______ determines the nature of the roots of
a quadratic equation.
A. Determinant
C. Range
B. Domain
D. Discriminant*
9. A father said to his son, "I was as old as you are
at the present at the time of your birth". If the
father's age is 38 years now, the son's age five
years back was:
A. 14 years old* C. 33 years old
B. 19 years old
D. 38 years old
2. The sum of the squares of three numbers is 138,
while the sum of their products taken two at a
time is 131. Their sum is:
A. 20*
C. 40
B. 30
D. 50
𝑥
10. If 𝑓(𝑥) =
A.
3. Let set A = {1, 2} and set B = {-3, 5}, find A x B:
A. {(1, 2), (1, -3), (2, 1), (2, 5), (2, -3), (1, 5)}
B. {(-3, 1), (-3, 2), (5, 1), (5, 2)}
C. {(1, -3), (1, 5), (2, -3), (2, 5)}*
D. none of the above
B.
1−𝑥
𝑥3
, find the value of 𝑓(𝑓(𝑓(𝑥))).
C.
1−𝑥 3
3𝑥
D.
1−3𝑥
𝑥
1−𝑥
𝑥
1−3𝑥
*
11. If set A has p elements and set B has q elements,
then the number elements in AxB is:
A. pq*
C. pq + 1
B. p + q
D. p + q + 1
4. Two or more than two angles with the same initial
and terminal sides are known as ____.
A. Reflective angles
B. Coterminal angles*
C. Obtuse angles
D. Explementary angles
12. Which of the following functions is equivalent to
the function:
𝑐𝑠𝑐⁡(𝑥)(1 − 𝑐𝑜𝑠 2 (𝑥))
𝑠𝑖𝑛⁡(𝑥)𝑐𝑜𝑠⁡(𝑥)
5. The constant term in the expansion of (𝒙𝟐 + 𝟑)𝟔
is:
A. 279
C. 729*
B. 297
D. 792
A. sin(x)
B. cos(x)
C. sec(x)*
D. cot(x)
13. What is the domain of the function:
𝑓(𝑥) = 4 − √3𝑥 3 − 7
6. The number of non-empty subsets of the set {1,
2, 3, 4} is:
A. 14
C. 16
B. 15*
D. 17
A. 𝑥
B.
7. The angle of elevation of the top of a tower from a
certain point is 30°. If the observer moves 20
meters towards the tower, the angle of elevation
of the top increases by 15°. Find the height of the
tower.
A. 27.32 m*
C. 13.66 m
B. 8.66 m
D. 17.32 m
≥
𝑥≥
4
*
3
5
3
C.
𝑥≥
D.
𝑥≥
6
5
4
7
14. A is 30% more efficient than B. How much time
will they, working together, take to complete a
job which A alone could have done in 23 days?
A. 13 days*
C. 17 days
B. 15 days
D. 20 days
15. The number of roots of the function:
8. In a survey of 85 people, it is found that 31 like to
drink milk, 43 like coffee and 39 like tea. Also 13
like both milk and tea, 15 like milk and coffee, 20
like tea and coffee and 12 like none of the drinks.
Find the number of people who like all the three
drinks.
A. 6
C. 10
B. 8*
D. 12
𝑦 = 2𝑠𝑖𝑛⁡(𝑥)
A. only 1
B. only two
C. infinite*
D. indeterminable
16. Let A is any set and U is a universal set. Which
algebra law on sets states that: 𝐴 ∩ 𝑈 = 𝐴
A. Idempotent
C. Domination
B. Absorption
D. Identity*
1
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
17. Find the 3rd term in the expansion: (6𝑥 3 − 5𝑦 2 )4
A. 1296x6y4
C. 5400x6y4*
6 4
B. -4320x y
D. -3000x6y4
25. If the roots of the quadratic equation ax2 + bx + c
= 0 are 3 and 2. Given that a, b and c are all
whole numbers, find a + b + c.
A. -2
C. -6
B. 6
D. 2*
18. A hot air balloon is observed from a point A at
22.23° angle of elevation and simultaneously from
a point B 1500 m from A at 48.11° elevation. Find
the height of the balloon.
A. 968 m*
C. 981 m
B. 976 m
D. 995 m
26. A tank can be filled in 9 hours by one pipe, 12
hours by a second pipe and can be drained when
full by a third pipe in 15 hours. How long will it
take to fill an empty tank with all pipes in
operation?
A. 7 hrs and 12 mins
C. 7 hrs and 42 mins
B. 7 hrs and 32 mins
D. 7 hrs and 50 mins*
19. Which of the following statement is not true?
A. All even numbers are natural numbers
B. Not all prime numbers are also odd numbers
C. All integers can be categorized as positive or
negative integers*
D. Natural numbers are part of whole numbers
27. Find the definite value of the inverse 𝑓 −1 (30) of
the function: 𝑓(𝑥) = 3√5𝑥
A. 10
C. 30
B. 20*
D. 40
20. The sum of the squares of two positive integers is
208. If the square if the larger number is 18 times
the smaller number, find the sum of the numbers.
A. 18
C. 22
B. 20*
D. 24
28. For any acute angle, sine A is equal to ____.
A. sin (180 - A)*
C. sin(180 + A)
B. sin(90 - A)
D. sin(A - 180)
21. A ________ is an ancillary theorem whose result
is not the target for the proof.
A. postulate
C. hypothesis
B. lemma*
D. theorem
29. Ten liters of 25% salt solution and 15 liters of
35% salt solution are poured into a drum
originally containing 30 liters of 10% solution.
What is the percent concentration of salt in the
mixture?
A. 19.55%*
C. 27.05%
B. 22.15 %
D. 25.72%
22. Let f(x) = x5 + ax4 – 3x3 + bx – 4. If (x) is divided
by x + 7, the remainder is -3805, when divided by
x + 1, the remainder is -1. What is the value of
a+b?
A. 5
C. 9*
B. 7
D. 11
23. Three men A, B, and C can do a piece of work in t
hours working together. Working alone, A can
do the work in 6 hours more, B in 1 hour more,
and C in twice the time if all working together.
How long would it take to finish the work if all
working together?
A. 20 mins
C. 40 mins*
B. 30 mins
D. 50 mins
30. A proposition that is incidentally proved in proving
another proposition.
A. lemma
C. axioms
B. theorem
D. corollary*
31. What is the cardinality of the power set of a
singleton set?
A. 0
C. 2*
B. 1
D. 3
24. Find the range of the function: 𝑦 = sec(𝑥)
A. {−∞ < 𝑥 ≤ −1} ∪ {1 ≤ 𝑥 < ∞}*
B. all real numbers
C. [-1, 1]
D. (0, ∞)
32. Find the domain of the function:
𝑦 = √𝑥 + 5
A. 𝑥 > −5
B. 𝑥 < −5
2
C. 𝑥 ≥ −5*
D. 𝑥 ≤ −5
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
33. Find the value of 's' in the given expression:
2𝑑2 − 𝑑 − 10
𝑑2 − 4𝑑 + 3
=
𝑑2 + 7𝑑 + 10 𝑑2 + 2𝑑 − 15
A. -2
C. 2
B. -4
D. 4*
40. Which of the following is not an even function?
A. 𝑦 = |𝑥|*
B. 𝑦 = 𝑠𝑒𝑐(𝑥)
C. 𝑦 = 𝑐𝑜𝑡(𝑥) 𝑠𝑖𝑛(𝑥)
D. 𝑦 = 𝑥 2 +𝑠𝑖𝑛(𝑥)
34. If 15 men can build a wall 108 meters long in 6
days, what length of similar wall can be built by
25 men in 3 days?
A. 75 m*
C. 100 m
B. 90 m
D. 105 m
41. Find the product wxy in the following equations:
3x – 2y + w = 11
x + 5y – 2w = -9
2x + y – 3w = -6
A. 3
B. -3
35. Out of 800 boys in a school, 224 played cricket,
240 played hockey and 336 played basketball. Of
the total, 64 played both basketball and hockey;
80 played cricket and basketball and 40 played
cricket and hockey; 24 played all the three
games. The number of boys who did not play any
game is:
A. 128
C. 240
B. 216
D. 160*
42. Find the set notation for the Venn Diagram shown
below:
A. 𝐴 ∩ (𝐵 ∪ 𝐶)
B. 𝐴 ∪ (𝐵 ∩ 𝐶)
C. 𝐴 ∩ (𝐵\𝐶)
D.⁡𝐴\(𝐵 ∪ 𝐶)*
43. Find the remainder if we divide 4y^3 + 18y^2 + 8y
– 4 by (2y - 3).
A. 11
C. 41
B. 35
D. 62*
36. Find the sum of all of the roots of the equation
𝑥 4 − 2𝑥 2 − 3 = 0.
A. 0*
B. 1
C. 6
D. -6*
C. 2
D. 3
44. If sin 3A = cos 6B then:
A. A + B = 180
B. A - 2B = 30*
37. If tan(θ) = 3/4 and 0 < θ < π/2 and 25Asin2(θ)
cos(θ) = tan2(θ), then the value of A is:
A. 7/64
C. 3/64
B. 9/64
D. 5/64*
C. A + 2B = 30
D. A + B = 30
45. A mason can do a given job in 4 hrs. His helper
can do the same job in 9 hrs. The mason begins
working and after 1 hr is joined by his helper. In
how many hours will they complete the job?
A. 2.08 hrs*
C. 3.75 hrs
B. 2.67 hrs
D. 3.83 hrs
38. Bus liner A departs every 30 mins, bus liner B
every 45 mins and bus liner C every 60 mins. At
12:00 p.m., one bus from each liner departed
simultaneously. What time after 12:00 pm will
another bus depart from each liner at the same
time?
A. 2:00 pm
C. 4:00 pm
B. 3:00 am
D.3:00 pm*
46. What is the discriminant of the equation: 4x^2 =
8x – 5?
A. 144
C. -16*
B. -144
D. 16
47. Pedro can paint a fence 50% faster than Juan
and 20% faster than Pilar, and together they can
paint a given fence in 4 hours. How long will it
take Pedro can paint the same fence if he had to
work alone?
A. 6 days
C. 10 days*
B. 8 days
D. 12 days
39. 2 years ago, Gemel is 2/3 as old as his sister. In 2
years, he will 3/4 as old as she. How old is
Gemel?
A. 8 years old
C. 6 years old
B. 10 years old*
D. 18 years old
3
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
48. It is the branch of mathematics that deals with
general statements of relations, utilizing letters
and other symbols to represent specific sets of
numbers, values, vectors, etc., in the description
of such relations.
A. Discrete Mathematics
B. Finite Mathematics
C. Algebra*
D. Combinatorics
55. 20 teachers of a school either teach mathematics
or physics. 12 of them teach mathematics while 4
teach both the subjects. Then the number of
teachers teaching physics only is:
A. 8
C. 16
B. 12*
D. 20
56. A vertical tower stands on a horizontal plane and
is surmounted by a vertical flagstaff of height h. At
a point on the plane, the angles of elevation of the
bottom and the top of the flag staff are α and β,
respectively. Then the height of the tower is:
A. h tan α / (tan β + tan α)
B. h tan α / (tan β - tan α)*
C. h tan β / (tan β + tan α)
D. h tan β / (tan β - tan α)
49. Find the range of the function 𝑦 = tanh⁡(𝑥).
A. (0, 1)
C. [0, 1]
B. (-1, 1)*
D. [-1, 1]
50. There are two windows in a house. A window of
the house is at a height of 1.5 m above the
ground and the other window is 3 m vertically
above the lower window. Ram and Shyam are
sitting inside the two windows. At an instant, the
angle of elevation of a balloon from these
windows is observed as 45° and 30° respectively.
Find the height of the balloon from the ground.
A. 7.598 m
C. 7.269 m
B. 8.269 m
D. 8.598 m*
57. Determine the lowest value of the range of the
function y = x2 – 4x + 3.
A. -1*
C. 2
B. 0
D. 4
58. The expression 3x4 + x2 + 7x + 1 = 0, contains
how many imaginary roots?
A. 1 or 2
C. 2 or 4*
B. 2 or none
D. 4
51. Find the coefficient of the term with y5 in the
expansion of (𝑥 + 3𝑦)8 .
A. 13608*
C. 18603
B. 16308
D. 18306
59. For any set A, universal set U and null set ∅
.Which of the following set relations is true?
A. 𝐴 ∪ 𝐴𝑐 = ∅
C. 𝐴 ∩ 𝐴𝑐 = 𝑈
𝑐
B. 𝐴 ∪ 𝐴 = 𝑈*
D. 𝐴 ∩ 𝐴𝑐 = 𝐴
52. The measure of the angles of a triangle are in the
ratio 2:7:11. Measures of angles are?
A. 26°, 56°, 88° C. 20°, 70°, 90°
B. 18°, 63°, 99°* D. 25°,175°,105°
60. The tops of two poles of height of 20 m and 14 m
are connected by a wire. If the wire makes an
angle of 30° with horizontal, then the length of the
wire is:
A. 6 m
C. 10 m
B. 8 m
D. 12 m*
53. Let set A = {1, 2} and B = {a, b, c}. Then A3 = ?
A. {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1),
(2, 1, 2), (2, 2, 1), (2, 2, 2)}*
B. {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1),
(2, 1, 2), (2, 2, 1)}
C. {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 2),
(2, 2, 1), (2, 2, 2)}
D. {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1),
(2, 1, 2), (2, 2, 1), (1, 2, 2)}
61. Let x and y be positive real numbers such that
1
1
𝑦 3
1
− 𝑦 − 𝑥+𝑦 = 0, what is the value of (𝑥 ) +
𝑥
𝑥 3
(𝑦) ?
A. √2
B. 2√2
54. It takes Butch twice as long as it takes Dan to do
a certain piece of work. Working together they
can do the work in 6 days. How long would it take
Dan to do it alone?
A. 9 days*
C. 11 days
B. 10 days
D. 12 days
C. √5
D. 2√5*
62. A father takes his twins and a younger child out to
dinner on the twins’ birthday. The restaurant
charges P495 for the father and P45 for each
year of a child’s age, where the age is defined as
4
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
72. If 𝑓𝑛+1 = 𝑓𝑛−1 + 2𝑓𝑛 for n = 2, 3, 4,… and 𝑓1 =
𝑓2 = 1, then 𝑓(5) =
A. 7
C. 17*
B. 11
D. 21
the age at the most recent birthday. If the bill is
P945, which of the following could be the age of
the youngest child?
A. 1
C. 3
B. 2*
D. 4
73. If the height of a tower and the distance of the
point of observation from its foot, both are
increased by 10% then the angle of elevation of
its top:
A. increases
B. deceases
C. remains unchanged*
D. cannot be determined
63. What is the range of the function: 𝑦 = 5 − √4 − 𝑥 2
A. {y | 3 ≤ y ≤ 5}*
C. {y | 3 < y ≤ 5}
B. {y | 3 < y < 5}
D. {y | 3 ≤ y < 5}
64. Set A = {{1,2,3}, {4,5}, {6,7,8}}. Which of the
following statement/s is/are true?
A. {1, 2, 3} ⊆ 𝐴
C. 1 ∊ 𝐴
B. 𝛷 ∊ 𝐴
D. 𝛷 ⊆ 𝐴*
65. Suppose a function satisfies that
𝑥. Find 𝑓(3).
A. 3/2
C. 2
B. 2/3
D. 1/2*
66. If 𝑠𝑖𝑛(𝑥) =
be:
A. a/b
B. a/b + 1
𝑎
√𝑎2 +𝑏 2
1
3𝑓 (𝑥) −
74. If the universal U = {0, 1, 2, 3, 4, 5, 6, 7, ... 15} A
= {2, 3, 4, 8, 10}, B = {3, 4, 5, 10, 12}, C = {4, 5, 6,
12, 14}. Find (𝐴 ∪ 𝐵)𝑐
A. {0, 1, 6, 7, 9, 11, 13, 14, 15}*
B. {2, 3, 4, 5, 8, 10, 12}
C. {2, 8}
D. {5, 12}
𝑓(𝑥) =
, then the value of cot(θ) will
75. The ratio of the length of a rod and its shadow is
1
C. b/a*
D. b/a +1
. The angle of elevation of the sun is:
√3
A. 30 degrees*
B. 45 degrees
67. In discrete mathematics, it is a declarative
sentence that is either true or false.
A. premise
C. theory
B. conclusion
D. proposition*
C. 60 degrees
D. 75 degrees
76. A can do a work in 15 days and B in 20 days. If
they work on it together for 4 days, then the
fraction of the work that is left is:
A. 1/4
C. 7/15
B. 1/10
D. 8/15*
68. For which value of c will the equation x(x − c) = 1
− c have exactly one solution?
A. 0
C. 2*
B. 1
D. 3
77. Find the positive value of x so that x, x2 - 5, 2x will
be in harmonic progression.
A. 3
C. 5*
B. 4
D. 6
69. If set 𝐴𝑛 = {𝑛𝑥|𝑥 ∊ 𝑁}, Find 𝐴3 ∩ 𝐴5
A. 𝐴3
C. 𝐴8
B. 𝐴5
D. 𝐴15 *
78. Solve for the value of x in the equation:
𝑥
70. If each side of an equilateral triangle is increased
by 10%, what is the increased in its area?
A. 10%
C. 20%
B. 11%
D. 21%*
1+
71. When (x + 2)(x – 4) + 4 is divided by x – k, the
remainder is k. Find the smallest possible value of
k.
A. -4
C. 1
B. -1*
D. 4
A. 9
B. 45
5
1+
𝑥
1+
= 10
𝑥
𝑥
1+1+⋯
C. 75
D. 90*
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
79. If
𝑓(𝑥) = √𝑥 2 − 1
𝑔(𝑓(3)) =
A. 0.2
B. 1.7
and
10
𝑔(𝑥) = 𝑥+2,
then
87. Find the domain of the function:
A. R\{2}*
B. N\{2}
C. 2.1*
D. 3.5
A. 1/(3x - 1)
B. x/(3x + 1)*
82. From the
equations:
=
89. Solve the inequality:
𝑥
system
of
<2
90. Two finite sets A and B have m and n elements
respectively. If the total number of subsets of A is
112 more than the total number of subsets of B,
then the value of m is
A. 12
C. 7*
B. 10
D. 5
C. 64
D. 81
91. Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9,
10}, with subsets A = {1, 2, 5} and B = {6, 7}.
Then 𝐴 ∩ 𝐵 ′ ⁡is equal to:
A. 𝐵 𝑐
C. 𝐴𝑐
B. 𝐴*
D. 𝐵
83. Simplify the trigonometric equation:
𝜋
𝑡𝑎𝑛( 2 − 𝑥) 𝑠𝑒𝑐(𝑥)
1 − 𝑐𝑠𝑐 2 (𝑥)
A. -sec(x)
B. -sec2(x)
2+𝑥
non-linear
𝑎⁡ + ⁡𝑏⁡ + ⁡𝑐⁡ = ⁡9
𝑎𝑏⁡ + ⁡𝑏𝑐⁡ + ⁡𝑎𝑐⁡ = ⁡26
𝑎𝑏𝑐⁡ = ⁡24
A. 29*
B. 48
𝑥
A. (− ∞ , − 4) ∪ (− 2 , ∞)*
B. (− ∞ , − 2) ∪ (− 2 , ∞)
C. (− ∞ , − 4) ∪ (− 4 , ∞)
D. none of the above
1−3𝑥
C. x/(3x - 1)
D. 3/(3x + 1)
following
𝑥−2
C. Z\{2}
D. none of the above
88. Marcia paid $36 for a dress that was on sale for
25% of the original price. What was the original
price of the dress?
A. 48 dollars
C. 60 dollars
B. 108 dollars
D. 144 dollars*
80. The roots of the quadratic equation 𝑥 2 ⁡ − ⁡51𝑥⁡ +
⁡𝑘⁡ = ⁡0 differ by 75, where k is a real number.
Determine the sum of the squares of the roots.
A. 5625
C. 3825
B. 4113*
D. 756
81. Determine the inverse function of: 𝑓(𝑥)
1
C. -sec(x) sin(x)
D. -sec2(x) sin(x)*
92. Julia and Janella want to build an obtuse triangle,
if two of the adjacent sides are 6 and 8, what
should be the value of the longest side?
A. equal to 10
C. greater than 10*
B. less than 10
D. any length will do
84. Let U be a universal set, Ø an empty set and A
and B be a finite set. The duality of the set
operation (U∪A)∩(B∪Ø) is:
A. (Ø∪A)∩(B∪U)
C. (Ø∩A)∪(B∩U)*
B. (U∩A)∪(B∩Ø)
D. (Ø∩AC)∪(BC∩U)
93. If (1, 3), (2, 5) and (3, 3) are three elements of
AxB and the total number of elements in A´B is 6,
then the remaining elements of AxB are:
A. (5, 3); (1, 5); (2, 3)
C. (1, 5); (2, 3); (5, 3)
B. (5, 1); (3, 2); (5, 3)
D. (1, 5); (2, 3); (3, 5)*
85. Let set S = {0, 1, 5, (4, -5), {2, 5}, 7, {}}. How
many subset can be made from set S?
A. 128*
C. 32
B. 64
D. 16
94. The numbers 28, x +2, 112 form a geometric
progression. What is the 10th term?
A. 1733
C. 16336
B. 14336*
D. 15336
86. The first and last term of a geometric progression
is 6 and 486 respectively. If the sum of all the
terms is 726, find the number of terms.
A. 5*
C. 7
B. 6
D. 8
95. In an angle, the ray of angle is known as:
A. arms*
C. apex
B. vertex
D. terminal
6
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
96. Find the coefficient of the last term of the binomial
expansion: (𝑎 − 2𝑏)5
A. 32
C. 1
B. -32*
D. -1
5.
For a quadratic equation ax^2 + cx + b = 0, the
equation of the discriminant is:
A. (b^2 - 4ac)
C. (c^2 - 4ab)*
B. (b^2 - 4ac)^1/2
D. (c^2 - 4ab)^1/2
97. A stack of bricks has 61 bricks at the bottom
layer, 58 bricks in the 2nd layer, 55 bricks in the
3rd layer and so on, until the top layer has 10
bricks. Determine the total number of bricks used.
A. 396
C. 936
B. 639*
D. 963
6.
Find the constant term of the binomial expansion:
98. For any acute angle, tan A is equal to ____.
A. tan(180 – A)
C. tan(180 + A)*
B. tan(90 – A)
D. tan(-A)
7.
99. If two sets A and B has no common elements,
then the intersection of A and B is a______.
A. singular set
C. void*
B. power set
D. none of the above
If the roots of an equation are zero, then they are
classified as _______.
A. extraneous solutions C. Conditional solution
B. trivial solutions*
D. Null solution
8.
100. This is being used in finding the coefficient of a
binomial expansion (𝑎 + 𝑏)𝑛
A. Euler's triangle
B. Pythagorean triangle
C. Pascal's triangle*
D. Egyptian triangle
The sum of three numbers, a, b, and c, is 400.
One of the numbers, a, is 40 percent less than
the sum of b and c. What is the value of b + c ?
A. 50
C. 150
B. 100
D. 250*
9.
The difference of the cubes of two positive
numbers is 2402 and the cube of their difference
is 8. Find the larger number.
A. 21*
C. 19
B. 20
D. 18
1.
2.
3.
4.
(𝑥 2 +
A. 465
B. 696
If the function P(x) = 2x3 - 3x2 + cx +7 is divided
by (x - 2), the remainder is 5. Find the value of c.
A. 3
C. 4
B. -3*
D. -4
1 12
)
𝑥2
C. 924*
D. 171
10. When taking the common/decimal logarithm of a
number, the fractional part is also called:
A. applicate
C. characteristic
B. cologarithm
D. mantissa*
Solve for the value of x in the inequality: 71 < 9x + 1 < 100.
A. (-11, -4)
C. (-8, 11]*
B. (-2, 4]
D. [-8, 11]
11. It is an irrational number which cannot be
expressed as a fraction or as a terminating or
recurring decimal.
A. Ordinate
C. Applicate
B. Surd*
D. Palyndrome
Nadine can finish a job in 30 days and Liza can
finish the same job in 15 days. If Kathryn help
Liza, they can finish the job 4 days earlier if
Nadine and Liza work together. How long it takes
for Kathryn to finish the job alone?
A. 4 days
C. 10 days*
B. 6 days
D. 15 days
12. Find the value/s of k so that x – 3 is a factor of x4
– k2x2 – kx – 39 = 0.
A. -7/2 or 2
C. -7/3 or -2
B. -7/3 or 2*
D. -7/2 or -2
13. The sum of the squares of three numbers is 138,
while the sum of their products taken two at a
time is 131. Their sum is:
A. 20*
C. 40
B. 30
D. 50
How many possible positive roots does the
equation x4 + 2x3 – 3x2 – x +1 = 0?
A. four or two or none
C. three or one
B. two or none*
D. one
7
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
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14. A can do a piece of work in 4 hours; B and C
together can do it in 3 hours, while A and C
together can do it in 2 hours. How long will B
alone take to do it?
A. 8 hours
C. 12 hours*
B. 10 hours
D. 24 hours
C. {(1, 1), (1, 2), (0, 1) (0, 2)
D. none of these
23. In a class of 30 pupils, 12 take needle work, 16
take physics and 18 take history. If all the 30
students take at least one subject and no one
takes all three then the number of pupils taking 2
subjects is:
A. 16*
C. 8
B. 6
D. 20
15. The equation whose roots are the reciprocals of
the roots of the equation 2x2 – 3x - 5 = 0 .
A. 5x^2 – 2x – 3 = 0
C. 5x^2 + 3x – 2 = 0*
B. 2x^2 – 5x – 3 = 0
D. 3x^2 – 5x – 2 = 0
24. Find the sum of the arithmetic sequence: 2, 5, 8,
.... 470.
A. 37502
C. 37520
B. 37052*
D. 37250
16. Which of the following is NOT considered as part
of the proper subset but still a subset of any set
A?
A. Power set
C. itself*
B. Null set
D. All of the above
25. What is the cardinality
given that A = {x | x ∈ N,
A. 8*
B. 32
17. This law states that "The union of set A and the
universal set is equal to the universal set"
A. Identity Law
C. Idempotent Law
B. Domination Law*
D. Universal Law
26. A class has 175 students. The following data
shows the number of students obtaining one or
more subjects. Mathematics 100, Physics 70,
Chemistry 40; Mathematics and Physics 30,
Mathematics and Chemistry 28, Physics and
Chemistry 23; Mathematics, Physics and
Chemistry 18. How many students have offered
Mathematics alone?
A. 35
C. 52
B. 48
D. 60*
18. The domain of the function:
𝑦 = 𝑙𝑜𝑔(1 − 𝑥) + √𝑥 2 − 1
A. [-1, 1]
B. (1, ∞)
of the power set of A
x < 10, 3|x }?
C. 128
D. 512
C. (-1, 0)
D. (-∞, -1]*
19. The middle and last term of a geometric
progression with 15 terms is 2187 and 4782969
respectively. What is the common ratio?
A. 2
C. 4
B. 3*
D. 5
27. In a pile of logs, each layer contains one more
than the layer above and the top contains only
one log. If you are to build 15 layers, how many
logs do you need?
A. 78
C. 105
B. 91
D. 120*
20. Let set A = {2, 1, 8, 11, 13, 20, 3} and set B = {x |
x is a natural odd numbers}. Find A\B.
A. {2, 8, 20}*
C. {1, 3, 5, 7, 8, 9,....}
B. {1, 3, 11, 13}
D. { }
28. Determine the sum of the progression if there are
7 arithmetic means between 3 and 35.
A. 182
C. 171*
B. 232
D. 216
21. In a certain community with 1000 population, 570
watch GMA channel, and 590 watch ABS-CBN
channel. If 180 of them is watching in both
channel, what percent of the population is not
watching any of the two stations?
A. 34%
C. 7%
B. 21%
D. 2%*
29. The numbers x, 2x+7 and 10x-7 will form a
geometric progression if the value of x is:
A. -5 or -3/7
C. 7 or 7/6
B. 7 or -7/6*
D. 8 or -1
22. If A = {1, 2} and B = {0, 1}, then AxB is:
A. {(1, 0) (1, 1), (2, 0) (2, 1)}*
B. {(1, 0), (2, 1)}
30. The side of a square is 10 m. A second square is
formed by joining, in the proper order, the
midpoints of the sides of the first square. A third
8
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
square is formed by joining the midpoints of the
second square, and so on. Find the sum of the
areas of all the squares if the process will
continue indefinitely.
A. 50 m^2
C. 200 m^2*
B. 100 m^2
D. 250 m^2
A. Quadrant I
B. Quadrant II
C. Quadrant III*
D. Quadrant IV
38. The angle of elevation at the top of tower B from
the top of the tower A is 28 deg and the angle of
elevation of the top of tower A from the base of
the tower B is 46 deg. The two towers lie in the
same horizontal plane. If the height of the tower
B is 120 m, find the height of tower A.
A. 73.9 m
C. 79.3 m*
B. 76.3 m
D. 93.7 m
31. The incenter of a triangle is the intersection of
the three ________ of the triangle.
A. altitudes
C. angle bisectors*
B. medians
D. none of the above
32. A 20 m high mast is in the top of the cliff whose
height above sea level is unknown. An observer
at the sea sees the top of the mast at an
elevation of 46°42’, the foot at 38°23’. The height
of the cliff is closest to:
A. 51 m
C. 57 m
B. 54 m
D. 59 m*
39. If the supplement of an angle A is 5/2 of its
complement, find the value of the A.
A. 10 degrees
C. 25 degrees
B. 20 degrees
D. 30 degrees*
40. Which of the following is equivalent to 180
degrees?
A. 400 grad
C. 3200 mils*
B. 400 gons
D. all of the above
33. The median of a triangle is the line connecting a
vertex and the midpoint of the opposite side. For
a given triangle, these medians intersects at a
point which is called the:
A. incenter
C. circumcenter
B. orthocenter
D. centroid*
41. A transit set up 40 m from the base of a vertical
chimney reads 32°30’ with crosshairs set on the
top of the chimney. With telescope level, the
vertical rod at the base of the chimney is 2.1 m.
Approximately how tall is the chimney?
A. 15 m
C. 28 m*
B. 26 m
D. 36 m
34. It is the only right triangle whose sides are three
consecutive integers (3, 4 and 5) satisfying the
Pythagorean theorem.
A. Perfect Triangle
C. Chinese Triangle
B. European Triangle
D. Egyptian Triangle*
42. The sides of a triangle are 8 cm, 10 cm and 14
cm. Find the difference of the length of the radius
of the circumscribing circle and inscribed circle.
A. 4.69 cm*
C. 7.14 cm
B. 6.49 cm
D. 8.41 cm
35. If sin(A) = 3/5 and A is in the second quadrant,
while cos(B) = 7/25 and B is in the first quadrant,
find sin(A + B)
A. 0.5
C. -0.5
B. 0.6
D. -0.6*
43. The shortest side of an isosceles triangle is 5, if
the angle opposite to it is 36.42 degrees, what is
the length of the other sides?
A. 8*
C. 12
B. 10
D. 14
36. A PLDT tower and a monument stand is on a
level plane. The angles of depression of the top
and bottom of the monument viewed from the top
of the PLDT tower are 13 deg and 35 deg,
respectively. The height of the tower is 50 m.
Find the height of the monument.
A. 33.51 m*
C. 51.51 m
B. 41.51 m
D. 61.51 m
44. An engineer left a point walking at 6.5 kph in a
direction E 20 N (that is bearing of 70 deg). A
cyclist leaves the same point at the same time in
a direction E 40 S (that is bearing 130 deg)
travelling at constant speed. Find distance
traveled by the cyclist after 5 hours if at this
instant the engineer and the cyclist are 80 km
apart.
A. 81.14 km
C. 101.14 km
B. 91.14 km*
D. 111.14 km
37. What quadrant cotangent is positive but sine is
negative?
9
ENGINEERING MATHEMATICS
WEEK 1 EXAMINATION
SCORE
________________________________________________________________________________
45. The base of a triangle is 3 units more than its
altitude. If the area of the is 27, what is the length
of the base?
A. 6
C. 11
B. 9*
D. 12
46. The observer from the top of a building 100 m
high found out that the angle of depression to
point A due East of it is 30°. From a point B due
to South of the building, the angle of elevation at
point B is 60°. Find the distance AB.
A. 155.238 m
C. 182.574 m*
B. 173.886 m
D. 209.612 m
47. One of the angles of a triangle is 35 degrees,
adjacent side to this angle is 5 and 8. What is the
area?
A. 9.11 sq. units
C. 11.47 sq. units*
B. 10.71 sq. units
D. 13.55 sq. units
48. If tan x = 1/3 and tan y = 1/2, what is the value of
tan (x + y) ?
A. 0
C. 2
B. 1*
D. indeterminate
49. An equilateral triangle is inscribed within a circle
whose diameter is 12 cm. In this triangle a circle
is inscribed; and in this circle, another equilateral
triangle is inscribed; and so on indefinitely. Find
the sum of the areas of all the triangles in cm2.
A. 62.35*
C. 65.32
B. 63.25
D. 66.67
50. If the area of an equilateral triangle increases by
10%, its perimeter increases by:
A. 1%
C. 4%
B. 2.5%
D. 5%*
10