Mathematics specialization 11

Question 1
• 1. Perform the operation given that:
A = {-4,-2,0,2,4}, B= {-4-2,0,3,4}
A U B =?
A. {4,2,0,3}
B. {-4,-2,0,2,3,4} ←
C. {-4-2,0-3}
D. {-4,-2,0,2,3,4,5}
A U B = distinct elements that are either in A or in B, so given that
A = {-4,-2,0,2,4},
B= {-4-2,0,3,4}
A U B = { -4, -2, 0, 2, 3, 4}

Question 2
• The cost of all items sold by Guzmart office
supply during the month of June is Php
95,000.00. What is the breakeven point ?
• A. Php 105,000.00
• B. Php 85,000.00
• C. Php 45, 000.00 ←
• D. Php 145,000.00

• Break-even point for a business is given by the
formula:
B = F/P – V
where B = units sold to break-even point,
F = fixed costs
P = price per unit
V = variable costs
Simply put, break even point means NO GAIN,
NO LOSS.

Question 3
• Simplify (a^2 – 5a)/(5 –a)
•
• A. a C. –a ←
• B. a-5 D. 5-a

Question 3
• (a^2 – 5a)/(5 – a)
• a(a – 5)/ (5 – a) common factoring
• a(a – 5)/ -(-5 + a) distributive property
• a(a – 5)/ -(a – 5) commutative property
• -a

Question 4
• Simplify the expression
←

Question 5
• List of four smallest elements of the set
{ y|y=2x+1, x ԑ natural numbers}
A. 1,2,3,4 C. 3,5,7,9 ←
B. 1,3,5,7 D. 3,4,5,6
• Natural numbers are the set of positive integers = {1, 2, 3, 4, …}
• if x = 1, then y = 2(1) + 1 = 3
if x = 2, then y = 2(2) + 1 = 5
if x = 3, then y = 2(1) + 1 = 7
if x = 4, then y = 2(1) + 1 = 9

Question 6
• Factor over the integers by grouping: 3x3+x2+6x+2
x2(3x + 1) + 2(3x+1)
(x2+ 2)(3x+1) ←

Question 6
• Factor over the integers by grouping: 3x3+x2+6x+2
• x2(3x + 1) + 2(3x+1)
• (x2+ 2)(3x+1)

Question 7
• Solve the rational expression:
A. x=1/3 C. x=-1/3
B. x=-3 ← D. x=3

Question 8
• use absolute value notation to describe the
given situation:
• the distance between x and 3.
A. -|x-3| C. –|x+3|
B. |x+3| D. |x-3| ←

Question 9
• Simplify this complex fraction :
←

Question 10
• Find the acute angle between two lines have
the direction numbers [1,1,0] and [2,1,2]
A. 20° C. 45° ←
B. 50° D. 30°

Question 11
• Simplify the given exponential expression:
←

Question 12
• By inspection, determine whether each
percentage is greater than, equal to, less
than, or less than and equal to the base ; 100%
of 0.12.
A. Percentage is less than the base.
B. Percentage is equal to the base. ←
C. Percentage is less than and equal to the
base.
D. Percentage is greater than the base.

Question 13
• Three fourths of the participants in a regional
training program are from private universities.
Two thirds of these are from Teacher
Education Institutions. If there are 96
participants, how many of them represent
private Teacher Education Institutions?
A. 72 C. 48 ←
B. 18 D. 24

Question 14
• If (x)=2x-3 and g( x) =
• find (f o f) (x)
←

Question 14
(f o f)(x) = f(f(x)) = f (2x -3)
= 2(2x -3) – 3
= 4x – 6 – 3
= 4x – 9

Question 15
• A total of PHP 75,000.00 is deposited into two
simple interest accounts. In one account the
annual simple interest rate is 5% and in the second
account the annual simple interest rate is 7%. The
amount of interest earned for 1 year was Php
4,050.00 . how much was invested in each?
A. At 5 %= Php 60,000.00; at 7%= Php 15,000.00 ←
B. At 5 %= Php 50,000.00; at 7%= Php 25,000.00
C. At 5 %= Php 55,000.00; at 7%= Php 20,000.00
D. At 5 %= Php 15,000.00; at 7%= Php 60,000.00

• Let x be the amount deposited in 5% account.
• Then 75000 – x is the amount deposited in the 7% account.
• Let I be the combined interest gained from the two accounts.
• Using the formula I = PRT
• where I = interest gained
• P = principal amount
• R = interest rate
• T = time in years
• There are two interests here so I = I1 + I2, where I1 is the interest from the 5% account and I2 is
from the 7% account. Since we are dealing with a 1 year term, we can ignore the T here.
• I = x(0.05) + (75000-x)(0.07)
• 4050 = 0.05x + 5250 – 0.07x
• -0.02x = -1200
• x = 60000
• thus 60000 was invested at 5% while 15000 was at 7%

Question 16
• Find the direction numbers for the line that joins the points
(1,3,4) and (-2,3,7).
A. [1,-1,0]
B. [1,0,-1]
C. [1,-1,2]
D. [-1,0,1] ←
Let A(1, 3, 4) and B(-2, 3, 7) define directed line segment AB. Then
its direction numbers l, m, n are given by
l = -2 – 1 = -3
m = 3 – 3 = 0
n = 7 – 4 = 3
(-3, 0, 3) or any of its multiple such as (-1, 0, 1)

Question 17
• Determine the percentage : Rate =200% , Base
=30
A. 60 ←
B. 2,400
C. 360
D. 120

Question 18
• The intersection of Sets A and B is defined by
A Ω B = {x/x ԑA and ԑB}
If A={a,b,c,d,e}, B={a,c,f,g}, find A Ω B
A. {b,c,g} C. {a,c} ←
B. {a,f,g} D. {a,b,c,g}

Question 19
• If i(x)=2x-3 and g(x)=
find (g o g) (x)
←

Question 20
• The sun is approximately meters
from the Earth. If the light travels
meters per second, how many minutes does it
take light from the sun to reach Earth?
A. 20 minutes C. 8 minutes ←
B. 28 minutes D. 10 minutes

Question 21
• Use absolute value notation to describe the given situation:
The distance between x and -2 is 4.
A. |x+2|=-4 C. |x+2|=4 ←
B. |x-2|=4 D. |x-2|=-4
• Use absolute value notation to describe the given situation:
The distance between x and -2 is 4.
|x – (-2)| = 4
|x + 2| = 4

Question 22
• Lyn Santos is paid a salary of
Php5,000.00/week plus 10% commission on a
net sale over Php50,000.00. what is her gross
wage if her weekly net sales are
Php70,000.00?
A. Php4,700.00 C. Php5,000.00
B. Php7,000.00 ← D. Php2,000.00

Question 23
• The number of subsets of a Set A with n
element is defined by 2ᶯ. If A= {1,2,3,4,5) find
the number of subsets of A.
A. 32 ← C.16
B. 20 D. 10
2ᶯ = 2^5
= 32

Question 24
• If f(x)=2x-3 and g(x)=
• Find(g o f) (x)
A. C. 4x-9
B. D.

Question 25
• In three dimensions, where is the point
located if x=y=z=0?
A. xz plane C. yz plane
B. origin ← D. xy plane

Question 26
• It cost a lady’s bag manufacturer Php 400.00
to produce a lady’s bag that sells for Php
550.00. How many lady’s bags must be
manufacturer sell to make a profit of Php
60,000.00?
A. 400 ← C. 250
B. 150 D. 200

Question 26
550 – 400 = profit per bag
= 150
150x = 60000, x is the number of bags needed to
be produced
x = 400

Question 27
• Annual interest at 8% for 3 months on P6,000.00
A. P480.00 C. P150.00
B. P120.00 ← D.P160.00
• I = PRT
• I = 6000(0.08)(3/12)
• I = 120

Question 28
• Find the units in {1,2,3,4,5,6,7}
A. 2 C. 1 ←
B. 4 D. 8
• Find the units in {1,2,3,4,5,6,7}
• The units in Zn are precisely those m in Zn, such that
gcd(m, n) = 1
• Thus, 1, 3, 5 and 7 are the units in Z8.

Question 29
• Four out of every five households have cellphone. If 10,000 households in a
certain barangay have cellphone, how many do NOT have cellphone? No
correct answer.
A. 7,500 C. 9,500
B. 2,000 D. 7,000
Let x be the number of cellphones.
(4/5)x = number of those who have cellphones
(4/5)x = 10000
x = 12500
That tells us that only 2500 do not have cellphones.

Question 30
Find the amount and compound interest
converted quarterly in 5 years on P20,000.00
at 8%
A. P19,600.95 C. P25,600.00
B. P29,718.95 ← D. P22,700.00

Question 31
• Perform the indicated operation and reduce to
lowest terms:
A. C.
•
B. D.

Question 32
• Express z as a function of x and y if z is
directly proportional to the product of x and y.
A. z= c/xy C. z= cxy ←
B. z=1/xy D. z= xy

Question 33
• Evaluate dy / dx
when x=2 for y = 8x -
A. 8
C. 4
B. -4 ←
D. 0

Question 34
• Point P(-3,-4) is on the terminal side of angle
Ɵ in the standard position. Find tan Ɵ.
A. 4/3 ← C. 3/4
B. -3/5 D. -4/5

Question 35
• Find the area of the region bounded by the
curves: y = x2,,y = x.
A. 1/ 6 ← C. 1/3
B. 1/2 D. 3/4

Question 36
• Perform the indicated operation and reduce
result to simplest form.
• A. C.
• B. D.

Question 36
result to simplest form. No correct answer.
• A. C.
• B. D.

Question 37
• A. C.
• B. D.

Question 38
• Find the distance between the points(-3,2)
and (5,3).
• A. √45 C. √65 ←
• B. √55 D. √56

Question 39
• Perform the indicated operation and reduce to
lowest terms:
• A. ← C.
• B. D.

Question 40
• Find the equation of an ellipse in the standard
form if the equation of the ellipse in the
general form is given by: 9x2+16y2+18y-
96y+9=0.
• A. C.
• B. D.

Question 41
• A. C.
• B. D.

Question 42
•
• Form of linear equation in one variable
A. ax+b =0 ← C. ax2+bx+c=0
B. ax2-by2+dx+ey=f=0 D. ax+by+c=0

Question 43
• Area of an isosceles triangle with base of 2
meters and perimeter of 12 meters.
A. 2√(6cm2)← C. 2m2
B. 4 m2 D. 6√(2m)

Question 44
• What is the area of a triangle with vertices at
(5,3)(11,13) and (8,8)? Not possible, there is
no triangle formed because the points are
collinear.
A. 30 C. 7
B. 15 D.24

Question 45
• Find the distance between the line 3x-y=0 and
the point(2,-4)
A. 10 C. -10
B. √10 ← D.-√10
•Find the distance between the line 3x-y=0 and the point(2,-4)
•10 C. -10
•√10 D.-√10

Question 46
• The approximate shape of the earth is
A. Sphere ← C. Cone
B. Circle D. Cube

Question 47
• The motion of a particle is given by the
equation s=t3-3t-5. Find the velocity when t=2.
A. 9 ← C. 3
B. 10 D. 5

Question 48
• Samantha laid tiles on the floor. She began
with 1 square tile at the corner of the room.
She added three tiles to form 2 x 2 tile square
and then 5 tiles to form 3 x 3 tiles square. She
continues in this way until the whole floor is
covered . Last , she adds 25 tiles. What is the
size of the floor?
A. 166 square tiles C. 167 square tiles
B. 168 square tiles D. 169 square tiles←

• Check the pattern,
• 1x1 --- 1
• 2x2 --- 3
• 3x3 --- 5
• 4x4 --- 7
• …
• nxn ---25
• This follows the pattern in arithmetic progression

• Hence, to find n:
• an = a1 + (n -1)d
• 25 = 1 + (n – 1)2
• 24 = (n – 1)2
• 12 = n – 1
• n = 13
• Thus there are 13 x 13 tiles = 169

Question 49
• Area of the Circle with equation: x2+ y2=4 is
A. 2π C. 4π ←
B. π D. 5π

Question 49
• x2+ y2=4 is a circle with center at the origin and r = 2.
Thus,

Question 50
• The surface on the earth between the topic of
cancer and the Arctic Circle is called
A. Plane C. cone
B. Circle D. zone ←

Question 51
• Nica received an aquarium as a graduation gift
from her mother. It has length, width and
height of 9 centimeters, 7 centimeters and 5
centimeters, respectively. Find its volume.
A. 315 cubic cm ← C. 314 cubic
cm
B. 316 cubic cm D. 318 cubic
cm

Question 52
• A cube has a volume of 64 cubic meters. What
are its dimensions?
A. 16cm x 2 cm. x 2 cm. C. 3 cm. x 3 cm. x 7 cm.
B. 8 cm. x 8 cm. x 1 cm.D. 4 cm. x 4 cm. x 4 cm. ←

Question 53
• The sum of the sides of a polygon is the
of the polygon.
A. Perimeter ← C. area
B. Leg D. volume

Question 54
• If the opposite sides of a quadrilateral are
equal, the figure is a
A. Rectangle C. parallelogram
B. Shambers D. square ←

Question 55
• The ULTRA football field is 100 meters from
goal line to goal line. If it is 360 meters around
a football field, how wide is the field?
A. 70 meters C. 86 meters
B. 85 meters D. 80 meters ←

Question 56
• The average of the ages of two friends is 19. If
one of them is 17, how old is the other which
equation will approximately solve this
problem?
A. x=(2)(19)-17 ← C. x=(2)(19)-19
B. x=(2)(19)+19 D. x=(2)(19)+17

Question 57
• The first angle of a quadrilateral is 50, the
second is twice the first and the third is equal
to the second. What is the fourth angle of the
quadrilateral ?
• 108 C.111
• 110 ← D.109

• Sum of interior angles of quadrilateral = 360
• 50 + 2(50) + 2(50) + x = 360
• 250 + x = 360
• X = 110
• Sum of interior angles of quadrilateral = 360
• 50 + 2(50) + 2(50) + x = 360
• 250 + x = 360
• X = 110

Question 58
• What is the value of x if x= log3 27?
A. 3 ← C. 9
B. 27 D. -3

Question 59
• What is the third side of the triangle if b=47,
c=58 and Ɵ=63°?
A. 8048.2 C.3090
B. 5573 D.√3097.8 ←

Question 60
• The statement of 3= log 10 (x+8)implies
A. 103=x+8 ←
B. 33=x+8
C. (x+8)10=3
D. (x+8)3=10

Question 61
• The given multiplication table represents a
cyclic group
• Find the order of the group
A. 2 C. 1
B. 3 D. 4 ←
Find the order of the group
1.2 C. 1
2.3 D. 4

• The order of the group is the number of
elements in that group.
• There are four elements (a, b, c, d) in the
group.

Question 62
• log216 equals _____________
•
A. 3 C. 2
B. 4 ← D. 1
• log 2 16 = x  2^x = 16
• Thus, x = 4

Question 63
• The given multiplication table represents a
cyclic group.
• Find d2
A. a C. b
B. d D. c ←

Question 64
• if sin ϴ =4/5 , and 0<ϴ<π/2, then cos 2Ɵ is
equal to
A. 24/25 C.-7/25 ←
B. 7/25 D. 44/125

Question 65
• Tan π/10 is equal to
A.[2 tan[π/5)]/[1-tan2(π/5)] C. sin(π/5)/[1+cos(π/5)] ←
B.(sin π/3)/[1-cos(π/5)] D.[2tan(π/20)]/[1+tan2(π/5)]

Question 66
• When a logarithm is expressed as an integer
plus a decimal, the integer is called the
A. Mantissa C. base
B. Characteristic ← D. antilogarithm
• Characteristic is the integer part while
mantissa is the decimal or fractional part.

Question 67
• If log a 16=12, then a equals No
answer. Answer is
A. 2 C. 8
B. 4 D. 32

Question 68
• The logarithm of the product of two numbers
is equal to the of the logarithms of
the factors
A. Sum ← C. difference
B. Product D.antilogarithm

Question 69
• What is the simplest form of (sin1/2x-
cos1/2x)2?
A. 1+sin x C. 1-cos x
B. 1+cos x D. 1-sin x ←

Question 70
• Cos(-π/12) is equal to
A. (√3+1)/2√2 ← C. (√2+√3)/4
B. (-1√3)/2√2 D.(√3-1)/2√2

Question 71
• What is the exact value of sin [(2π/3)+(π/4)]?
A. (√6-√2)/4 C. √3
B. √2+1 D. (√6+√2)/4 ←

Question 72
• If tan Ɵ=1/3, then cot 2 Ɵ equals
A. 4/3 ← C.3/2
B. 2/3 D. 3/4

Question 73
• Which among the measures of central
tendency is not influenced by outliers?
A. Mean C. Mode
B. Weighted Mean D. Median ←
• Note: Median is most reliable when there are
outliers in the given data set but mode is not
influenced by the outlier.

Question 74
• He invented a method of determining the
optimal values of a linear function subject to
certain constraints. This method is known as
linear programming. Who is he?
A. George Canter
B. Richard Dedekind
C. Bertrand Russel
D. George Dantzig ←

Question 75
• The figure shows
A. Same positive correlation
B. Same negative correlation
C. perfect positive correlation ←
D. perfect negative correlation

Question 76
• A random sample of 200 adults are classified by sex and
their level of education attained.
If a person is picked at random from this group,
find the probability that the person is male.
A. 95/112 C. 11/25 ←
B. 14/39 D.45/25

Question 77
• The figure shows
A. Same negative correlation
B. Perfect positive correlation
C. Perfect negative correlation
D. Same positive correlation ←

Question 78
• To express that there is significant difference between
the income of family A and that of the income of Family
B.
←

Question 79
• A subset of the sample space is
A. Discrete variable
B. Event ←
C. Phenomenon
D. Continuous variable

Question 80
• A ball is drawn at random from a box
containing 6 red balls, 4 white balls and 5 blue
balls. Find the probability that it is white.
A. 1/3
B. 4/5
C. 4/15 ←
D. 4/13

Question 81
• If a die is rolled, what is the probability of
getting a number divisible by 2?
A. 1/6
B. 1/4
C. 1/2 ←
D. 1/3

Question 82
• He was a 16th century mathematician, who was
the first to define that the probability of an
event to happen is the quotient of the number
of the favorable outcomes and the number of
all outcomes. Who was he?
A. Stephen Baldwin
B. Blaise Pascal ←
C.Girolamo Cardano
D. Richard Dedekind

Question 83
• There are 5 types of correlation
between paired data: perfect
positive correlation, perfect
negative correlation, same positive
correlation, same negative
correlation and no correlation
The figure shows
A. Same negative
B. Same positive correlation
C. Perfect positive correlation
D. No correlation ←

Question 84
• For a sequence of events A,B, and C
• P(A U B U C )= P(A),+P(B/A), P(C/A U B)
A. Subtraction rule C. General rule
B. Addition rule ← D. Multiplicative
rule

Question 85
• For mutually exclusive events A and B,
• P(A U B)=P(A) +P(B)
A. Addition rule ← C. Subtraction
rule
B. General rule D. Multiplicative
rule

Question 86
• A sample of 500 respondents was selected
in a large metropolitan are in order to
determine various information concerning
behavior. Among the question asked was.
“ Do you enjoy shopping for clothing ?” of
240 males, 136 males answered yes of 260
females, 224 answered yes.

Question 86
• Find the probability that the respondent
chosen at random is a female.
• 12/25 C. 13/25 ←
• 6/25 D. 18/25
Find the probability that the respondent chosen at random is a female.
1.12/25 C. 13/25
2.6/25 D. 18/25

Question 87
• To express that there is significant difference between
the food values of the nutrition students and those of
the nursing students:

Question 88
• Find the absolute maximum value of f(x) =x(2/3)
on the interval (-2,3)
A. 3√9 ← C. 0
B. 1 D. √9

Question 89
• Find the area of the triangle with vertices; (-
2,0)(2,3) and (5, 0)
A. 12 ½ C. 12
B. 11 D. 10 ½ ←

Question 90
• Find two positive numbers whose product is 64
and whose sum is minimum.
A. 8 and 8 ← C.1 and 64
B. 32 and 2 D. 63 and 1

Question 91
• Find the equation of an ellipse in the general
form if the equation of the ellipse in the
standard
A. 25x2-4y2-350x+16y +1141 = 0
B. 25x2+4y2-350x-16y+1141=0
C. 25x2-4y2-350x-16y+1141=0
D. 25x2+4y2-350x-16y-1141=0
1.25x -4y -350x+16y +1141 = 0
2.25x2+4y2-350x-16y+1141=0
3.25x2-4y2-350x-16y+1141=0
4.25x2+4y2-350x-16y-1141=0

Question 92
• Find the absolute minimum value of f(x)=x2/3
on the interval (-2,3)
A. 0← C. 1
B. √9 D. 3√9

Question 93
• Evaluate:
A. 3 C. 2
B. 0 ← D. 1

Question 94
• Find the derivative of f(x)=(x-3)(x+5)
A. 2x C. x+2
B. 2(x+1) ← D. x+1
• Find the derivative of f(x)=(x-3)(x+5)
f’(x) = (x – 3)(1) + (x+5)(1)
= (x – 3) + (x + 5)
= 2x – 2
= 2(x – 1)

Question 95
• Find the distance between the points (-3,2)
and (5,3).
A. √55 C. √65 ←
B. √56 D.√45

Question 96
• Find the area of the isosceles triangle that can
be inscribed in a circle with radius of 6 inches.
A. 27√3 ← C. 29
B. 27 D. 29√3
•Find the area of the isosceles triangle that can be inscribed in a circle with radius of 6 inches.
1.27√3 C. 29
2.27 D. 29√3

Question 96
• Find the area of the isosceles triangle that can
be inscribed in a circle with radius of 6 inches.
• Question is a bit insufficient so we will just
assume we are solving for the largest area of
the isosceles triangle that can be inscribed.
• The area is maximum when the triangle is
equilateral. (Equilateral triangle are always
isosceles in nature but isosceles are not always
equilateral.)
1.27√3 C. 29
2.27 D. 29√3

Question 96
• Side s of equilateral triangle inscribed in circle is given
by s = r √3
1.27√3 C. 29
2.27 D. 29√3

• Consider the right triangle in yellow shade. Height H can
easily be computed by inspection (1,2 ,√3) or
Pythagorean Theorem.
H = 9
So Area of
triangle =
½(9)(6 √3)
= 27√3

Question 97
• Find the equation of the parabola in the
standard form if the equation of the parabola
is the general form is given by: y2-12x-23=0
A. (y+1)2=12(x+2) C. (y-1)2=-12(x+2)
B. (y-1)2=12(x+2) D. (y-1)2=-12(x-2)

Question 97
y2 – 12x – 23=0
y2 = 12x+23
y2 = 12(x + 23/12)

Question 97
No correct answer
A. (y+1)2=12(x+2) C. (y-1)2=-12(x+2)
B. (y-1)2=12(x+2) D. (y-1)2=-12(x-2)

Question 98
• Find the derivative of f(x) = x2-2x+5
A. 3 C. 1
B. 0 D. 2

f(x) = x2-2x+5
f’(x) = 2x – 2

Question 98
• Find the derivative of f(x) = x2-2x+5
A. 3 C. 1
B. 0 D. 2
• No correct answer due to insufficient
information.

Question 99
in the general form is given by; x2+ 2x-4y-3=0
A. (x-1)2=4(y+1) C. (x+1)2=-4(y+1)
B. (x+1)2=-4(y-1) D. (x+1)2=4(y+1) ←

x2+ 2x-4y-3=0
x2+ 2x + ___ = 4y+ 3 + ____
x2+ 2x + 1 = 4y+3 + 1
(x + 1)2 = 4(y + 1)

Question 100
• Find the volume of the cone generated by
revolving about y-axis the area bounded by the
line 2x+y=2 and the coordinate axes
A. π C. 2/3 π
B. 1/3 π D. 2π

Question 101
• Find the pairs of lines that are perpendicular.
A. 2x-y+3=0,2x-y-5=0 C. x-y-=0, 2x+3y-
5=0
B. x=1, y=5 ← D. 3x-y-5=0, x-
3y+21=0

Question 102
• If a line is extended from A(2,3) through B(-
2,0) to a point C so that AC= 4AB, find the
coordinates of C.
A. (-14,-10) C.(-14,10)
B. (14,10) D. (14,-10)

Question 103
• Find the range of the function y=5-2x2
A. All real numbers
B. y≤0
C. y≠5
D. y≥5

Question 103
y=5-2x2 is a parabola that opens downward
Given y= ax2 + bx + c, the range is the set of all y such
that
y ≤ (4ac – b2)/4a
Hence, y ≤ (4(-2)(5) – 02)/4(-2)
y ≤ 5

Question 103
A. All real numbers
B. y≤0
C. y≠5
D. y≥5
• No correct answer

Question 104
• evaluate the limit:
A. undefined ← C. 0
B. 2 D. 1
•

Question 105
• If 22≡12 mod 5 and -1 ≡ 14 mode 5, find the
sum of the two congruences.
A. 21≡26 mod 5 ← C. 21≡26 mod 10
B. 23≡ 2 mod 5 D. 20≡26mod 5

Question 106
• If 22≡mod 5 and -1≡14 mode 5, find the
product of the two congruences.
A. -22≡168 mod 5 ← C. 21≡168 mod 25
B. -22≡ 168 mod 25 D. 22≡168mod 5

Question 107
• Find the area of the region bounded by the
curves: y=x2, y=x
A. 3/4 C. 1/2
B. 1/6 D. 1/3

Question 108
• Find the domain of the function y=5-2x2
• x≥2 C. x≥0
• x≥5 D. all real
numbers

Question 109
• evaluate:
A. 33 1/3 C. 39 3/5
B. 393/10 ← D. 39 ½

Question 110
• Find the distance between the parallel lines
3x-4y-10 = 0 and 3x -4y-20=0
A. -2 C. 2 ←
B. √2 D. -√2

Question 111
• The trace of the square matrix A, to (A), is the sum of
its diagonal elements. If
Find the relationship between tr (A+B) and tr (A)+ tr(B).
A. tr(A+B)< tr(A)+tr(B)
B. tr(A+B)>tr(A)+tr(B)
C. tr(A+B) not equal tr(A)+tr(B)
D. tr(A+B)=tr(A)+tr(B) ←

Question 112
• the set G= {a,e,b,c} forms a group with the operator O.
The group table is given by:
• Find the inverse of c.
A. c C. a
B. e ← D. b
•

Question 113
The trace of the square matrix A, to (A), is the sum of its
diagonal elements if
Find tr (A)+tr(B)
A. 19 C. 21 ←
B. 26 D. 24

Question 114
• Which is true for subgroups of a group?
A. Subgroups for a partition of a group
B. The intersection of two subgroups is empty
C. The union of two subgroups is also a group
D. The intersection of two subgroups is also a group ←

Question 115
Find the x and y intercepts of the following: y=
2x2-3x-2
A. (0,-2),(2,0),(-1/2,0) ← C.
(2,0),(2,0),(-1/2,0)
B.(0,2),(1,0),(-1/2,0) D.(0,-
2),(2,0),(-2.0)

• y= 2x2-3x-2
• Let y = 0
• 0 = 2x2-3x-2
• (2x + 1)(x – 2) = 0
• x = -1/2 and x = 2
• Let x = 0 in y= 2x2-3x-2
• y = -2
• Thus intercepts are (0, -2), (-1/2, 0) and (2, 0)
•

Question 116
• Find the determinant of the co-factor of q33 of
• 30 C. 13
• 23 D. -13 ←

• Determinants of q33
• = q11 x q22 – q21 x q12
• = 2(1) – 5(3)
• = 2 – 15
• = -13

Question 117
• He has been described as the greatest“ might-
have-been” in the history of mathematics.
A. Blaise Pascal ← C. Bonaventura
Cavalier
B. Gaspard Monge D. Gregorio de Saint

Question 118
• Who published a treatise on trigonometry
which contains the earliest use of our
abbreviation : sin, tan, sec, for sine, tangent
and secant?
A. Gregorio de Saint C. Albert Gerard
←
B. John Napier D. Johann Herdde

Question 119
• He invented a method of determining the
optical values of a linear function subject to a
certain constraints. This method is known as
linear programming. Who is he?
A. George Canter C. George Dantzig ←
B. Bertrand Russel D. Richard Dedelind

Question 120
• An 18th century Swiss Mathematician , he
introduced the “ Law of Large numbers” in his
(The art of Conjecture). In statistics, this
implies that the larger the sample, the more
likely will the sample become representative
of the population. Who was he?
A. Girolamo Cardano C. Jacob Bernouli
←
B. Bertrand Ruseel D. Stephen
Baldwin
•An 18th century Swiss Mathematician , he introduced the “ Law of Large numbers” in his (The art of Conjecture). In statistics, this implies that the larger the sam
1.Girolamo Cardano C. Jacob Bernouli
2.Bertrand Ruseel D. Stephen Baldwin

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