By Jonai Republica, ECE#46314
Factor the expression x3 - 27
a. (x-3)(x2+3x+9)
b. (x-3)(x2+9x+6)
c. (x-3)(x2+6x+12)
d. (x-3)(x2+6x+9)
Which of the following is a factor
of the polynomial 3x4 – x3 –5x2
+7x + 6.
a. 2x + 3
b. x + 2
c. 2x - 5
d. 3x + 2
If kx3 –(k+3)x2 +13 is divided by
(x-4), the remainder is 157. What
is the value of k?
a. 4
c. 1
b. 2
d. 3
Ex: For the sequence 61, 54, 47,
40, 33….
a) What is the 10th term?
b) Which term has a value of
5?
c) Find the 100th term
d) Which term is -331?
e) What is the sum of the first
50 terms?
Find the 30th term of the A.P. 4,
7, 10…
a. 75
c. 90
b. 88
d. 91
Ex: For the geometric series 2,
6, 18….
a) What is the 7th term?
b) Which term has a value
of 162?
c) Find the 12th term
d) What is the sum of the
first 12 terms?
The number 28, x+2, 112 form a
G.P. What is the 10th term?
a. 14336
c. 16443
b. 13463
d. 16344
A lady started a chain letter by
writing to 4 friends and requesting
each to copy the letter and send it
to 4 other friends. If the chain was
unbroken until the 5th set of letters
was mailed, how much was spent
for postage at P8 per letter?
a. P11,432
b. P12,364
c. P10,912
d. P11,834
Solve for x and y in 3x + 2y = 12
and x +2y = 8 by elimination
a. (-1,2)
c. (2,3)
b. (1,2)
d. (-2,1)
Simplify (1+i)5 where i is an
imaginary number.
a. 1- i
b. (1+i)
c. -4(1+i)
d. 4(1+i)
What is the absolute value of
(3i – 2)6
a. 2197
c. 13
b. 169
d. 0
cos
If sinA=4/5, A is in QII and
sinB=7/25, B in QI. Find
sin(A+B)
a. 3/5
c. 4/5
b. 3/4
d. -2/5
A line is passing through (5, -1) and (8, 3)
a) What is the equation of the
line?
b) What is the slope?
c) What is the value of y when
x=1?
d) What is the value of x when
y=7?
e) What is the x- intercept?
f) What is the y- intercept?
Find the equation of the line
passing through (4, 8) with a
slope of 3/4
a. 4x + 3y = 20
b. 3x - 4y = 10
c. 3x - 4y = -20
d. 4x + 5y =20
Find the slope of the
following lines
a) 4x + 5y = 9
b) 3x - 2y = 1
c) y=3
d) x=1
Find the equation of the line
passing through (8, -6) and
perpendicular to 4x + y = 9
a. x - 4y = 32
b. 2x - 4y = 10
c. -2x + 8y = 32
d. -x + 4y = 32
Find the acute angle formed
by the intersection of the
lines 3x + 5y =12
and 2x – 4y = 5
a. 58.2°
b. 70.21°
c. 57.52°
d. 72.51°
What is the perimeter of the
triangle whose vertices are
A(3,5) B(-4,3) C(4,-1)
a. 10.1
b. 22.31
c. 12.12
d. 12.21
Find the coordinates of the
point equidistant from (1,-6)
and (5, -6)
a. (2, -3)
b. (3,-2)
c. (3,-3)
d. (2,2)
Locate the center and find
the area of the curve x2 + y2 +
8x +4y -61 = 0
a. (4,2), 64π
b. (4,2), 81π
c. (-4,-2), 64π
d. (-4,-2), 81π
2
x
Given the parabola 4y = –
6x + 21, find the vertex and
the length of the latus
rectum.
a. (-3,-3), 4
c. (3,3), 4
b. (2,2), 8
d. (-2,-2), 8
Given the equation of the
curve as 16x2 + 25y2 -128x 150y + 381=0, find the length
of the minor axis.
a. 3
b. 4
c. 5
d. 6
Find the eccentricity of the
curve
2
2
9x – 4y – 36x + 8y +4 = 0
a. 1.8
b. 3
c. 1.2
d. 4/5
The volume of water in a
spherical tank having a
diameter of 4 m is 5.236 m3.
Determine the depth of water
in the tank.
a. 1.4
b. 1.2
c. 1.5
d. 1.0
The volume of water in a
spherical tank having a
diameter of 4 m is 5.236 m3.
Determine the depth of water
in the tank.
a. 1.4
b. 1.2
c. 1.5
d. 1.0
The bases of the frustum of a
cone are 6cm and 10cm in
radius respectively. If the
altitude is 18cm, what is the
volume of the frustum?
a. 1170pi
b. 1180pi
c. 1176pi
d. 1185pi
The bases of the frustum of a
cone are 6cm and 10cm in
radius respectively. If the
altitude is 18cm, what is the
volume of the frustum?
a. 1170pi
b. 1180pi
c. 1176pi
d. 1185pi
The upper base of the frustum
of a rectangular pyramid is 8cm
by 80cm, and the lower base us
10cm x 100cm. the altitude is
5cm. Find the volume of the
pyramid.
a. 4066.67
b. 5066.67
c. 6066.67
d. 7066.67
Evaluate the limit of sin(1/x)
as x approaches 0
a. infinite
b. doesn’t exist
c. 0
d. negative infinity
Jodi wishes to use 100 feet of
fencing to enclose a
rectangular garden.
Determine the maximum
possible area of her garden.
a. 1000 sq. ft. b. 625 sq. ft.
c. 500 sq. ft.
d. 225 sq. ft.
An open box is to be
constructed from a 12 × 12-inch
piece of cardboard by cutting
away squares of equal size from
the four corners and folding up
the sides. Determine the size of
the cutout that maximizes the
volume of the box.
a. 1
b. 2
c. 1.5.
d. 2.5
A piece of wire 24 inches long is
to be used to form a square
and/or a circle. Determine their
minimum combined area.
a. 20.16
c. 11.52
b. 22.11
d. 25.12
Find the area of the region
bounded by the curve
r2=16cosθ
a. 16
c. 30
b. 32
d. 25
Lemniscate
Cardioid
Spiral of Archimedes
Rose
Find the area of the region
bounded by the curve
r2=16cosθ
a. 16
c. 30
b. 32
d. 25
The population of a country
doubles in 50 years. How many
years will it be 5 times as much?
Assume that the rate of
increase is proportional to the
number of inhabitants.
a. 100 years
b. 116 years
c. 120 years
d.98 years
A thermometer reading 18°C is
brought into a room with
temperature of 70°C. 1 minute
later, the thermometer reading
is 31°celcius . Determine the
thermometer reading 5 mins
after it is brought into the room.
a. 62.33oC
b. 58.99oC
c. 56.55oC
d. 57.66oC
Find the solution of the D.E.
x2 dy -2xydx –y3dx =0
3
4x
3
2
3x y
2
Cy
a.
+
=
b. 2x3 + 3x3y = Cy
c. 4x2 + x3y2 = Cy2
d. 3x4 + 2x3y2 = Cy2
What is the acute angle of
intersection of the two planes
2i - 4j + 5k and 3i + j - k
a. 97.22°
c. 77.12°
b. 82.25°
d. 25.22°
Find the value of the determinant
4 -1 2 3
2 0 2 1
10 3 0 1
14 2 4 5
a. 28
c. 14
b. -28
d. -14
Mr. Reyes borrowed P10000 which
is to be paid in 24 equal monthly
payments with an interest rate of
12% effective.
a) If payments are done at the beginning of
each month, what is the monthly payment?
b) If payments are done at the end of each
month, what is the monthly payment?
c) If the payments are delayed such that the 1st
payment is given in the 7th month, what
should be the monthly payment?
An employee obtained a loan of
P10,000 at the rate of 6%
compounded annually to repair
a house. How much must he
pay monthly to amortize the
loan within a period of 10
years?
a. 110.22
b. 112.02
c. 125.25
d. 121.22
A machine has a first of P80,000
and a salvage value of P2,000 at
the end of its life of 10 years.
Find the book value at the end
of sixth year using straight line
method of depreciation.
a. P32,900
b. P34,300
c. P35,000
d. P33,200
A broadcasting corporation
purchased an equipment that
costs 7000, last 8 years and has
a salvage value of P350.
Determine the book value
during the 4th year using
declining balance method.
a. P1711
b. P5166
c. P1565
d. P1645
An equipment costs P500,000
has a salvage value of P25,000
after its 25 years of useful life.
What will be the book value of
the equipment at the end of 8
years? Use Double Declining
Balance method
a. P234,524.00 b. P256,609.55
c. P242,223.12 c. P243,166.21
A telephone company purchased a
microwave radio equipment for P6M.
Freight and installation charges
amounted to 3% of the purchase price. If
the equipment shall be depreciated over
a period of 8 years with salvage value of
5%, determine the depreciation charge
during the 5th year using Sum of Years’
Digit method.
a. P563,444,33
b. P653,333.33
c. 635,333.33
d. 536,444,44
Compute the present value and future
worth of 5 arithmetic gradients, the
initial value of money is P100 and
increasing P100 every year. Interest rate
is 10%.
a. P1783.22 and P2022.63
b. P1128.25 and P1988.63
c. P1065.26 and P1715.61
d. P1724.22 and P1222.63
Compute for the present worth of a
geometric gradient where money
initially cost P150 is increasing at
12% each year, if the interest rate is
10% the rate of gradient increase is
accepted for 5 years.
a. 653.78
b. 700.12
c. 801.42
d. 707.07
The direct labor cost and material
cost of a certain product are P300
and P400 per unit respectively. Fixed
charges are P100,000 per month and
other variable costs are P100 per
unit. If the product is sold at P1,200
per unit, how many units must be
produced and sold to break even?
a. 250
b.225
c. 260
d. 200
The End