GenEd_math.pdf

GENERAL INSTRUCTIONS
Please do not answer yet. We will answer the
test at the same time. A timer shall be utilized.
Remember to recall the test-taking strategies
you’ve learned from the review sessions.
HUWAG MAKULIT, WALA MUNANG
MAGSASAGOT!!!!!

91-100 – Potential
topnotcher.
76-90 – VS Passer!
51-75 – In a delicate
position, still a passer!
0-50 – Wag naman uy!

1. Regala Company manufactures beds; in its
catalogue, a double bed is priced at
PhP5, 000.00 less a discount of 20%. What
will Rizza have to pay for the bed she
ordered?
A. PhP 4,150.00
B. PhP 4, 100.00
C. PhP 4,200.00
D. PhP 4, 000.00

100% - 20% = 80%
X= (0.80) 5,000
X=Ph4,000

2. Rowena Castro works as a sales clerk.
She is paid a salary of PhP3, 000.00 a week
plus 2% commission on sales over PhP4,
000.00. Find her gross pay for a week in
which her sales are PhP9, 500.00
A. PhP 3,500.00
B. PhP 3,110.00
C. PhP 3, 190.00
D. PhP 3, 210.00

Commission = sales x rate
Commission= 9,500 x 0.02
Commission= 190.00
Rowena’s gross pay = commission + weekly salary
= Php190 + Php3000
= Php3, 190.00

3. A Toyota car travelling at a rate of 70 kph
leaves the house 2 hours after a Kian car
has left and overtakes it in 5 hours at what
rate was the Kia car travelling?
A. 40 KpH
B. 30 KpH
C. 50 KpH
D. 20 KpH

3. A Toyota car travelling at rate of 70km.
per hour leaves the house 2 hours after a
Kia car has left and overtakes it in 5 hours.
At what rate was the Kia car travelling?
1 2 3 4 5 6 7
Toyota 70 140 210 280 350
Kia 50 100 150 200 250 300 350

4. How many prime numbers are there
between 1 and 100?
A. 24
B. 23
C. 22
D. 25

5. What number must be subtracted from
both numerator and denominator of the
fraction 11/23 to give a fraction whose
value is 2/5?
A. 4
B. 2
C. 5
D. 3

11
23
−
4
4
=
7
19
11
23
−
3
3
=
𝟖
𝟐𝟎
𝒐𝒓
𝟐
𝟓
11
23
−
5
5
=
6
18
𝑜𝑟
1
3
11
23
−
2
2
=
9
21
𝑜𝑟
3
7

6. The fraction halfway between 3/7
and 4/7 is ____.
A. ½
B. 1/8
C. ¼
D. 1/3

Get the midpoint of 3 and 4 which is 3.5 then
copy the denominator
𝟑. 𝟓
𝟕
𝐨𝐫
𝟏
𝟐

7. A recipe calls for 2 cups of milk for every 7
cups of flour. A chef will use 28 cups of flour,
how many cups of milk must he have?
A. 12
B. 10
C. 14
D. 8

Ratio and Proportion
2 cups of milk : 7 cups of flour : : n cups of milk: 28 cups
of milk
2:7::n:28
N=
(28)2
7
N= 8

8. If Karl has an average of 76% on his first
two tests and has an average of 85% on the
next four test, what is his final average on
all six tests?
A. 82.5%
B. 80.5%
C. 81.3%
D. 82.0%

Let X be the final average on six tests
X=
2 76 +4(85)
6
X=
492
6
X= 82

9. A room is 30ft long, 25ft wide and 14ft
high. If 42 balloons are inside the room,
how many cubic feet of space does this
allow for each balloon?
A. 175
B. 215
C. 200
D. 250

Volume of rectangle = L x W x H
= 30 ft X 25 ft X 14ft
= 10, 500 ft3
To compute for the space for each balloon
divide the computed volume with the total
number of balloons
= 10, 500 / 42
= 250

10. What percent of 75 is 15?
A. 30%
B. 40%
C. 20%
D. 38%

Part = percent x whole
Part= 15
Percent= N
Whole= 75
15 = 𝑁 75
15
75
= N
N= O.20
=0.20 OR 20%

11. All right angles are _______.
A. parallel
B. oblique
C. supplementary
D. equal

12. The side opposite the right angle of
a high triangle is the ______ and each
of the other two sides is ________.
A. hypotenuse, leg
B. opposite, adjacent
C. leg, hypotenuse
D. adjacent, opposite

13. A 10 meter board leans against the
wall. The foot of the board is 8 meters
from the wall. How far up the wall does
the board reach?
A. 10 meters
B. 4 meters
C. 6 meters
D. 8 meters

10
𝑎 = 𝑐2 − 𝑏2
𝑎 = 102 − 82
𝑎 = 100 − 64
𝑎 = 36 𝑜𝑟 𝟔
8
?

14. The sum of the sides of a polygon is
the _________ of the polygon.
A. volume
B. area
C. legs
D. perimeter

15. If two legs of one right triangle are
equal respectively to two legs of another,
the right triangles are __________.
A. congruent
B. complementary
C. supplementary
D. adjacent

16. Find the least common multiple of
8, 6, 3
A. 24
B. 48
C. 72
D. 96

8 = 2 x 2 x 2
6 = 2 x 3
3 = 3 x 1
= 2 x 2 x 2 x 3
= 24

17. Perform the indicated operation
40x²y²
4xy⁴
÷
27xy
8x²y²
A.
40x³
81y
B.
40x
81
C.
40𝑥2
27y
D.
80𝑥2
27y

Perform the indicated operation:
40x2y2 27xy
-------- ÷ -------
4xy4 8x2y2
40𝑥2𝑦2
24𝑥𝑦4 ∗
8 𝑥2𝑦2
27𝑥𝑦
=
320 𝑥4𝑦4
108𝑥2𝑦5 =
80 𝑥2
27𝑦

18. The measure of an angle is 25 more than
its supplement. What is the measure of the
larger angle?
A. 102.5 degrees
B. 77.5 degrees
C. 110.5 degrees
D. 95.5 degrees

Supplementary angles – two angles whose sum is 180
Larger angle = n+25
180= [(n+25) +n)
180= 2n + 25
180- 25 = 2n
155 = 2n
155/2 = 2n/2
n= 77.5
77.5 + 25 = 102.5

5, 2, 7.
A. 140
B. 35
C. 15
D. 70

20. Simplify:
3𝑥−9
𝑥2−9
A.
3
(𝑥+3)
B.
3
(9−3)
C.
(𝑥+3)
3
D.
(𝑥−3)
3

3𝑥 − 9
𝑥2 − 9
=
3 (𝑥 − 3)
𝑥 + 3 (𝑥 − 3)
=
𝟑
(𝒙 + 𝟑)

21. Simplify:
(8𝑥−24)
2𝑥2−𝑥−15
A.
(𝑥−4)
(𝑥+4)
B.
4
(𝑥−13)
C.
8
(2𝑥+5)
D.
(𝑥−3)
3

Factoring
(8𝑥 − 24)
2𝑥2 − 𝑥 − 15
8(𝑥 − 3)
(2𝑥 + 5)(𝑥 − 3)
8
(2𝑥 + 5)

22. The grades in Mathematics of the
students in section A are as follows: 80, 74,
60, 95, and 100. What is the range of their
group?
A. 80-95
B. 60 – 100
C. 60 – 95
D. 70 - 100

Range = Highest score – Lowest score

23. Which among the measure of central
tendency is not influenced by outliers?
A. Mean
B. Weighted Mean
C. Median
D. Mode

OUTLIER is an observation point that is
distant from other observations. An outlier
may be due to variability in the measurement
or it may indicate experimental error; the
latter are sometimes excluded from the data
set.

24. Which among the measure of
central tendency can best describe the
size of T-shirt commonly worn by
teenagers?
A. mode
B. mean
C. range
D. median

25. If a die is rolled, what is the
probability of getting a number divisible
by 2?
A. ½
B. 1/6
C. 1/3
D. ¼

Probability =
𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝟑
𝟔
𝐨𝐫
𝟏
𝟐

26. In a Physics test, 9 students obtained
the following scores: 80, 86, 78, 88, 90, 82,
76, 84, and 92. What is the median score?
A. 84
B. 82
C. 86
D. 88

76, 78, 80, 82, 84, 86, 88, 90, 92

27. It illustrates a particular data series
through rectangles.
A. Bar graphs
B. Line Graphs
C. Circle graphs
D. Pie graphs

28. It can be used to show the progress
in academic grades over four quarters.
A. Bar graph
B. Pie graph
C. Line graph
D. Circle graph

29. Simplify: x-3y (x-8y) – (-6xy+7x)
A. -6x+3xy+24y²
B. 6x-3xy-24y²
C. -6x+3xy
D. -6x-3xy

Simplify: x-3y (x-8y) – (-6xy+7x)
X – 3xy +24y2 +6xy -7x
X-7x -3xy + 6xy +24y2
-6x +3xy +24y2

30. A recipe calls for 2 cups of milk for every
7 cups of flour. A chef will use 28 cups of
flour. How many cups of milk must he have?
A. 10
B. 8
C. 12
D. 14

Ratio and Proportion
2 cups of milk : 7 cups of flour :: n cups of milk: 28 cups
of milk
2:7::n:28
N=
(28)2
7
N= 8

31. How many seconds are there in
a 24-hour day?
A. 86,400
B. 1, 690
C. 1, 779
D. 84, 600

1 hour = 60 minutes
1 minute = 60 seconds
3, 600 x 24 = 86, 400 seconds
𝟐𝟒 𝒉𝒐𝒖𝒓𝒔 =
𝟔𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
𝟏 𝒉𝒐𝒖𝒓
=
𝟔𝟎 𝒔𝒆𝒄𝒐𝒏𝒅𝒔
𝟏 𝒎𝒊𝒏𝒖𝒕𝒆
24 (60) (60 seconds) = 86, 400 seconds

32. Among the given decimals, which is
equivalent to 9%?
A. 9.0
B. 0.009
C. 0.09
D. 0.9

33. Simplify: 5 - {2-(-4)+11-8}
A. 4
B. 9
C. -4
D. 6

PEMDAS RULE
5 - {2-(-4)+11-8}
5- {6+11-8}
5-9= -4

34. The sum of three consecutive
integers is 123. What are the integers?
A. 42, 44, 46
B. 40, 41, 42
C. 39, 40, 41
D. 41, 43, 45

N+ N+1+ N+2 = 123
3N+3= 123
3N=123-3
3N/3= 120/3
N=40
N+1= 41
N+2= 42
40+ 41+ 42 = 123

35. What is the total amount after
adding 8% interest for 3 months of
PhP6,000.00?
A. PhP 11,500.00
B. PhP 6, 120.00
C. PhP 10,500.00
D. PhP 11, 050.00

P + (PRT)
= 6, 000 + (6,000 𝑥 0.08 𝑥
3
12
)
= 6, 000 + 120
= 6,120

36. Subtract 5a-2b from the sum of
7a+5b and a+b
A. 3a+4b
B. b. -3a+4b
C. 8a+2b
D. 3a-4b

= {(7a + 5b) + (a + b)} – (5a – 2b)
= {7a + a + 5b + b} – 5a + 2b
= 8a + 6b – 5a – 2b
= 3a + 8b

37. Which are the prime factors of 56?
A. 7, 4, 2
B. 14,2,2
C. 7, 8
D. 7, 2, 2, 2

9a²-1, 6a³- 2a², 9a+3
A. 6a³ (3a+1) (3a-1)
B. 6a(3a+1)(3a-1)
C. 6a³ (3a²+1) (3a-1)
D. 6a² (3a+1)(3a-1)

9a²-1, 6a³- 2a², 9a+3
9a²-1 (3a+1) (3a-1)
6a³- 2a² 2a² (3a-1)
9a+3 3 (3a+1)
6a² (3a-1) (3a+1)

39. If 50% of x is 20, what is 20% of x?
A. 16
B. 27
C. 8
D. 12

Part= Percent x Whole
Part= 20
Percent= 0.50
Whole= X
20= (0.50) x
𝟐𝟎
𝟎. 𝟓𝟎
=
𝟎. 𝟓𝟎𝒙
𝟎. 𝟓𝟎
X= 40
(40).20 = 8

40. What is the interest of PhP 6,000 at
5% for 3months?
A. PhP150.00
B. PhP120.00
C. PhP 75.00
D. PhP 250.00

41. The least common multiple (LCM) of 2,
3 and 4 is ___________.
A. 24
B. 14
C. 13
D. 12

2 4 6 8 10 12
3 6 9 12 15 18
4 8 12 16 20 24

42. The Greatest Common Factor (GCF)
of 22, 15, 7 is ______________.
A. 1
B. 3
C. 2
D. 4

22 {1,2,11,22}
15 {1,3,5,15}
7 {1,7}

43. The largest common factor of two or
more numbers is called?
A. GCF
B. Prime Factor
C. Composite Factors
D. LCM

44. Factor: 2x² + 7x-15
A. (x-5)(2x+3)
B. (x+5)(2x-3)
C. (2x+5)(x-3)
D. (2x-5)(x+3)

45. The island of Luzon is estimated to be
100,000 square kilometers. In exponential
from can be expressed as ______.
A. 1 x 10⁶
B. 10⁵
C. 1 x 10⁴
D. 10⁶

46. Mr. Conde had incurred the following
expenses in his trips to the Mindanao islands:
PhP3,200.00; Php2,500.00 and Php1,500.00.
What percent of this total monthly budget of
PhP40, 000.00 did he spend for this trip?
A. 35%
B. 18%
C. 30%
D. 20%

Part = Percent X Whole
Part = 2,500+3,200+1,500
= 7,200
Whole = 40, 000
We are looking for percent
𝑷𝒆𝒓𝒄𝒆𝒏𝒕 =
𝒑𝒂𝒓𝒕
𝒘𝒉𝒐𝒍𝒆
𝑷𝒆𝒓𝒄𝒆𝒏𝒕 =
𝟕, 𝟐𝟎𝟎
𝟒𝟎, 𝟎𝟎𝟎
= 0.18
=0.18 x 100
=18%

47. In a University, the ratio of female
professors to the male professors is 8:5. If
there are 75 male professors, how many are
female professors?
A. 180
B. 120
C. 375
D. 225

Female professors to Male professors
8:5
Male= 75
Female= 8x
8x+ 5x= 75 + 8x
5x=75
5x/5 =75/5
X= 15
Female professors = (15 x 8)
= 120

48. Simplify:
(x² −y²)
(x –y)
A. –x – y
B. x – y
C. x + y
D. y - x

Factoring
(x² − y²)
(x – y)
=
(x−y)(x+y)
(x –y)
= x+y

49. Simplify: 6-{3-(4)+11+8}.
A. 26
B. -26
C. 12
D. -12

49. Simplify: 6-{3-(4)+11+8}.
6 -3 +4 - 11 - 8
-12

50. Which are the prime factors of
63?
A. 7,9
B. 3, 21
C. 7, 3, 3
D. 7, 3, 2

51. The grades in Mathematics of the
students in section A are as follows: 80, 75,
60, 95, and 100. What is the population
variance of their group?
A. 206
B. 260
C. 216
D. 224

Population variance- all members of a
specified group
steps:
1. find the mean of the data set
2. subtract each number from the mean
3. square the result
4. add the result together
5. divide the result of total numbers in the
data

80 -2 4
75 -7 49
60 -22 484
95 13 169
100 18 324
82
206

52. The grades in mathematics of the students in
section A are as follows scores: 12, 10, 13, 11,
15, 20, 19, and 17. What is the population
standard deviation of their group?
A. 3.50
B. 3.48
C. 3.51
D. 3.49

12 -2.625 6.890625
10 -4.625 21.39063
13 -1.625 2.640625
11 -3.625 13.14063
15 0.375 0.140625
20 5.375 28.89063
19 4.375 19.14063
17 2.375 5.640625
14.625 97.875
SD =
97.875
7
SD = 13.9821
SD = 3.74

53. In how many ways can 5 girls be
seated in a row of 5 seats?
A. 95
B. 100
C. 105
D. 120

54. Which of the following is a product
of 13 and an integer?
A. 1326
B. 1323
C. 1343
D. 1333

55. In an English test, eight students
obtained the following scores: 12, 10, 13,
11, 15, 20, 19, 17. What is the median
score?
A. 15.5
B. 14
C. 16.5
D. 17

10 11 12 13 15 17 19 20
𝟏𝟑+𝟏𝟓
𝟐
= 14

56. A rectangular block of steel has
dimensions of 5 meters x 10 meters x 15
meters and weights, 1,000 N. How should
this block be placed on a surface to exert
the least pressure on the surface?
A. On the 10 meters by 15 meters side
B. On the 5 meters by 15 meters side
C. On the 5 meters by 10 meters side
D. All sides have equal pressure

57. The grades in Mathematics of the students
in section A are as follows: 80, 75, 60, 95, 100.
What is the mean absolute deviation of this
group?
A. 12.4
B. 13.2
C. 14.61
D. 11.7

80 2
75 7
60 22
95 13
100 18
62
12.4

58. 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
blue.
A. 1/3
B. 2/5
C. 3/5
D. 4/5

■# of balls = 6 + 4 +5 = 15
■# of blue balls = 5
■
5
15
or
1
3

59. The altitude of a triangle is 5 meters
and the base is 20 meters. What is the
area of the triangle?
A. 50 sq. m
B. 20 sq. m
C. 24 sq. m
D. 60 sq. m

Area of triangle = ½ base(height)
=1/2 (20)(5)
= ½ (100)
= 50sq m

60. A traveler was helped by other passengers
of a plane for his extra weight of 112 kg. There
were three of them who gave their allotment of
25 kg each. How much more weight will the
traveler still need to pay?
A. 37 Kg
B. 38 Kg
C. 75 Kg
D. 87 Kg

Let X be the weight the traveler
still needs to pay
X= 112 kg – (3 x 25 kg)
X= 112 kg – 75 kg
X= 37 Kg

61. How many twenty thousands
are there in one million?
A. 50
B. 100
C. 150
D. 1000

K= number of twenty
thousand in a million
𝑘 =
1,000,000
20,000
= 50

62. A policeman caught a pusher carrying prohibited
drugs. Each package weighed 14 kg,10
3
4
kg, 9
5
8
kg, and
17 kg. What is the total weight of the confiscated
drugs?
A. 50
2
3
kg
B. 50
3
8
kg
C. 51
3
8
kg
D. 51
1
4
kg

63. What is the product of (3 + 20)(6 –
30)?
A. -1440
B. -552
C. 552
D. 828

N=(3 + 20)(6 – 30)
N=(23)(-24)
N= -552

64. If a =
b
5
, and 10a = 14, what is b?
A. 7
B.
7
5
C. 14
D.
5
7

Get the value of a
10a = 14
10𝑎
10
=
14
10
a=1.4
Substitute then compute for the value of b
a =
b
5
or b=5a
b= 5(1.4)
b=7

65. If you were converting the height of
your room for better ventilation, what
would 1.55 m be equivalent to?
A. 15.5 cm
B. 1.55 dm
C. 1550 mm
D. 155 cm

66. A picture 10 cm by 8
1
2
cm is mounted on a
piece of cardboard. If there is a margin of 2
1
2
cm around the picture, what is the perimeter of
the cardboard used?
A. 47 cm
B. 52 cm
C. 57 cm
D. 87 cm

67. The initial cost of a diamond ring is P25,
000. If its value appreciates exponentially at an
annual rate of 15%, how much will be its cost in
5 years?
A. P187 500.00
B. P62 500.00
C. P50 284.00
D. P43 750.00

Interst
A= P (1 + rt)
P= principal amount
R= rate
T= time period
A= 25,000 (1+(.15)^ 5
= 25,000 (2.0113)
= 50,284

68. Twenty people won prizes in a state
lottery. Assuming there were no ties, how
many ways for these 20 to win 1st, 2nd, 3rd,
and 4th prizes?
A. 180 200
B. 116 280
C. 4 845
D. 480

Permutation- set of ordered arrangement of n
objects taken r at a time
nPr
n= 20
r= 4
20P4 or 20 x 19 x 18 x 17
=116, 280

69. In buying a house, a man pays P100 000
in cash and agrees to pay P75 000 two years
later. At 6% compounded semi-annually, find
the cash value of the house.
A. P166 636.50
B. P166 500.00
C. P156 636.50
D. P16 663.6

P = principal amount (the initial amount you borrow or
deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed
for.
A = amount of money accumulated after n years, including
interest.
n = number of times the interest is compounded per year

Compounded Interest
Amount = Principal (1 +
𝑟
𝑛
)𝑛𝑡
Amount = 75,000
R = 6 t = 2 n=2
Cash Value = Principal + Amount
75,000 = P (1 +
.06
2
) 2 (2)
75,000 = P (1 + .03)4
75,000 = P 1.12550881
1.12550881 1.12550881
66, 636.50 = P
CV = 100,000.00
+ 66,636.50
166,636.50

70. A sales representative of an appliance
company is given 20% of the total sales she
makes every week. What are her earnings if her
total sales for the week is P74,380?
A. P1 487.60
B. P7 438
C. P14 876
D. P59 504

Part= Percent x Whole
total sales in a week= P74, 380
Percentage of part given to her= 20%
earnings = Percentage of part given to her X total sales
in a week
= P74, 380 (0.20)
= P14, 876

71. In a school, the ratio of boys to girls is 4 :
3. If there are 672 students in all, how many
are girls?
A. 168
B. 224
C. 288
D. 384

Boys to girls is 4:3
Total students = 672
Boys = 4x
Girls= 3x
4x + 3x = 672
7x= 672 (divide both sides by 7)
X= 96
Girls = 3(96)
Girls = 288

72. Find the equation of the line
perpendicular to x + 2y – 6 = 0 and
passing through the origin.
A. 2x + y = 0
B. 2x – y = 0
C. -2x – y = 0
D. –x + 2y = 0

Two lines are perpendicular if the
product of their slope is -1
Get the slope of the line using the slope intercept form
y=mx+b
m is the slope
Change the for of the equation to slope intercept form
X+2y-6= 0 2y= -x+6
Get the slope
2𝑦
2
=
−𝑥
2
+
6
2
y=
−𝑥
2
+ 3
Slope is -1/2
The slope of the perpendicular line must be ½, therefore:
y=
𝑥
2
+ 0 or –x+2y=0

73. Solve for x: x2 – 5x + 6 > 0
A. x = 3 or x = 2
B. x > 3 or x < 2
C. 3 > x > 2
D. x > 3 or x > 2

74. Simplify: 2(3r – 7t) – 5(2r + 3t)
+ (5r + t)
A. r – 28t
B. r + 28t
C. 28t – r
D. -28t – r

2(3r – 7t) – 5(2r + 3t) + (5r + t)
6r – 14t – 10r -15t + 5r + t
6r-10r+5r – 14t – 15t + t
r – 28t

75. A room is 12 m by 8 m. There is a 6
m by 7.5 m carpet in the middle. What
percent of the room is uncovered?
A. 33.75%
B. 46.875%
C. 53.125%
D. 66.25%

Let r be the uncovered part of the room
R = (12m x 8 m) – (6m x 7.5m)
= 96- 45
= 51m
Percent of uncovered = uncovered/ total
measurement of room
= 51 m/ 96 m
= 0. 53125
= 0. 53125 x 100
= 53. 125%

76. Out of 6750 examinees, only 775 did
not pass in the Teachers’ Licensure
Examination. What is the passing
percentage?
A. 8.71%
B. 11.48%
C. 88.51%
D. 88.52%

Number of examinees who passed = 6750 – 775
= 5975
Percentage = part/ whole
= 5975 / 6750
= 0.885185
=0.885185 x 100
=88. 518 or 88.52%

77. What is the range of the following: 86,
71, 83, 90, 85, 74, 79, 81, 87
A.12
B.15
C.19
D.20

Range = highest number – lowest
number
Range = 90- 71
= 19

78. Why is
1
5
called a unit fraction?
A. The fraction is less than one.
B. The number is the denominator.
C. Unit fractions have 1 as the numerator.
D. It is between 0 and 1.

A unit fraction is a rational number
written as a fraction where the
numerator is one and the denominator
is a positive integer. A unit fraction is
therefore the reciprocal of a positive
integer, 1/n.
Examples are 1/1, 1/2, 1/3, 1/4 ,1/5,
etc

79. A rectangle has sides of 10 and 12 units.
How can the area of a square be computed if it
has the same perimeter as the rectangle?
A. Add 10 and 12, double the sum, then multiply by 4.
B. Add 10 and 12, double the sum, divide by 4, then
multiply by 2.
C. Add 10 and 12, double the sum, divide by 4, then
multiply by 4.
D. Add 10 and 12, double the sum, divide by 4, then
square the quotient.

80. Which of the following gives the sum
of the polynomials (a2 + b2 + ab) and (3a2
+ 4ab – 2b2)?
A. 4a2 + 5ab – b2
B. 5a2 + 5b2 + 5ab
C. 4a2 + b2 + 5ab
D. 3a2 + 5ab + 2b2

(a2 + b2 + ab) + (3a2 + 4ab – 2b2)
a2 + 3a2 + ab + 4ab + b2 – 2b2
= 4a2 + 5ab - b2

81. Of the 150 students enrolled in the subject
Assessment and Evaluation, 90% took the final
examination at the end of the semester. Two-
thirds of those who took the final examination
passed. How many students did not pass?
A. 45
B. 90
C. 100
D. 135

Let y be the number of students who did not pass
Let m be the total number of students who took
the exam
m = (150 x 0.90)
m= 135
Y= 135 – (2/3 x m)
Y = 135 – (2/3 x 135)
Y= 135 – (90)
Y= 45

82. What is the volume of a cube whose
edge is 4 cm?
A. 64 cm2
B. 64 cm3
C. 96 cm3
D. 144 cm3

Volume of a cube = 𝑠3
= 43
= 64𝑐𝑚3

83. If a function is defined by the set of
ordered pairs (1,2) , (2,4) , (3,8) , (4,16),
(5,N), then the value of N is _____.
A. 10
B. 20
C. 25
D. 32

84. Which of the following is the numerical
form for “three hundred forty-six and five
hundred eight-one ten thousandths”?
A. 346,581
B. 346.0581
C. 346.5801
D. 346.5810

85. A map is drawn to scale such that 1.5 cm on
the map corresponds to 55 km in actual
distance. How many cm on the map would
represent the distance between two towns which
are 297 km apart?
A. 3.6 cm
B. 5.2 cm
C. 5.4 cm
D. 8.1 cm

𝑥 =
297𝑘𝑚
55𝑘𝑚
𝑥 1.5 𝑐𝑚
X= 5.4 x 1.5 cm
X= 8.1 cm

86. How much greater is the sum of the
first 50 counting numbers than the sum of
the first 30 whole numbers?
A. 1710
B. 1275
C. 840
D. 810

Counting numbers (1, 2, 3, … 50)
Whole numbers ( 0, 1, 2, 3, … 29)
𝑆𝑛 =
𝑛
2
𝑎1 + 𝑎𝑛
𝑆50 =
50
2
1 + 50
𝑆50= 1275
𝑆29 =
29
2
0 + 29
𝑆29= 435
𝑆50- 𝑆29
1275- 465= 840

87. Which of these statements is always TRUE?
A. The sum of 5 consecutive numbers is always
divisible by 5.
B. The sum of two square numbers CANNOT be
even.
C. The sum of 3 consecutive pages of a book is
always odd.
D. The sum of two consecutive page numbers of
a book is even

A.4+5+6+7+8 = 30
B. 𝟕𝟐
+𝟑𝟐
= 58 X
C.1+2+3 =6 X
D.17+18 = 35 X

88. From a 75 m roll of clothing material,
28 school uniforms are made. If each
uniform uses 2.25 m of clothing material,
how many meters are left?
A. 63 m
B. 47 m
C. 33 m
D. 12 m

X= cloth left in meters
X= 75m – (28 x 2.25m)
X= 75 m– 63m
X= 12 m

89. In a playground for Kindergarten
kids, 18 children are riding tricycles or
bicycles. If there are 43 wheels in all,
how many bicycles are there?
A. 7
B. 8
C. 9
D. 11

90. Simplify 5√75 - 4√12
A. 13√5
B. √63
C. 17√3
D. 33√3

91. The readings on a water meter in April and
May are 417.8 kl and 430.4 kl. If there is a
basic charge of P23 and the cost per kl is P20,
how much is the billing for water consumption
between the two months?
A. P272
B. P275
C. P2520
D. P2543

April = (417. 8)20 + 23
= 8379
May= (430.4) 20 + 23
=8631
8631- 8379
= 252

92. How many glasses each to be filled
with 150 cu. cm. of Cola can be made
from 5 family-size bottles each containing
1.5 litres?
A. 40
B. 45
C. 50
D. 60

Total Volume of soda: (5)(1.5 L)(1000 cu cm)/(1 L)
Total Volume of Soda: 7500 cu cm
To get the number of glasses: 7500 cu cm / 150 cu cm
Answer: 50

93. The edges of a cubical frame are made
from plastic straws. How much longer is the
total length of the plastic edges of a cube
whose edge is 12 cm compared to a cube
whose edge is 9 cm?
A. 18 cm
B. 36 cm
C. 144 cm
D. 252 cm

(12) (12) – (12)(9) = 12(3) = 36

94. How many different rectangles can be found
in the diagram below?
A. 6
B. 9
C. 12
D. 18

95. If the width of a rectangle is reduced
by 20% and the length is also reduced by
20%, what percent of the original area is
the new area of the rectangle?
A. 80%
B. 64%
C. 60%
D. 36%

■ Original dimension = 100%
■ Condition: reduced by 20% -> 100 – 20 = 80%
■ A = l x w
■ A = .8 x .8
■ A = .64 x 100%
■A = 64%

96. What day follows the day before
yesterday if two days from now will
be Sunday?
A. Saturday
B. Thursday
C. Friday
D. Wednesday

2 Days from now is Sunday
So, from Sunday, we count back
Saturday, Friday
Yesterday’s Friday is Thursday
The day before Thursday is Wednesday
The day that follows Wednesday is THURSDAY

97. Kendra bought 120 towels at P10 each.
Then, she sold them at 3 for P50. If she
sold all the towels, how much profit did she
make?
A. P170
B. P400
C. P733
D. P800

Gross Profit = Total revenue- explicit
cost
Let x be the total profit Kendra made
X= (120/3)50 – (120)10
X= 2,000 – 1,200
X= 800

98. Mr. Bonita is 47 years old. He was 23 years
old when his eldest daughter was born, who is
six years older than his youngest son. How old is
Mr. Bonita’s youngest son now?
A. 17
B. 18
C. 23
D. 24

Let x be the age of the older sister
Let y be the age of the youngest
Y= X-6
X= 47- 23
X=24
Substitute the value of X
Y= 24- 6
Y= 18

99. What is the sum of all two-digit
numbers which are divisible by 5?
A. 1050
B. 960
C. 950
D. 945

Arithmetic series
𝑆𝑛 =
𝑛
2
2𝑎1 + 𝑛 − 1 𝑑
10 – 95
n=18
a1=10
d=5
𝑆18 =
18
2
2(10) + 18 − 1 5
𝑺𝟏𝟖 = 𝟗 𝟐𝟎 + 𝟖𝟓
S18= 945

100. Mr. Perez owns a 10 ½-hectare tract of
land. He plans to subdivide this land into ¼-
hectare lots. He must first set aside
1
6
of the
total land for roads. How many lots will this tract
yield?
A. 45
B. 42
C. 35
D. 3

1
6
x 10½ = 1¾ hectares
10½ - 1¾ = 8¾ hectares left
8 ¾ ÷ ¼ = 35 lots

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