REVIEW

1. How many permutations can be made out of the letters of the word, "ENGINEERING"?*
1 point
277,700
6,625,800
277,200
6,652,800
How much water must be evaporated from 10 kg solution which has 4% salt to make a solution of
10% salt?*
1 point
7 kg
5.5 kg
4 kg
6 kg
The points (a,1), (b,2), and (c,3) are collinear. Which of the following is TRUE?*
1 point
c - a = b - a
c - b = b - a
c - b = c - a
c - a = a - b
What is the degree of this polynomial?*
1 point
11
9
5
18
When all odd numbers from 1 to 101 are added, the result is __________.*
1 point
3,500
2,500
2,741
2,601
The expression [2^(log x)] [4^(log x)] is equals to _________.*
1 point

2. Option 3
Option 2
Option 1
Option 4
A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the next layer above, 55 bricks in
the third layer from the bottom, and so until there are 10 bricks in the last layer. How many bricks
are there altogether?*
1 point
640
639
636
638
Determine k so that the equation 4x^2 + kx + 1 = 0 will just have one real solution.*
1 point
4
7
6
5

3. The sum of Kim's and Kevin's ages is 18. In 3 years, Kim will be twice as old as Kevin. What are
their ages now?*
1 point
Kim is 3 years old while Kevin is 15 years old.
Kim is 6 years old while Kevin is 12 years old.
Kim is 7 years old while Kevin is 11 years old.
Kim is 5 years old while Kevin is 13 years old.
A person has 2 parents, 4 grandparents, 8 great-grandparents, and so on. How many ancestors
are there during the 15 generations preceding his own, assuming no duplication?*
1 point
131,070 ancestors
65,534 ancestors
32,766 ancestors
16,383 ancestors
The value of the square of the quantity 3 to the 2.5th power is equal to:*
1 point
243
81
729
140
Carry out the following multiplication and express your answer in cubic meter: (8 cm) x (5 mm) x (2
m)*
1 point
8 x 10^(2)
8 x 10^(-2)
8 x 10^(-3)
8 x 10^(-4)
Find the value of the logarithm of 48 to the base 8.*
1 point
1.86
1.89
1.68
1.78
Choose the correct answer.*
1 point
I, II, and III only
I only
I, II, III, and IV

4. II and IV only
Which of the following points out the ERROR in the given process?*
1 point
The base of the logarithm should be 10.
The process should involved FOIL method.
There is no error in the solution.
The last part should show that the right side must have an exponent of 2x and a base of 3.
Evaluate the following expression and follow the GEMDAS rule:*
1 point
-5
5
1
-1
Find the inclination of the line passing through (-5,3) and (10,7).*
1 point
14.43
14.93
14.83
14.73
How many four-letter words beginning and ending with a vowel without any letter repeated can be
formed from the word, "PERSONNEL"?*
1 point
20
312
40
480
A father tells his son, "I was your age now when you were born." If the father is 38 years old at
present, what is the age of the son 2 years ago?*

5. 1 point
13
17
14
19
Which is NOT a prime number?*
1 point
3
2
5
1
According to the multiplication property of inequality, given real numbers a and b, if a > b and c is
a negative number, then, __________.*
1 point
ac < bc
ac > bc
ac ≥ bc
ac ≤ bc
What is the solution set of the inequality 4(y - 2) ≥ 5(y + 2)?*
1 point
{y | y ≤ -2}
{y | y ≥ -18}
{y | y ≤ -18}
{y | y ≥ -2}
It is the distance of a number from zero.*
1 point
Trichotomy Property
Distance Theorem
Degree
Absolute Value
What is the product of (2x - 5y)^3?*
1 point
8x^3 - 60(x^2)y - 150x(y^2) - 125y^3
8x^3 + 60(x^2)y + 150x(y^2) + 125y^3
8x^3 - 60(x^2)y + 150x(y^2) - 125y^3
8x^3 - 60(x^2)y + 150x(y^2) + 125y^3
What is the area of the shaded region?*
1 point

6. 3x^2 + 21
3x^2 - 9
3x^2 - 21
3x^2 - 29
Find the harmonic mean between 3 and 1/3.*
1 point
3/5
4/5
2/5
5/2
Multiply the following: (2x+5y)(5x-2y)*
1 point
10x^2 - 21xy - 10y^2
-10x^2 - 21xy + 10y^2
10x^2 - 21xy + 10y^2
10x^2 + 21xy - 10y^2
Which of the following numbers cannot be written as a power of 2?*
1 point
square root of 32
1
6
1/256
A polynomial of fifth-degree is called _______.*
1 point
linear
quartic
quintic
quadratic
Give the factors of a^2 - x^2.*
1 point
2x - 2a
(a+x)(a+x)
2a - 2x
(a+x)(a-x)
In the equation: x^2 + x = 0, one is root is equal to ___________.*

7. 1 point
0.25
1
5
none among the choices
A machine can pump out water from a tank in 11 hours. Another machine can pump out water
from the same tank in 20 hours. How long will it take both machines to pump out the water in the
tank?*
1 point
6 hours
7 hours
7.5 hours
6.5 hours
Which is the equivalent decimal number for forty-nine thousandths?*
1 point
0.49
0.049
4.9
0.0049
Which of the following statements is FALSE?*
1 point
3 is the common difference of the arithmetic sequence 8, 11, 14, 17.
The 8th term of the arithmetic sequence 3, 5, 7, 9 . . . is 17.
2, 4, 6, 8, 10 is a sequence.
7, 8, 10, 11, 14 is an arithmetic sequence.
Which of the following statements is FALSE?*
1 point
The solution set of the absolute value |-3x + 5| + 5 > 2 is the set of all real numbers.
A three part inequality consists of two separate inequality combined into one. It may be classified as a
conjunction or a disjunction.
The values included in the interval notation makes the given inequality a true statement.
Parentheses and brackets in interval notations are meant to be used separately, and should not be used in
one interval.
If f(x) = 2x^2 + 2x + 4, what is f(2)?*
1 point
16
4x + 2
x^2 + x + 2
8
Find the sixth term of (3x - 4y)^8.*
1 point
-1,548,288(x^3)(y^5)
-154,288(x^3)(y^5)
-148,288(x^3)(y^5)
-548(x^2)(y^5)

8. The nth term of the sequence 5,3,1,-1,-3,-5,… is __________.*
1 point
3 + 2n
7 - 2n
2n + 5
2n- 7
0.125 is to 1/8 as 0.666 is to __________.*
1 point
2/3
5/4
1/3
3/2
What is the product of the roots in 3x^2 = 2x - 1?*
1 point
3
3/2
2/3
1/3
Find the product of two numbers such that when the first number is added to the second will result
to 19, and three times the first is 21 more than the second.*
1 point
90
63
32
24
Find the mean proportional of 4 and 36.*
1 point
20
12
72
44
Ten liters of 25% salt solution and fifteen liters of 35% salt solution are poured into a drum
originally containing thirty liters of 10% salt solution. What is the percent concentration of salt in
the mixture?*
1 point
27.05%
22.15%
19.55%
25.72%
0.63 is what percent of 0.9?*
1 point
63%
77%
70%

9. 75%
What value will satisfy the equation?*
1 point
19/11
13/9
1/11
13/11
Find the sum of the first 30 natural numbers.*
1 point
712
465
345
652
How many times will a grandfather's clock strikes in one day if it strikes only at the hours and
strikes once at 1 o'clock, twice at 2 o'clock, and so on?*
1 point
300
210
24
156
What is one-half of 8^300?*
1 point
4^150
2^599
4^300
2^899
If cos 65° + cos 55° = cos θ, find θ in radians.*
1 point
0.765 radians
0.087 radians
1.213 radians
1.421 radians
Choose the correct answer.*
1 point
-2
-3
3
2

10. Luciah, Monicah, and Jeof can mow the lawn in 4, 6, and 7 hours respectively. What fraction of the
yard can they mow in 1 hour if they work together?*
1 point
84/47
47/84
39/60
45/84
Rhea is twice as old as John now. In 5 years, the sum of their ages is 58. What is John’ present
age?*
1 point
32
12
18
16
Which of the following statements is TRUE?*
1 point
When using the Sigma notation, the value of the variable “n” is the starting point.
“Divergent series” is to “getting closer to one” as “convergent series” is to “getting too large to be
evaluated”.
The geometric mean is also called the average of the arithmetic sequence.
When a negative base is raised to an odd exponent, the result is always negative.
Find the value of a.*
1 point
12
10
11
9
What is the sum of the roots in x^2 + 5 = 0?*
1 point
0
-5
5
1
A 7 kg mass is suspended in a rope. What is the tension in the rope in SI?*
1 point
72 N
70 N
68.67 N
71.67 N
Choose the correct answer.*
1 point

11. II only
I, II, and III only
I, II, and IV only
I and IV only
Find the ninth term of the harmonic sequence: 1/3,1/5,…*
1 point
1/21
1/19
1/22
1/17
Find the sum of the first ten terms of the Fibonacci sequence starting with 0.*
1 point
92
90
88
94
Find the fraction such that, if 2 is subtracted from its terms it becomes 1/4, but, when 4 is added to
its terms it becomes 1/2.*
1 point
5/14
3/2
5/12
6/13
Give the sum of the first 10 prime numbers.*
1 point
205
98
129
112
What are your setbacks for the board examination? Please share simple thoughts.
Your answer
Find the term involving y^5 in the expansion of (2x^2 + y)^10.*
1 point
4,068(x^5)(y^5)
8,046(x^10)(y^5)
8,064(x^10)(y^5)
8,046(x^5)(y^5)
Which value of x satisfies the equation 4(3^x ) = 234?*

12. 1 point
4
2
1
3
Simplify the quotient of 3x^3 and 4x^5.*
1 point
3x^2 / 4
4x^2 / 3
3 / 4x^2
4 / 3x^2
The area of a circle is 89.42 square inches. What is its circumference?*
1 point
32.25 inches
35.33 inches
35.55 inches
33.52 inches
210 is 600% of what number?*
1 point
35
65
42
50
What is the number of permutations of the letters in the word, "BANANA"?*
1 point
42
36
60
52
Fill in the blank. “The __________ is used to join two intervals of the disjunction.”*
1 point
word “nor”
symbol “∪”
word “or”
symbol “&”
If the logarithm of 10 to the base a is equals to 0.25, what is the value of the logarithm of a to the
base 10?*
1 point
4
6
2
10
What is the measurement of the interior angle of a regular hexagon?*
1 point

13. 180 degrees
150 degrees
120 degrees
90 degrees
Simplify: log⁡ 2 + log⁡ 3.*
1 point
log 1
log (2/3)
log 6
log 7
The sum of three arithmetic means between 34 and 42 is _________.*
1 point
114
124
144
134
What is the simplified form of the given algebraic expression?*
1 point
4a - 2b - 3c
4a + 8b - 3c
6a - 2b - 3c
6a + 8b - 3c
There are 8 bananas in each box. How many bananas are in 58 boxes.*
1 point
464
256
576
318
From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock
describes an arc having which measure?*
1 point
270 degrees
90 degrees
540 degrees
180 degrees
Which of the following statements is TRUE?*
1 point
The graph of an untransformed logarithmic function will always pass (0,1).
The logarithm of a quotient is equal to the sum of the logarithm of each factors.
The logarithm is an exponent.
The natural logarithm of 1 is e.

14. Glenn can paint a house in 9 hours while Stewart can paint the same house in 16 hours. They
work together for 4 hours. After 4 hours, Stewart left and Glenn finished the job alone. How many
more days did it take Glenn to finish the job?*
1 point
2.50 hours
2.75 hours
2.25 hours
3 hours
If x to the power of 3/4 results to 8, then x is equals to _________.*
1 point
6
9
-9
16
The fourth and sixth terms of a geometric progression are 216 and 1,944 respectively. Find the
eighth term.*
1 point
17,649
17,964
16,749
17,496
Which set of properties is correct for the function, y = 4^x?*
1 point
domain: x ∈ R range: y ≥ 0
domain: x ∈ R range: y ≤ 0
domain: x ∈ R range: y > 0
domain: x ∈ R range: y < 0
This property states that one and only one of the following is true: a = b, a < b, a > b.*
1 point
Trichotomy Property of Inequality
Addition Property of Inequality
Closure Property of Inequality
Multiplication Property of Inequality
Solve: |3x + 2| = |x - 6|.*
1 point
x = {1}
x = {-1,4}
x = {1,-4}
x = {-1}
This property of equality states: If a = b, then a may replace b or b may replace a in any situation.*
1 point
Reflexive Property
Substitution Property
Addition Property

15. Symmetric Property
Kris starts with 5 pens. He buys 76 more. How many pens does Kris end with?*
1 point
72
84
81
75
The graph of y=e^x is translated 6 units to the right and 4 units upward. What is the equation of
this function?*
1 point
y = e^(x+4) + 6
y = e^(x-6) + 4
y = e^(x-4) + 6
y = e^(x+6) + 4
What is the value of the expression if a = 1, b = 2 and c = -1?*
1 point
25
3
23
5
Once a month, a man puts some money into a cookie jar. Each month he puts 50 centavos more
into the jar than the month before. After 12 years, he counted his money. He collected Php 5,436.
How much money did he put in the jar in the last month?*
1 point
Php 85.50
Php 84.50
Php 73.50
Php 63.50
Which of the following statements is TRUE?*
1 point
A bracket is always used next to the infinity symbol.
There is only one solution if the absolute value is equated to a negative real number.
If the absolute value is equated to another absolute value, two possible interval solutions may be obtained.
An absolute value that is greater than zero has no solution.
Choose the correct answer.*
1 point
(147/x^21)
(343/x^15)
(343/x^21)

16. (147/x^15)
Choose the correct answer*
1 point
four
three
two
one
Find the simple interest on $2000 invested at 12% per annum for 3 years.*
1 point
Php 60
Php 240
Php 720
Php 480
Simplify the following expression:*
1 point
-3a
-7a
-5a
-9a
In a club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How
many like both?*
1 point
12
13
10
11
Simplify the following expression:*
1 point
2(x^2)(y^5)
-2(x^5)(y^5)
-2(x^5)(y)
2x(y^5)
What is the solution set of |2x - 3| ≤ 1?*

17. 1 point
{x | 1 ≤ x and x ≥ 2}
{x | 1 ≤ x or x ≤ 2}
{x | 1 ≥ x ≥ 2}
{x | 1 ≤ x ≤ 2}
Describe the graph for the solution of 7x - 9 ≥ 2x + 11.*
1 point
The graph shows a filled circle on 4 and a line going to positive infinity.
The graph shows a filled circle on 20/9 and a line going to positive infinity.
The graph shows a filled circle on 20/9 and a line going to negative infinity.
The graph shows a filled circle on 4 and a line going to negative infinity.
Choose the correct answer.*
1 point
9x^3 + 4x^2 - 3x + 8
3(x)^3 - x + 8
-3(x)^3 + x - 8
-(x)^3 -10x^2 + 13x + 8
If eight is added to the product of nine and the unknown number, the sum is seventy-one. Find the
unknown.*
1 point
7
9
8
5
Ben had 24 bookmarks. He had 3 more bookmarks than Ron. How many bookmarks did Ron
have?*
1 point
23
24
22
21
Find the quotient when 3x^5 - 4x^3 + 2x^2 + 36x + 48 is divided by x^3 - 2x^2 + 6.*
1 point
3x^2 - 4x - 8
3x^2 + 4x + 8
3x^2 - 6x - 8
3x^2 + 6x + 8
The expression x^2 + x/3 -12 is a polynomial. Which statement is agreeable?*
1 point
The expression has a fractional exponent.
The expression has a negative exponent.
None of the choices answers the question.
The expression has no variable in the denominator.

18. Which mathematical concept is ERRONEOUS in the process?*
1 point
exponent
numerical coefficient
symbol
denominator
What is the interval notation of 23 < 4x + 5 ≤ 35?*
1 point
x = (15/2,9/2]
x = (9/2,15/2)
x = (9/2,15/2]
x = [15/2,9/2)
Choose the correct answer.*
1 point
III only
I, II, III, and IV
III and IV only
II, III, and IV only
Add: √48 + √75*
1 point
11√3
9√3
6√2
√123
What is the area of the larger rectangle?*
1 point

19. x^2 - 25
x^2 + 25
4x^2 + 25
4x^2 - 25
Choose the correct answer.*
1 point
I and II only
I, III, and IV only
I, II, III, and IV
IV only
Choose the correct answer.*
1 point
I and IV only
I, II, and III only
I only
II, III, and IV only
Which of the expressions is NOT equal to (log⁡ 4096)?*
1 point
3 log 16
4 log 1,024
6 log 4
2 log 64
Which of the following is equivalent to 1 hectare?*
1 point
10,000 square meters
50,000 square feet

20. 2 acres
10 ares
Which of the following is the graph of the following function?*
1 point
Option 1
Option 2
Option 3

21. Option 4
A test has 20 questions. If peter gets 80% correct, how many questions did Peter missed?*
1 point
2.5
2
4
5
Fill in the blank. “The number of terms in a binomial expansion __________."*
1 point
is one more than the power
is one equal to the power
is one less than the power
none of the choices given
What is the value of the variable in h(x) = ln x if x is equals to the square of e?*
1 point
e
5
e^3
2
What is the solution set of |12 - 3x| ≥ 0?*
1 point
x = {x | x ∈ R and x ≠ 3}
x = {x | x ∈ R and x ≠ 4}
x = {x | x ∈ R}
x = ∅
What is the 20th multiple of 3?*
1 point
60
36
45
40
What are the roots of the equation: 2x^2 - 5x - 3 = 0?*

22. 1 point
-0.5
2.5
2
-3
Find the distance between A (4,-3) and B (-2,5).*
1 point
8
9
10
12
Which of the following statements is FALSE?*
1 point
The fundamental property of rational expressions is used in dividing out common factors to express the
rational expression in lowest terms.
A rational expression is a quotient of two polynomials.
Evaluating rational expressions involves substituting a value of x to solve the expression.
A rational expression is undefined if the expression is equal to zero.
Find the value of x in this expression:*
1 point
414
144
524
625