The document covers various concepts related to linear inequalities, functions, and logical statements, including how to graph inequalities, solve systems of linear inequalities, and understand conditional statements. It also discusses examples of mathematical problems involving functions and reasoning methods like inductive and deductive reasoning. Additionally, it presents multiple-choice questions about these topics, indicating comprehension checks in mathematics.

2. What is the graph of linear
inequality in two variables?
a.Straight line
b. Parabola
c. Half -Plane
d. Solid line

3. Bianca has some ₱ 10- coins and ₱5- coins.
The total amount of these coins is at most (≤)
₱900. What is the highest number of ₱ 5-
coins, if there are 50 pieces of ₱10 coins?
a.80 pieces
b. 90 pieces
c. 100 pieces
d. 110 pieces

4. What will be the graph of
inequality with < or > symbol?
A. Solid line
b. broken line
c. straight line
d. curve line

5. Which of the following is a system
of linear inequality in two variables?
a.x + y = 4, 2x -7y > 3
b. x < 3, y > 4
c. x + 4y < 4, 2x -7y > 3
d. 2x + 3y = 4, 2x -7y = 3

6. How will you solve system of linear
inequalities in two variables?
a.Graphically
b. algebraically
c. both a and b
d. none of these

7. Which of the following is not a way
to represent a relation?
a.Table
b. Mapping Diagram
c. Rule
d. illustration

8. It represents persons or objects that can
be manipulated, controlled, or merely
measured for the sake of research.
a.Variables
b. data
c. Measurement
d. Survey

9. In the Statement “The number of hours of
work and salary in a private company of a
certain employee”, which is the dependent
variable?
a. The number of hours work
b.The company
c. the Salary of employee
d. the employee

10. A ________ is defined by f(x) = mx + b ,
where m and b are real numbers. Its
graph is a line with slope b and y-
intercept
a. Linear function
b. Quadratic function
c. cubic function
d. none

11. At what point will the graph of ( ) =
𝑥
2 − 10 intersects the -axis?
𝑥 𝑦
a.(0, −5)
b. (5,0)
c. (0, −10)
d. (0,10)

12. A pay phone service charges Php 5 for the first
three minutes and Php 1 for every minute
additional or a fraction thereof. How much will
a caller have to pay if his call lasts for 8
minutes?
a.Php 10
b. Php 15
c. Php 20
d. Php 25

13. Sarah earns Php 42 an hour in a dress factory
with an additional of Php 50 for her daily meal
allowance. What equation describes her
earning for one day ?
a.f(x) = 42x + 50
b. f(x) = 50x + 42
c. f(x) = 4x + 50
d. f(x) = 50x + 4

14. Mr. Castro placed part of his separation pay
amounting to Php 40,000 in some business
venture. If it earns Php 5,000 a month, in how
many months will his money be twice the
original amount?
a.15 months
b. 16 months
c. 20 months
d. 24 months

15. If it is a right angle, then it measures 90
degrees. What do you call the bolded
portion in this conditional statement?
a.Conclusion
b. Hypothesis
c. Conjecture
d. Inverse

16. The If-then form of the statement “Parallel lines
never intersect,” is:
a. If two lines intersect, then they are parallel.
b. If two lines are not parallel, then they intersect.
c. If two lines are parallel, then they never
intersect.
d. If two lines intersect, then they are not parallel.

17. What is the conclusion in the statement “If
the slope is positive, then the graph of the line
is increasing”
a.Graph of a line is increasing
b.Then the graph of a line is increasing
c. Slope is positive
d. If the slope is positive

18. A statement joining two events together
based on a condition in form of “If
something, then something”.
a.Conditional
b. Converse
c. Inverse
d. Contrapositive

19. The inverse statement in terms of
“if x, then y” is
a.If not x, then not y
b.If y, then x
c. If not y, then not x
d. If not y, then x

20. The contrapositive statement “If it rained last
night, then the sidewalk is wet”.
a. If the sidewalk is wet, then it rained last night.
b. If the sidewalk is not wet, then it did not rain
last night.
c. If it did not rain last night, then the sidewalk is
not wet.
d. If it rained last night, then the sidewalk is not
wet.

21. How can we say that the conditional
statements are equivalent statements?
a. If they have the same truth value
b. If they are both true
c. If they are both false
d. all of the above

22. What is the shorthand for “if and
only if” in biconditional statement?
a.If
b. iff
c. fof
d. if -o-if

23. Given the statements below, what the equivalent of converse?
Conditional Statement: If it rains, then the ground is wet. (T)
Converse: If the ground is wet, then it rained. (F)
Inverse: If it does not rain, then the ground is not wet. (F)
Contrapositive: If the ground is not wet, then it did not rain. (T)
a.Converse
b. inverse
c. contrapositive
d. none of these

24. Reasoning uses basic and/or general
statements to arrive at a conclusion.
a.Inductive
b. deductive
c. logic
d. all of these

25. Is a logical argument in which each statement
you make is supported or justified by given
information, definitions, axioms, postulates,
theorems and previously proven statements?
a.reasoning
b. logic
c. proof
d. deductive

26. Which of the following is not a way
to write a proof?
a.Paragraph
b. two-column
c. flow chart
d. table

27. Which of the following is not a linear
inequality in two variables?
a.2x + 3y ≤ 5
b. 3x - 3y < -2
c. x – 2y > 4
d. 4x – 2y = 5

28. Ashley bought five oranges and ten apples.
The total amount that she paid is at least
Php 140. How much should an apple cost if
an orange cost ₱8?
a.More than Php 10.00
b. Less than Php 10.00
c. Php 10.00
d. Php 20.00

29. The difference between the scores of Cathy
and Cindy in the game lawn tennis is less than
nine points. If Cathy’s score is 27 points; what
could be the score of Cindy?
a.Above 18
b. lower than 18
c. equals to 18
d. above 19

30. What will be the graph of
inequality with ≤ or ≥ symbol?
a.Solid line
b. broken line
c. straight line
d. curve line

31. Which of the following ordered pairs
satisfy both 2 + 7 > 5 and 3 −
𝑥 𝑦 𝑥 𝑦
< 2?
a.(0, 0)
b. (10, -1)
c. (-4,6)
d. (2, -8)

32. Which of the following is a graph of a
system of linear inequalities in two
variables?

33. How will you identify if a given set of
ordered pairs are function?
a. If there is no repletion on the y-values
b.It should be a set of ordered pairs
c. If there is no repetition on the x-
values
d. There is many to one correspondence

34. In the Statement “The number of hours of
work and salary in a private company of a
certain employee”, which is the independent
variable?
a. The number of hours work
b.The company
c. the Salary of employee
d. the employee

35. What is the domain of the function
f(x) = 2x -1?
a.All real numbers
b. greater than 2
c. less than 2
d. 2 and positive infinity

36. Which of the following functions
shows a slope of 1?
a.f( ) = −3 + 1
𝑥 𝑥
b. f( ) = − + 2
𝑥 𝑥
c. f( ) = −3
𝑥 𝑥
d. f( ) = + 9
𝑥 𝑥

37. Emman often rides a taxi from one place to
another. The standard fare in riding a taxi is php 40
as a flag down rate plus Php 3.50 for every 200
meters. how much he would pay if the taxi
covered the distance of 600 meters?
a. Php 45
b. Php 43.5
c. Php 47
d. Php 50.50

38. A motorist drives at a constant rate of 60 kph.
If his destination is 240 kilometers away from
his starting point, how many hours will it take
him to reach the destination?
a.5 Hours
b. 4 hours
c. 3 hours
d. 3 hours

39. Sarah earns Php 260 an hour in a dress
factory with an additional of Php 50 for her
daily meal allowance. how long did she work
for that day?
a. 3 hours
b. 4 hours
c. 5 hours
d. 6 hours

40. If garbage is disposed properly, then dengue
diseases will be prevented. What do you call
the underlined portion in this conditional
statement?
a.Conclusion
b. Hypothesis
c. Conjecture
d. Inverse

41. If it is a right angle, then it measures 90
degrees. What do you call the underlined
portion in this conditional statement?
a.Conclusion
b. Hypothesis
c. Conjecture
d. Inverse

42. What is the hypothesis in the statement
“If it’s right angle, then it measures
exactly 90 degrees”
a. If it’s right angle
b. Measures 90 degrees
c. Right Angle
d. angle measures 90 degrees

43. What is the inverse of the statement “If the number is
divisible by 2 and 3, then it is divisible by 6.”
a.If the number is divisible by 6, then it is divisible by 2
and 3.
b.If the number is not divisible by 2 and 3, then it is not
divisible by 6.
c.If the number is not divisible by 6, then it is not
divisible by 2 and 3.
d.If the number is divisible by 2 and 3, then it is not
divisible by 6

44. The statement switching the hypothesis
and conclusion from the conditional
statement.
a. Conditional
b. Converse
c. Inverse
d. Contrapositive

45. It is written in the form “if not q,
then Not p?
a.Conditional
b. Converse
c. Inverse
d. Contrapositive

46. When is the time that a conditional
statement will be false based on Truth
Table?
a.If p is true and q is false
b.If p is true and q is true
c. If p is false and q is true
d. if p is false and q is false

47. A statement combing a conditional
statement with its converse
a. Inverse
b. converse
c. biconditional
d. contrapositive

48. Given the statements below, what the equivalent of
conditional statement?
Conditional Statement: If it rains, then the ground is wet. (T)
Converse: If the ground is wet, then it rained. (F)
Inverse: If it does not rain, then the ground is not wet. (F)
Contrapositive: If the ground is not wet, then it did not rain.
(T)
a.Converse
b. inverse
c. contrapositive
d. none of these

49. Reasoning which uses specific examples
to arrive at a general rule,
generalizations or conclusions.
a.Inductive
b. deductive
c. logic
d. all of these

50. It is the science of correct
reasoning?
a.Inductive
b. logic
c. proof
d. deductive

51. Is a method of reasoning usually written in
paragraph form. The opposite of the
statement to be proven is assumed true until
the assumption leads to a contradiction.
a.Direct proof
b. indirect proof
c. proof
d. all of these