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WorksheetsREVIEWER IN MATH 8
Total questions: 50
Worksheet time: 25mins
In a Grade 8 math class, students are asked to identify examples of linear inequalities in two variables. The teacher writes several expressions on the board.
Which of the following is NOT a linear inequality in two variables?
x + y < 5
y > 2x + 7
x < 0
x + y ≥ 12
Mario wants to show to his friend an example of different forms of linear inequality in two variables.
Which of the following would NOT be an example of a linear inequality in two variables?
Ax + By < C
Ax + By = C
Ax + By > C
Ax + By ≤ C
In a game, players earn points based on two activities, Activity X and Activity Y. The total points, represented by the equation x + y > 8, must be greater than 8 for the player to advance to the next level. Each ordered pair (x, y) represents a possible combination of points from Activity X and Activity Y.
Which of the following point combinations will satisfy the condition x + y > 8 and allow the player to advance?
(3, 4)
(4, 4)
(5, 6)
(-10, 1)
The graph of x + y > 5 is presented on the right, examine which ordered pair will satisfy the given linear inequality.
(0, 5)
(6, 3)
(1, -2)
(-5, -1)
A park boundary is mapped using a linear inequality. The shaded area on the map shows all points within the park, and any point in this area is a solution to the inequality.
Based on this, how many solutions does a linear inequality in two variables have?
0
1
2
infinite
In Pasay City, a community organization plans to establish a pedestrian-friendly zone near a busy intersection. They decide that all points within the zone must satisfy the condition where the combined distances from two specific markers, represented by x and y, are less than 4 kilometers. This requirement is represented by the inequality x + y < 4.
Which of the following graphs shows the correct area where x + y < 4?
Write a linear inequality that represents this situation: The amount consisting 50 bills (f) and Php 100 bills (h) is greater than Php 500.
50f + 100h = 500
50f + 100h > 500
50f + 100h ≥ 500
A. 50f + 100h < 500
Maria is making bags and wallets from recycled materials. It takes 5 hours to make a bag (x) and 2 hours to make a wallet (y). If she can work no more than 34 hours a week, and she makes 4 bags, what is the maximum number of wallets she can make in the remaining time?
5
6
7
8
Determine the solution of the system of linear inequality,
(2, 4)
(6, -2)
(0, 2)
(3, 0)
In Manila, two environmental zones are defined on a map, represented by a system of linear inequalities that restricts certain types of construction. The shaded region on the graph represents the area where both inequalities overlap, indicating the safe zone for green infrastructure projects.
Given the graph at the right, which point is a solution that satisfies both inequalities in this system?
(2, 3)
(1, 6)
(-3, 4)
(3, -2)
In Quezon City, the local government is designating an area on a map for eco-friendly business development. The boundaries of this zone are defined by a system of linear inequalities. The shaded area on the graph represents all possible locations that meet the city’s criteria for eco-friendly development.
Based on the graph on the right, which of the following systems of linear inequalities best represents the shaded area?
Kristine has a weekly food budget of Php 500. She wants grilled chicken and bangus for dinner. She finds that chicken (x) sells at Php 150 per kilogram and bangus (y) sells at Php 160 per kilogram.
Which of the following number of kilos will not fit her budget?
1 kg of chicken and 1 kg of bangus
2 kg of chicken and 2 kg of bangus
2 kg of chicken and 1 kg of bangus
1 kg of chicken and 2 kg of bangus
Kristine has a weekly food budget of Php 500. She wants grilled chicken and bangus for dinner. She finds that chicken (x) sells at Php 150 per kilogram and bangus (y) sells at Php 160 per kilogram.
Formulate a system of linear inequalities that represent the problem?
A
B
C
D
In a math class, students are learning about different terms related to sets of ordered pairs. The teacher asks the class, "What do we call any set of ordered pairs?"
Which of the following correctly defines a set of ordered pairs?
Domain
Function
Range
Relation
Given the set of ordered pairs below. Which of the following represents a function?
{(8, 3), (8, 6), (8, 9)}
{(3, 8), (5, 11), (7, 15)}
{(-7, 9), (7, 6), (-7, 4)}
{(-1, 0), (-1, 1), (-1, 2)}
Which table of values best illustrate a function?
A
B
C
D
It is a function since the vertical line will touch the graph at three points.
It is a function since the vertical line will touch the graph at exactly one point.
It is a mere relation since the vertical line will touch the graph at three points.
It is a mere relation since the vertical line will touch the graph at exactly one point.
Examine each function below. Which does not represent a linear function?
f(x) = x + 2
f(x) = -50x + 3
f(x) = -9x
f(x) = 3x2 + 8
Marites wants to know the effect of the new fertilizer on the growth of her plants. In the situation, what is the independent variable?
the new fertilizer
Marites’ experiment
the growth of plants
the new fertilizer and plant growth
The teacher asked John to determine the domain of the given set of ordered pairs {(1,1), (2,4), (3,4), (−2,1), (−4,5)}. His answer is
{-4, -2, 1, 2, 3}.
Is he correct?
Yes, since the numbers are decreasing.
Yes, because domain is the set of first coordinates.
No, numbers 1, 1, 4, 4, and 5 are the first coordinates of the ordered pairs.
No, because the elements should be written once and the answer is {1, 4, 5}
Mr. Reyes is a dealer of poultry eggs. The table shows the cost for each number of trays. The no. of trays of eggs (x) and cost in pesos (y) presented horizontally.
How many trays of egg are needed if the customer pays Php 630 to Mr. Reyes?
2
3
4
5
Mr. Reyes is a dealer of poultry eggs. The table shows the cost for each number of trays. The no. of trays of eggs (x) and cost in pesos (y) presented horizontally.
How much would it cost if the customer wants to buy six trays of eggs?
Php 1260
Php 1470
Php 1680
Php 1890
Use the figure at the right and answer the following question. What is the domain of the given graph?
{x ∈ R | -2 < x < 2}
{x ∈ R | -2 < x ≤ 2}
{x ∈ R | -2 ≤ x < 2}
{x ∈ R | -2 ≤ x ≤ 2}
You are asked by your teacher to find the range of the linear function f(x)xx+1 . Which of the following should be the correct answer?
{y ∈ R | y ≠ 0}
{y ∈ R | y ≠ 1}
{y ∈ R | y ≠ 2}
{y ∈ R | y ≠ 3}
Identify the statement that best describe the graph of the given set of ordered pair?
S = {(−𝟑, 𝟑), (−𝟐, 𝟐), (−𝟏, 𝟏), (𝟎, 𝟎), (𝟏, −𝟏)}
the graph is a straight line and is drawn diagonally and rises from left to right.
the graph is a straight line and is drawn diagonally and declines from left to right.
the graph is a straight line and is drawn horizontally.
the graph is a straight line and is drawn vertically.
A survey of out-of-school youth in a barangay was conducted. From year (x) 2020 to 2023, the number of out-of-school youths, y, was tallied and was observed to increase at a constant rate as shown in the table below.
If the pattern continues, what is the number of out of school-of-youths (y) by the following year (2024)?
58
68
78
88
A survey of out-of-school youth in a barangay was conducted. From year (x) 2020 to 2023, the number of out-of-school youths, y, was tallied and was observed to increase at a constant rate as shown in the table below.
If you graph the table of values above, how will you describe it?
the graph is a straight line and is drawn diagonally and rises from left to right.
the graph is a straight line and is drawn diagonally and declines from left to right.
the graph is a straight line and is drawn horizontally.
the graph is a straight line and is drawn vertically.
What is the linear function of the given graph on the right?
y = 3x + 3
y = 3x – 3
y = x + 3
y = 3x + 1
You are asked by your teacher to graph the linear equation whose slope (m) and y-intercept (0, b) are given. What will you do first?
Plot the y-intercept (0, b).
Draw a line passing the points.
Use the slope (m) to identify the rise and the run
From the given point, count out the rise and run
Cassy sells packed lunch online. She gets Php 10 for every packed lunch sold and a Php 100 incentive each day from the store owner. How much does she earn if she sells 50 packed lunches in a day?
Php 200
Php 350
Php 450
Php 600
“If you are practicing Reduce, Reuse and Recycle, then you are helping to save the environment”. Which is the hypothesis in the given statement?
Saving the environment.
Reduce Reuse and Recycle.
You are helping to save the environment.
You are practicing Reduce Reuse and Recycle.
Consider the statement: “If angles are vertical, then they have equal measures.” What is the conclusion in the statement?
Angles are vertical.
They have equal measures.
They don’t have equal measures.
Vertical angles have equal measures.
Write the if-then conditional statement given the hypothesis and conclusion below:
p: A number is prime.
q: It has exactly two divisors.
If the number is prime, then it has exactly two divisors.
If it has exactly two divisors, then the number is prime.
If the number is not prime, then it does not have exactly two divisors.
If it does not have exactly two divisors, then the number is not prime.
Find the inverse of the conditional statement, “If angles form a linear pair, then they are supplementary.”
If angles are supplementary, then they form a linear pair.
If angles do not form a linear pair, then they are supplementary.
If angles are not supplementary, then they do not form a linear pair.
If angles do not form a linear pair, then they are not supplementary.
Karl was asked by his Mathematics teacher to write the inverse form of the statement “If you are a second-year student, then you are a sophomore”. His answer is written this way “If you are a sophomore, then you are a second-year student”. What can you conclude about the answer of Karl?
His answer is correct since it is in the inverse form.
His answer is wrong since it is in converse form.
His answer is wrong since it is in contrapositive form.
His answer is correct since it is in conditional (if-then) form.
Jessa says that the converse of the statement “If a number has 1 and itself as factors, then it is prime” is “If a number is prime, then it has 1 and itself as a factor”. Which of the following reasons would support her statement?
To write the converse, negate both hypothesis and conclusion.
To write the converse, interchange the hypothesis and conclusion.
To write the converse, interchange the hypothesis and conclusion of its inverse.
To write the converse, interchange and negate both hypothesis and conclusion
In a Grade 8 class, Mr. Imperial asked students to rewrite the statement “If today is Monday, then tomorrow is Tuesday” into its converse statement. Maria volunteered to write her answer on the board. Her answer is written this way, “If tomorrow is Tuesday, then today is Monday”. Was her answer correct?
Yes, because to write the converse, interchange the hypothesis and conclusion.
No, because the answer should be “If tomorrow is not Tuesday, then today is not Monday.”
No, because the answer should be “If today is not Monday, then tomorrow is not Tuesday”.
No, because the answer should be “If today is not Monday, then tomorrow is Tuesday”.
Jenny asked her friend Jacky to help her write the contrapositive of the statement
“If 3x + 1 = 7, then x = 2.”. To write it correctly, which of the
following should be the answer of Jacky?
If 3x + 1 ≠ 7, then x ≠ 2.
If x ≠ 2, If 3x + 1 ≠ 7.
If x = 2, then 3x + 1 = 7.
If 3x + 1 = 7, then x ≠ 2.
“If a shape is a quadrilateral, then it is a polygon”. What is the truth value of its contrapositive if the hypothesis is true and the conclusion is false?
True
False
Undefined
Necessarily true
Which of the following is the equivalent of converse statement, “If I love you, then I care for you.”?
If I care for you, then I don’t love you.
If I don’t care for you, then I love you.
If I care for you, then I love you.
If I don’t care for you, then I don’t love you.
What decision can you create to an implication of a converse if the hypothesis is true, and conclusion is false?
True
False
Undefined
Necessarily True
Which of the following best describes deductive reasoning?
making a conclusion based on logical reasons.
making a conclusion based on specific examples.
making a conclusion based on accepted statements
making a conclusion based on personal feelings and emotion
What conclusion can be logically deduced based on the following statements? “If a student passes an entrance exam, then the student will be accepted into college. Magdalena passed the entrance exam.”
Magdalena can choose any course.
Magdalena shall take another exam.
Magdalena will be accepted into college.
Magdalena will not be accepted into college.
Using the figure at the right, which postulate best describe the statement
m∠MOP + m∠NOP = m∠MON?
Angle addition
postulate
Line intersection
postulate
Line-point postulate
Two-point postulate
Which theorem justifies the statement,
“If ∠A and ∠B, form a linear pair then
m∠A + m∠B = 180°”?
Linear Pair Theorem
Point-Line-Plane Theorem
Complementary Angle Theorem
Vertical Angles Theorem
Use the given flowchart proof to answer the question .
Given: ∠1 and ∠3 are congruent.
∠1 and ∠2 are supplementary.
Prove: ∠2 and ∠3 are supplementary.
Which reason best describe the statement ∠2 and ∠3 supplementary?
Definition of supplementary angles.
Definition of complementary angles.
Definition of vertical angles.
Definition of congruent angles.
What definition or reason does the proof used to prove that m∠LOE + m∠EOV = 90°?
Definition of congruent angles.
Definition of complementary angles.
Definition of supplementary angles.
Definition of vertical angles.
What is the reason for the statement
2(3𝑚) − 2(5) = 8 in Step 2?
Addition Property of Equality
Subtraction Property of Equality
Distributive Property of Equality
Transitive Property of Equality
Which statement is true using Addition Property of Equality in Step 4?
6𝑚 − 10 − 8 = 8 − 8
6𝑚 − 10 + 8 = 8 + 8
6𝑚 − 10 + 10 = 8 + 10
6𝑚 − 10 − 10 = 8 – 10
Sandra wants to prove the statement “If x is an even integer, and y is an odd integer, then x + y is odd.” She started with the assumption that x + y is even.
What kind of proof did Sandra used?
direct proof
indirect proof
formal proof
two-column-proof
