Second Periodical Test in Mathematics Reviewer
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Questions and Answers

What is the maximum cost of a kilo of pechay if Mitchie paid less than P175 for 4 kilograms of pechay and 5 kilograms of beans at P20 per kilogram?

  • P17
  • P19
  • P16
  • P18 (correct)

If Jules's score is 27 points and the difference between scores is not more than 4 points, what could Gerly's score be?

  • between 23 and 31 (correct)
  • 23 to 26 (correct)
  • 31 and above
  • 23 and below

Which inequality correctly represents Ricky's purchase of 4 big notebooks and 5 small notebooks with a minimum payment of P125?

  • 4b + 5s < 125
  • 4b + 5s ≤ 125
  • 4b + 5s ≥ 125 (correct)
  • 4b + 5s > 125

Which expression is NOT an example of a linear inequality in two variables?

<p>$13x - 4y = 21$ (D)</p> Signup and view all the answers

What is the correct mathematical statement representing Angie's total spending of at least P355.50 on calls?

<p>6x + 6.50y ≥ 355.50 (A)</p> Signup and view all the answers

Which of the following mathematical expressions is in standard form?

<p>$2x + 3y &lt; 12$ (B)</p> Signup and view all the answers

If Donna paid less than P500 for 1.4 kg of milkfish at P160 per kg and tilapia, what could be the maximum cost of a kilogram of tilapia?

<p>above P185 (B)</p> Signup and view all the answers

Which of the following statements is NOT a linear inequality in two variables?

<p>$\frac{3}{y} &lt; 10 - 2x$ (A)</p> Signup and view all the answers

Richelyn has P50 and buys 3 pens for P8 each. What is the maximum number of pencils she can buy?

<p>3 (A)</p> Signup and view all the answers

Which verbal phrase does NOT represent a linear inequality in two variables?

<p>the total number of male and female students is 20 (B)</p> Signup and view all the answers

Jonard bought 16 bacons at P12 each. What is the maximum number of P8 eggs he can buy with at most P300 in total?

<p>12 (D)</p> Signup and view all the answers

Which one of the following is a valid linear inequality in two variables?

<p>$11 + 2t \geq 3t - 11$ (D)</p> Signup and view all the answers

Michelle's total amount for two types of facemasks is at most P333. If she bought 4 pieces at P35 each, what could be the maximum price of 6 pieces of the other facemask?

<p>P194 (A)</p> Signup and view all the answers

Which inequality represents 'the sum of x and y is at most 15'?

<p>$x + y \leq 15$ (C)</p> Signup and view all the answers

Which is true regarding the graphical solutions of a linear inequality in two variables?

<p>It is a region of points bounded by a line. (C)</p> Signup and view all the answers

The statement 'the sum of two numbers is at least 29' can be expressed as?

<p>$x + y \geq 29$ (D)</p> Signup and view all the answers

How many points does a vertical line intersect the graph of a function?

<p>At exactly one point (C)</p> Signup and view all the answers

Which given set of ordered pairs is an example of a one-to-one relation?

<p>{(a, p), (b, q), (c, r), (d, s), (e, t), (f, u), (g, w), (h, x)} (D)</p> Signup and view all the answers

Which option does NOT represent a possible way to present relations?

<p>Shape (D)</p> Signup and view all the answers

Which set of ordered pairs shows a one-to-one relation?

<p>{(1, -1), (2, -2), (3, -3)} (D)</p> Signup and view all the answers

What correspondence is best described by the pairs {(Ana, sandwich), (Juan, sandwich), (Peter, sandwich)}?

<p>Many-to-One (C)</p> Signup and view all the answers

What is the value of f(0) for the function f(x) = 7x - 3?

<p>-3 (C)</p> Signup and view all the answers

What is the correct mathematical model for a computer rental charge of P10 plus P15 per hour?

<p>f(x) = 15x + 10 (C)</p> Signup and view all the answers

In the cost to rent an apartment versus time rented, which is the independent variable?

<p>The length of time it is rented (C)</p> Signup and view all the answers

Is John correct in stating the range of the set of ordered pairs {(1,1), (2,4), (3,4), (−2,1), (−4,5)} as {1, 1, 4, 4, 5}?

<p>No, because the elements should be written once and the answer is {1, 4, 5}. (C)</p> Signup and view all the answers

What is the domain of the function given the bicycle rental cost of ₱20/hour for a maximum of 4 hours?

<p>Domain: {0, 1, 2, 3, 4} (A)</p> Signup and view all the answers

What is the range of the function if the bicycle rental costs ₱20/hour for a stay of up to 4 hours?

<p>Range: {20, 40, 60, 80} (C)</p> Signup and view all the answers

Which of the following is the standard form of a linear function?

<p>𝑓(𝑥) = 𝑚𝑥 + 𝑏 (B)</p> Signup and view all the answers

Which statement best describes the x-intercept of a line?

<p>The x-intercept of a line is the intersection of the graph and the x-axis. (A)</p> Signup and view all the answers

Which coordinate represents the y-intercept?

<p>(0, b) (A)</p> Signup and view all the answers

How much would Mr. Nilo receive for 3 hours of tutoring a day over 12 days?

<p>₱7,200 (C)</p> Signup and view all the answers

What is the x-intercept of the function f(x) = x + 3?

<p>(-3, 0) (D)</p> Signup and view all the answers

Which of the following statements is NOT true?

<p>Letters T and F, respectively are assigned for truth values False and True. (B)</p> Signup and view all the answers

What conclusion can be logically deduced from the statement: 'If a student passes an entrance exam, then the student will be accepted into college. Magdalena passed the entrance exam.'?

<p>Magdalena will be accepted into college. (A)</p> Signup and view all the answers

What assumption would you make from the statement that, 'There can be only one 90° angle in a triangle' using indirect proof?

<p>There can be more than one 90° angle in a triangle. (B)</p> Signup and view all the answers

Which statement does NOT accurately describe the slope of a line?

<p>The slope of a line depends on the value of the y-intercept. (D)</p> Signup and view all the answers

If you were proving that a given line 𝑙 is perpendicular to another line 𝑗 using indirect proof, what would your initial assumption be?

<p>Assume that line 𝑙 is not perpendicular to line 𝑗. (A)</p> Signup and view all the answers

Which reasoning involves making a conclusion based on specific examples?

<p>Inductive reasoning (D)</p> Signup and view all the answers

What would be the implication if a student passes an entrance exam according to logical reasoning?

<p>The student might be accepted into college. (C)</p> Signup and view all the answers

Flashcards

Linear Inequalities in Two Variables - Examples

Equations like 9𝑥 + 3𝑦 ≥ 24, 13𝑥 − 24𝑦 < 32, or 2𝑥 - y > 6 represent relationships where both variables are part of an inequality.

Linear Inequalities in Standard Form

Linear inequalities in two variables are written with variables on one side and a constant on the other, like 2𝑥 + 3𝑦 < 12.

Linear Inequalities in Two Variables - Exception

An expression like 3/𝑦 < 10 − 2𝑥 is NOT a linear inequality in two variables. It has 𝑦 in the denominator.

Verbal Phrase – Linear Inequality (Example)

The phrase 'the total number of male and female students in the learning center is 20' is an equation, not an inequality. But phrases like 'is at most', 'is greater than', or 'is less than or equal to' create an inequality.

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Linear Inequality in Two Variables

An expression like 4𝑎 − 3𝑏 > 5 shows a relationship between two variables using inequality symbols (like >, <, ≤, or ≥).

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Inequality for "Sum is at most 15"

The phrase translates to 𝑥 + 𝑦 ≤ 15.

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Graph of Linear Inequality in Two Variables

The solution is a region(not a single line) of points in a graph bounded by a line; it shows all the possible values of x and y that satisfy the inequality.

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Inequality for "Sum is at least 29"

The given phrase translates to 𝑥 + 𝑦 ≥ 29.

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Relation

A set of ordered pairs that shows a connection between two sets of information.

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One-to-One Relation

A relation where each input (first element of the ordered pair) has exactly one unique output (second element) and vice versa.

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Many-to-One Relation

A relation where multiple inputs can have the same output, but each input has only one output.

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Function

A special kind of relation where every input has exactly one output. Every input has a unique output.

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Domain

The set of all possible input values of a function or relation.

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Range

The set of all possible output values of a function or relation.

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Independent Variable

A variable whose value does not rely on any other variable. Its value is set independently.

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Dependent Variable

A variable whose value depends on another variable (usually the independent variable).

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Maximum cost of pechay (pesos)

The highest possible price, in pesos, for one kilogram of pechay, given that less than 175 pesos was spent on 4 kilograms of pechay and 5 kilograms of beans at 20 pesos per kilogram.

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Gerly's Math test score range

The possible scores for Gerly's Math test, given that the difference between Jules's and Gerly's scores is no more than 4 points and Jules scored 27 points.

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Inequality representing notebook costs

The mathematical expression that describes the situation where Ricky paid at least 125 pesos for 4 big notebooks and 5 small notebooks, where 'b' represents the cost of a big notebook and 's' represents the cost of a small notebook.

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Total call cost inequality

The inequality that represents the total amount Angie spent on phone calls from two different networks, given that the cost is at least 355.50 pesos over 5 days. 'x' represents the minutes of calls to the first network, and 'y' represents the minutes of calls to the second network.

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Tilapia cost range

The possible price range, in pesos, for one kilogram of tilapia, given that Donna spent less than 500 pesos on 1.4 kg of milkfish (160 pesos/kg) and 1.5 kg of tilapia.

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Maximum pencils

The greatest number of pencils Richelyn can buy with 50 pesos, if she already bought 3 pens at 8 pesos each and pencils cost 12 pesos each. Round to the nearest whole number.

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Maximum eggs with limited budget

The maximum number of 8-peso eggs Jonard can buy with a 300-peso budget, if he has already bought 16 bacons, and bacons cost 12 pesos each.

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Maximum facemask cost

The maximum price, in pesos (rounded to the nearest peso), for 6 pieces of a second type of facemask, given that 4 pieces of a first type of facemask (35 pesos each) were bought, and the total for both types is at most 333 pesos.

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Range of a Set of Ordered Pairs

The range of a set of ordered pairs is the set of all the second coordinates (y-values).

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Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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Range of a Function

The range of a function is the set of all possible output values (y-values) that the function can produce.

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What is the x-intercept?

The x-intercept of a line is the point where the graph intersects the x-axis. It has a y-coordinate of 0.

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What are the coordinates of the y-intercept?

The y-intercept of a line is the point where the graph intersects the y-axis. It has an x-coordinate of 0.

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Slope of a Line

The slope of a line measures its steepness. It is the ratio of vertical change (rise) to horizontal change (run).

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How does y change when x increases?

In a linear function, if the slope is positive, y increases as x increases. If the slope is negative, y decreases as x increases.

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Finding a Point on a Linear Function

To find the value of a linear function, f(x), at a specific x-value, simply substitute that x-value into the function's equation and solve for f(x).

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Standard Form of a Linear Function

The standard form of a linear function is written as 𝑓(𝑥) = 𝑚𝑥 + 𝑏, where 𝑚 is the slope (representing the rate of change) and 𝑏 is the y-intercept (the point where the line crosses the y-axis).

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Polynomial Function

A polynomial function is an equation where the highest power of the variable is a non-negative integer. It can have multiple terms with different powers of the variable, but all coefficients must be constants.

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Linear Function

A type of polynomial function where the highest power of the variable is 1. This means it represents a straight line.

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Quadratic Function

A polynomial function where the highest power of the variable is 2. Its graph is a parabola (U-shaped).

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Deductive Reasoning

A type of reasoning where you reach a logical conclusion based on accepted premises or known facts. You start with general truths and apply them to specific situations.

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Inductive Reasoning

A type of reasoning where you develop a conclusion based on observations of specific examples or patterns. You use specific instances to form a general principle.

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Indirect Proof (Proof By Contradiction)

A method of proof where you assume the opposite of what you're trying to prove, and then show that the assumption leads to a contradiction. This contradiction proves that the original assumption must be false, and therefore the original statement is true.

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Contrapositive

A statement obtained by switching the hypothesis and conclusion of an if-then statement, and negating both parts. The original statement and its contrapositive are always logically equivalent.

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Study Notes

Second Periodical Test in Mathematics 8

  • Question 1: The following expressions are examples of linear inequalities in two variables EXCEPT 13x – 4y = 21. This is an equation, not an inequality.

  • Question 2: The mathematical expression 2x + 3y < 12 is in standard form.

  • Question 3: The mathematical statements that are NOT linear inequalities in two variables are -10 ≤ 2x and 23 ≤ 3x + 2y. These do not fit the typical structure of ax + by ≤ c or ax + by ≥ c.

  • Question 4: The verbal phrase that does not represent a linear inequality in two variables is "the total number of male and female students in the learning center is 20." A linear inequality needs to express a relationship of 'more than,' 'less than,' or 'equal to.'

  • Question 5: The linear inequality in two variables is 11 + 2t ≥ 3t - 11.

  • Question 6: The inequality representing "the sum of x and y is at most 15" is x + y ≤ 15.

  • Question 7: The graphical solutions of a linear inequality in two variables is a region of points bounded by a line.

  • Question 8: The statement "the sum of two numbers is at least 29" can be expressed as x + y ≥ 29.

  • Question 9: The inequality represented by the given graph is 3x + 2y > 2. (Note: The graph is necessary to determine the exact inequality)

  • Question 10: The correct inequality for the shaded region is y < -x - 1. (Note: The graph is necessary to determine the exact inequality)

  • Question 11: Given the graph of y ≥ 2x - 5, the ordered pair (2, 5) satisfies the inequality. (Note: The graph is necessary to determine the exact answer)

  • Question 12: The maximum cost of a kilo of pechay is PhP 17, given the context. Mitchie paid less than P175 for 4 kg of pechay and 5 kg of beans.

  • Question 13: If Jules's score is 27 points and the difference between Jules' score and Gerly's score is not more than 4 points, then Gerly's score could be between 23 and 31.

  • Question 14: The inequality representing the given situation (Ricky buying notebooks) is 4b + 5s ≥ 125.

  • Question 15: Angie's phone bill situation is represented by 6x + 6.50y ≥ 355.50 (where x and y are the minutes).

  • Question 16: Donna paid less than P500 for 1.4 kg of milkfish and 1.5 kg of tilapia. Given the price of milkfish, the price of tilapia must be below P184.

  • Question 17: Richelyn bought 3 pens, and has P50 in her pocket. She can buy a maximum of two pencils.

  • Question 18: Jonard wants to buy at most P300, buying 16 bacons for P12 each leaves him with a maximum of 11 eggs costing P8 each.

  • Question 19: Michelle bought 4 pieces of one type of facemask for P35 each. The maximum price she could pay for 6 pieces of the other type of facemask is PhP 194 if paying at most P333.

  • Question 20: Every function is a relation.

  • Question 21: The relation {(Mickey, mouse), (Bugs, Bunny), (Cosmo, Wanda)} is a function.

  • Question 22: A vertical line intersects the graph of a function at exactly one point.

  • Question 23: {(1, 1), (2, 2), (3, 3)} is an example of a one-to-one relation (Note: See Example graph.)

  • Question 24: Relations can be presented with graphs, equations or rules but not tables (Note: See example)

  • Question 25: The following ordered pairs shows one-to-one relation: {(1, 2), (3, 4), (5, 6)}.

  • Question 26: The relationship is many-to-one - each object in the first set (Ana, Juan, Peter) is related to the same object in the second set (sandwich).

  • Question 27: f(0) = -3

  • Question 28: The correct mathematical model representing the rental cost situation is f(x) = 15x + 10, where x is the time in hours

  • Question 29: The independent variable is the length of time the apartment is rented.

  • Question 30: The powdered milk is called elements, or more correctly, inputs or outputs.

  • Question 31: The correct answer for this question involves a set of ordered pairs.

  • Question 32: The range is {1, 4, 5}, the second coordinates.

  • Question 33: The domain (the hours) is {0, 1, 2, 3, 4}

  • Question 34: The range (the possible amounts) is {0, 20, 40, 60, 80}.

  • Question 35: The x-intercept is the intersection of the graph and the x-axis.

  • Question 36: The y-intercept is the coordinate when x = 0 (which is (0, b)).

  • Question 37: The x-intercept for f(x) = x + 3 is (-3, 0).

  • Question 38: The y-intercept for f(x) = 2x + 5 is (0, 5).

  • Question 39: The slope of a horizontal line is zero.

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G8 Mathematics Second Periodical Test PDF

Description

Test your understanding of linear inequalities with this second periodical assessment for 8th-grade mathematics. The quiz covers concepts such as standard forms and graphical representations related to linear inequalities in two variables.

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