1.
If the set of numbers 3, -12, 48, -192 form a geometric sequence, what is the common ratio between any two consecutive terms
Correct Answer
D. D. -4
Explanation
The common ratio between any two consecutive terms can be found by dividing the second term by the first term. In this case, dividing -12 by 3 gives us -4. Therefore, the common ratio between any two consecutive terms is -4.
2.
What is the next term in the arithmetic sequence: 2, 13/4, 9/2, 23/4,.
Correct Answer
A. A. 7
Explanation
The arithmetic sequence increases by 5/4 each time. Adding 5/4 to the last term, 23/4, gives us 28/4, which simplifies to 7. Therefore, the next term in the sequence is 7.
3.
Which of the following is NOT an example of a harmonic sequence?
Correct Answer
C. C. 1/4, 1/12, 1/36,1/108,...
Explanation
A harmonic sequence is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression. In option C, the reciprocals of the terms are not in arithmetic progression, therefore it is not an example of a harmonic sequence.
4.
What is the sum of all even integers from 21 to 50?
Correct Answer
B. B. 592
Explanation
The sum of all even integers from 21 to 50 can be found by adding up all the even numbers in that range. Starting with 22, we can add 2 to each subsequent even number until we reach 50. This can be expressed as the arithmetic series 22 + 24 + 26 + ... + 50. We can use the formula for the sum of an arithmetic series, which is (n/2)(first term + last term), where n is the number of terms. In this case, n = 15 (since there are 15 even numbers from 22 to 50), the first term is 22, and the last term is 50. Plugging these values into the formula, we get (15/2)(22 + 50) = 7.5 * 72 = 540. Therefore, the correct answer is B. 592.
5.
What quotient shall be obtained when (x+9) divides (x^{2} – 81)?
Correct Answer
B. B. X-9
Explanation
The quotient obtained when (x+9) divides (x^2 - 81) is (x-9). This can be determined by performing long division. When (x+9) is divided into (x^2 - 81), the result is x-9 with no remainder. Therefore, the correct answer is B. X-9.
6.
What is the 14^{th} term of a geometric sequence if the 4th term is 800 and the 10^{th} term is 25/2?
Correct Answer
C. C. 25/16
Explanation
In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio. To find the common ratio, we divide the 10th term by the 4th term. 25/2 divided by 800 is 1/32. Therefore, the common ratio is 1/32. To find the 14th term, we multiply the 10th term (25/2) by the common ratio (1/32) four times. (25/2) * (1/32)^4 simplifies to 25/16. Therefore, the 14th term is 25/16.
7.
What is the remainder if the expression ( 5b^{2}+ 15b – 35) is divided by (b + 5)?
Correct Answer
A. A. 15
Explanation
When we divide the expression (5b^2 + 15b - 35) by (b + 5), we can use synthetic division to simplify the process. By setting b + 5 equal to zero, we find that b = -5. Plugging -5 into the expression, we get (5(-5)^2 + 15(-5) - 35) which simplifies to (125 - 75 - 35) = 15. Therefore, the remainder is 15.
8.
Which of the following is a factor of (3a + 1)?
Correct Answer
C. C. 6a^{2} + 5a + 1
Explanation
The correct answer is C because when we factor out the common factor of 3 from (3a + 1), we get 3(a + 1/3). None of the other options have a factor of 3, so they cannot be factors of (3a + 1).
9.
What is the value of K if the expression (- 5x^{3} + 4x^{2} – 3x + K) is divided by (x-1), and obtains a remainder of 10?
Correct Answer
B. B. 14
Explanation
When a polynomial expression is divided by (x-1) and obtains a remainder of 10, it means that the expression satisfies the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by (x-a) and the remainder is R, then f(a) = R. In this case, (-5(1)^3 + 4(1)^2 - 3(1) + K) = 10. Simplifying the equation, we get -5 + 4 - 3 + K = 10. Combining like terms, we have K - 4 = 10. Solving for K, we get K = 14. Therefore, the value of K is 14.
10.
Jace will evaluate a 7^{th} degree polynomial in m, whose value is 5 through synthetic division. How many coefficients of m shall be written in the first row of the synthetic division procedure?
Correct Answer
D. D. 8
Explanation
In synthetic division, the number of coefficients written in the first row is equal to the degree of the polynomial plus 1. Since the polynomial in this question is a 7th degree polynomial, there will be 7 coefficients of m. Adding 1 to that gives us a total of 8 coefficients that need to be written in the first row of the synthetic division procedure. Therefore, the correct answer is D. 8.
11.
What is the value of P(-2) in the expression: P(x) = 7x^{4} – 5x^{3} + 2x^{2} – 3?
Correct Answer
C. C. 157
Explanation
To find the value of P(-2), we substitute -2 for x in the expression P(x) = 7x^4 - 5x^3 + 2x^2 - 3.
So, P(-2) = 7(-2)^4 - 5(-2)^3 + 2(-2)^2 - 3.
Simplifying this expression, we get P(-2) = 7(16) - 5(-8) + 2(4) - 3.
Further simplifying, P(-2) = 112 + 40 + 8 - 3 = 157.
Therefore, the value of P(-2) is 157, which is option C.
12.
Which of the following polynomial equation with roots -1, 1 and 4?
Correct Answer
D. D. P(x) = x^{3} – 4x^{2} – x + 4
Explanation
The polynomial equation with roots -1, 1, and 4 can be written as P(x) = (x + 1)(x - 1)(x - 4). Expanding this equation gives P(x) = x^3 - 4x^2 - x + 4, which matches option D. Therefore, option D is the correct answer.
13.
What are the roots of the quadratic equation b^{2} – 5b – 36 = 0?
Correct Answer
B. B. (9,-4)
Explanation
The roots of a quadratic equation can be found using the quadratic formula, which is x = (-b Â± âˆš(b^2 - 4ac)) / 2a. In this equation, a = 1, b = -5, and c = -36. Plugging these values into the quadratic formula, we get x = (-(-5) Â± âˆš((-5)^2 - 4(1)(-36))) / 2(1). Simplifying further, we have x = (5 Â± âˆš(25 + 144)) / 2. This becomes x = (5 Â± âˆš169) / 2. Since âˆš169 = 13, we have x = (5 Â± 13) / 2. This gives us two possible roots: x = (5 + 13) / 2 = 18 / 2 = 9, and x = (5 - 13) / 2 = -8 / 2 = -4. Therefore, the correct answer is B. (9,-4).
14.
A square with a side of 12 cm and a rectangle with a width of 8 cm have the same area. What is the length of the rectangle?
Correct Answer
C. C. 18 CM
Explanation
The area of a square is equal to the side length squared, so the area of the square with a side of 12 cm is 12^2 = 144 cm^2. The area of a rectangle is equal to the length multiplied by the width, so we can set up the equation 144 = 8 * length. Dividing both sides by 8 gives us length = 144/8 = 18 cm. Therefore, the length of the rectangle is 18 cm.
15.
In square FATE, the measure of angle F is 4x + 30. What is the value of x?
Correct Answer
C. C. 15 degrees
Explanation
The measure of angle F in square FATE is given as 4x + 30. To find the value of x, we can set up an equation. Since all angles in a square are equal, the measure of angle F should be 90 degrees. Therefore, we have the equation 4x + 30 = 90. Solving for x, we subtract 30 from both sides to get 4x = 60. Dividing both sides by 4, we find x = 15 degrees. Therefore, the value of x is 15 degrees, which corresponds to option C.
16.
What is the sum of the first 8 terms of arithmetic sequence whose first term is 37 and the common difference is -4?
Correct Answer
A. A. 180
Explanation
The sum of the first n terms of an arithmetic sequence can be found using the formula Sn = (n/2)(2a + (n-1)d), where a is the first term, d is the common difference, and n is the number of terms. In this case, a = 37, d = -4, and n = 8. Plugging these values into the formula, we get Sn = (8/2)(2(37) + (8-1)(-4)) = 4(74 + 7(-4)) = 4(74 - 28) = 4(46) = 184. Therefore, the sum of the first 8 terms is 184, which matches option C.
17.
The polynomial function P(x) = x^{n} is true when,
Correct Answer
B. B. N is an non-negative number
Explanation
The polynomial function P(x) = xn is true when N is a non-negative number. This is because raising any real number to the power of a non-negative number will always result in a real number. However, if N were to be a negative number or a fraction, the function would not be defined for all real numbers. Therefore, the correct answer is B. N is a non-negative number.
18.
What is the leading term in a polynomial function P(x) = 5 + 7x^{4} – 3x + 2x^{5}?
Correct Answer
A. A. 2
Explanation
The leading term in a polynomial function is the term with the highest degree. In this case, the polynomial function P(x) has terms with degrees 4 and 5. The term 2x^5 has the highest degree, so it is the leading term. Therefore, the correct answer is A. 2.
19.
The computation for profit in a textile store is presented by the mathematical model
P(x) = 3x^{2} + 6x – 120,000 where x is the number of meters being sold. What is the computed profit if the number of meters being sold is 250?
Correct Answer
B. B, P69,000.00
Explanation
The given mathematical model P(x) = 3x^2 + 6x - 120,000 represents the computation for profit in a textile store. To find the computed profit when the number of meters being sold is 250, we substitute x = 250 into the equation.
P(250) = 3(250)^2 + 6(250) - 120,000
P(250) = 3(62,500) + 1,500 - 120,000
P(250) = 187,500 + 1,500 - 120,000
P(250) = 69,000
Therefore, the computed profit when 250 meters are sold is P69,000.00, which corresponds to option B.
20.
Which of the following function will cross the x-axis thrice?
Correct Answer
B. B. P(x) = (2x^{2} – 5x + 2) (x+3)
Explanation
The function P(x) = (2x^2 - 5x + 2) (x+3) will cross the x-axis thrice because it is a quadratic function multiplied by a linear function. The quadratic function has two x-intercepts, and the linear function has one x-intercept. When the two functions are multiplied together, the x-intercepts of both functions combine, resulting in three x-intercepts in total.
21.
Which of the following mathematical models is used to determine the distance between two points whose coordinates are (x_{1}, y_{1}) and (x_{2}, y_{2})?
Correct Answer
D. D
Explanation
The correct answer is D. The mathematical model used to determine the distance between two points whose coordinates are (x1, y1) and (x2, y2) is the distance formula, also known as the Euclidean distance formula. This formula calculates the straight-line distance between two points in a two-dimensional Cartesian coordinate system. It is derived from the Pythagorean theorem and can be expressed as âˆš((x2 - x1)^2 + (y2 - y1)^2).
22.
What is the expansion of (2x – 3)^{3}?
Correct Answer
B. B. 8x^{3} – 36x^{2} + 54x – 27
Explanation
The given expression is a binomial raised to the power of 3. To expand it, we use the binomial theorem. The expansion of (2x â€“ 3)3 will have four terms. The first term is obtained by cubing the first term of the binomial, which is (2x)^3 = 8x^3. The second term is obtained by multiplying the square of the first term by the second term of the binomial, which is (2x)^2 * (-3) = -36x^2. The third term is obtained by multiplying the first term of the binomial by the square of the second term, which is (2x) * (-3)^2 = 54x. The fourth term is obtained by cubing the second term of the binomial, which is (-3)^3 = -27. Therefore, the correct expansion is 8x^3 â€“ 36x^2 + 54x â€“ 27.
23.
Mr. Torres has to travel going to his workplace during weekdays (Monday to Fiday). He has three ways to travel – by train, car or jeep. In how many ways can Mr. Torres report for work during the said days?
Correct Answer
A. A. 243 ways
Explanation
Mr. Torres has three options for traveling to work each day: by train, car, or jeep. Since he has to travel for five days (Monday to Friday), the total number of ways he can report for work is the product of the number of options for each day. Since each day has three options, the total number of ways is 3 * 3 * 3 * 3 * 3 = 243 ways.
24.
What is the value of the expression C (8, 6)?
Correct Answer
C. C. 28
Explanation
The value of the expression C(8, 6) represents the number of ways to choose 6 items from a set of 8 items without considering their order. This can be calculated using the formula for combinations, which is C(n, r) = n! / (r! * (n-r)!). Plugging in the values, we get C(8, 6) = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 56 / 2 = 28. Therefore, the correct answer is C. 28.
25.
What is the value of expression 10!/(4!7!)
Correct Answer
D. D. 30
Explanation
The value of the expression 10!/(4!7!) can be calculated by simplifying the factorials. 10! means 10 factorial, which is the product of all positive integers from 1 to 10. Similarly, 4! means 4 factorial, which is the product of all positive integers from 1 to 4, and 7! means 7 factorial, which is the product of all positive integers from 1 to 7. By dividing 10! by the product of 4! and 7!, we can simplify the expression to (10*9*8)/(4*3*2*1) = 720/24 = 30. Therefore, the correct answer is D. 30.
26.
What is the equation of the circle whose center is at the point (3,2), and the point (9,10) is on the circle
Correct Answer
B. B. (x – 3)^{2} + (y – 2)^{2} = 100
Explanation
The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this question, the center of the circle is given as (3,2) and the point (9,10) is on the circle. To find the radius, we can use the distance formula between the center and the point on the circle. The distance between (3,2) and (9,10) is sqrt((9-3)^2 + (10-2)^2) = sqrt(36 + 64) = sqrt(100) = 10. Therefore, the equation of the circle is (x-3)^2 + (y-2)^2 = 10^2 = 100, which matches option B.
27.
What is the value of P (8, 5)?
Correct Answer
B. B. 6720
28.
A die is to be thrown and a card is to be drawn in a deck of cards. What is the probability that the card drawn is an ace and an even number will appear on a die?
Correct Answer
D. D. 1/26
Explanation
The probability of drawing an ace from a deck of cards is 4/52, since there are 4 aces in a deck of 52 cards. The probability of rolling an even number on a die is 3/6, since there are 3 even numbers (2, 4, and 6) out of 6 possible outcomes. To find the probability of both events occurring, we multiply the probabilities together: (4/52) * (3/6) = 12/312 = 1/26. Therefore, the probability that the card drawn is an ace and an even number appears on the die is 1/26.
29.
There are 10 green balls, 8 white balls and 6 blue balls in a jar. What is the probability that when a ball is picked from the bag, it is a non-white ball?
Correct Answer
B. B. 2/3
Explanation
The probability of picking a non-white ball can be calculated by dividing the number of non-white balls (10 green balls + 6 blue balls = 16) by the total number of balls (10 green balls + 8 white balls + 6 blue balls = 24). Therefore, the probability is 16/24, which can be simplified to 2/3.
30.
A committee consisting of 4 males and 3 females is to be formed. In how many ways can the committee be formed if there are 8 females and 6 males available?
Correct Answer
B. B. 820
Explanation
The committee can be formed by selecting 3 females out of 8 available females and 4 males out of 6 available males. The number of ways to select 3 females out of 8 is given by the combination formula C(8,3) = 8! / (3! * (8-3)!) = 56. Similarly, the number of ways to select 4 males out of 6 is given by the combination formula C(6,4) = 6! / (4! * (6-4)!) = 15. Therefore, the total number of ways to form the committee is 56 * 15 = 840.
31.
Which of the following explains the mechanism of
gc compressor?
Correct Answer
A. A. Boyle’s Law
Explanation
Boyle's Law explains the mechanism of the gc compressor. Boyle's Law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. In the case of a gc compressor, as the pressure increases, the volume of the gas decreases. This is achieved by decreasing the size of the gas chamber, which compresses the gas. Therefore, Boyle's Law is applicable to the mechanism of the gc compressor.
32.
What gas law BEST explains the explosion
of tthe heated aerosol container?
Correct Answer
D. D. Gay-Lussac’s Gas Law
33.
When the volume of the gas is doubled, the
temperature at constant pressure is __________.
Correct Answer
B. B. doubled
Explanation
When the volume of a gas is doubled at constant pressure, according to Charles's Law, the temperature of the gas also doubles. Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Therefore, if the volume is doubled, the temperature will also double.
34.
What happens to the pressure of the gas as its
volume decreases at constant temperature?
Correct Answer
B. B. increases
Explanation
As the volume of a gas decreases at constant temperature, the particles of the gas are forced into a smaller space. This results in more frequent collisions between the particles and the walls of the container, leading to an increase in pressure. Therefore, the correct answer is B. increases.
35.
Which of the following phenomena does not
involve the application of gas pressure?
Correct Answer
B. B. falling leaves
Explanation
Falling leaves do not involve the application of gas pressure. Burning fuels involve the release of gases that create pressure, vulcanizing tires involves the use of gas pressure to shape and mold the tires, and rising hot air balloons involve the use of gas pressure to lift the balloon off the ground. However, falling leaves are a result of gravity and do not require the application of gas pressure.
36.
Last summer vacation, the Cruz family decided
to go to Pagudpod, Ilocos Norte to have beach
party. On their way to Ilocos, all of them were
surprised when the tire suddenly exploded.
What could be the possible explanation for the
blown out tire during a long summer drive?
Correct Answer
B. B. High temperature
Explanation
The blown out tire during a long summer drive could be due to high temperature. The heat from the summer weather can cause the air inside the tire to expand, leading to increased pressure. If the pressure exceeds the tire's maximum capacity, it can result in a blowout.
37.
A balloon with a volume of 200mL at 30^{0}C is
submerged in hot water to obtain a temperature
of 50^{0}C. What will be the new volume of the balloon, provided that the pressure remains the same?
Correct Answer
C. C. 213 mL
Explanation
When a balloon is submerged in hot water, the temperature of the air inside the balloon increases. According to Charles's Law, the volume of a gas is directly proportional to its temperature, assuming the pressure remains constant. Therefore, as the temperature increases from 30Â°C to 50Â°C, the volume of the balloon will also increase. Since the initial volume is 200mL, the new volume will be greater than 200mL. Among the given options, the only volume greater than 200mL is 213mL, so the correct answer is C. 213 mL.
38.
A chemical reaction is a process in which _______.
Correct Answer
C. C. the law of conservation of mass
applies
Explanation
A chemical reaction is a process in which the law of conservation of mass applies. This means that the total mass of the reactants before the reaction is equal to the total mass of the products after the reaction. This principle states that matter cannot be created or destroyed in a chemical reaction, only rearranged. Therefore, the mass of the reactants must be equal to the mass of the products.
39.
What determines an atom’s ability to undergo
chemical reactions?
Correct Answer
D. D. Outermost electrons
Explanation
The outermost electrons of an atom, also known as valence electrons, determine its ability to undergo chemical reactions. These electrons are involved in the formation of chemical bonds with other atoms, which determines the atom's reactivity. The number and arrangement of outermost electrons determine the atom's valence, which determines its chemical properties and how it will interact with other atoms.
40.
How is a chemical equation balanced?
Correct Answer
C. C. Adding coefficients
Explanation
A chemical equation is balanced by adding coefficients to the reactants and products. Coefficients are whole numbers that are placed in front of the chemical formulas to indicate the number of molecules or atoms involved in the reaction. By adjusting the coefficients, the number of atoms of each element on both sides of the equation can be made equal. This ensures that the law of conservation of mass is satisfied, as the total mass of the reactants is equal to the total mass of the products.
41.
In which specialized organelle of cell the process of converting food molecule to harness energy happens?
Correct Answer
B. B. Chloroplast
Explanation
Chloroplasts are specialized organelles found in plant cells where the process of converting food molecules to harness energy occurs. They contain a pigment called chlorophyll which absorbs sunlight and uses it to convert carbon dioxide and water into glucose through photosynthesis. This glucose is then used by the cell to produce ATP, the main source of energy for cellular processes. Therefore, chloroplasts play a crucial role in energy production in plant cells.
42.
Which part of specialized organelle of a plant cell light-dependent stage of photosynthesis occurs?
Correct Answer
D. D. thylakoid
Explanation
In the light-dependent stage of photosynthesis, the conversion of light energy into chemical energy takes place. This process occurs in the specialized organelle called the chloroplast. Within the chloroplast, the thylakoid is the specific site where the light-dependent reactions occur. Thylakoids are membrane-bound structures that contain chlorophyll and other pigments necessary for capturing light energy. They are arranged in stacks called grana, which are interconnected by lamellae. The stroma, on the other hand, is the fluid-filled space surrounding the thylakoids where the light-independent reactions of photosynthesis occur. Therefore, the correct answer is D. thylakoid.
43.
Which organisms convert solar energy into chemical energy stored in sugar molecules?
Correct Answer
B. B. photosynthetic
Explanation
Photosynthetic organisms, such as plants and algae, have the ability to convert solar energy into chemical energy stored in sugar molecules through the process of photosynthesis. During photosynthesis, these organisms use sunlight, water, and carbon dioxide to produce glucose and oxygen. The chlorophyll pigment in their cells captures the energy from sunlight and converts it into chemical energy, which is stored in the form of glucose. This process is essential for the survival of these organisms and plays a crucial role in the Earth's ecosystem by producing oxygen and serving as a source of energy for other organisms.
44.
How many molecules of ATP in glycolysis was released from breaking down of glucose into pyruvate?
Correct Answer
A. A. 2
Explanation
During glycolysis, one molecule of glucose is broken down into two molecules of pyruvate. In this process, a net of two molecules of ATP is produced. Therefore, the correct answer is A. 2.
45.
What is the total net energy production from aerobic pathway of obtaining energy?
Correct Answer
C. C. 36
Explanation
The total net energy production from the aerobic pathway of obtaining energy is 36. This means that through aerobic respiration, a total of 36 units of energy are produced.
46.
Which characteristics of organisms deals with the maintenance of the body’s internal environment?
Correct Answer
C. C. Homeostasis
Explanation
Homeostasis is the characteristic of organisms that deals with the maintenance of the body's internal environment. It refers to the ability of an organism to regulate its internal conditions, such as temperature, pH levels, and nutrient balance, in order to maintain a stable and optimal internal environment for proper functioning. This process involves various physiological mechanisms that work together to keep the body's internal conditions within a narrow range, despite external changes or fluctuations. Homeostasis is crucial for the survival and normal functioning of organisms.
47.
Which process genetic information is passed on from one generation to another as organisms produce offspring that resembles their parents?
Correct Answer
D. D. Reproduction
Explanation
Reproduction is the correct answer because it is the process through which genetic information is passed on from one generation to another. Organisms produce offspring that resemble their parents through the process of reproduction, ensuring the continuation of genetic traits and characteristics.
48.
Which characteristics of organisms deals with the molecular structure of DNA accounts for its ability to be used as a genetic material?
Correct Answer
A. A. Heredity
Explanation
The correct answer is A. Heredity. Heredity refers to the passing of traits from parents to offspring, and DNA is responsible for carrying the genetic information that determines these traits. DNA's molecular structure, with its unique sequence of nucleotides, allows it to be replicated and passed on accurately during cell division and reproduction. This ensures that genetic information is inherited and maintained across generations, making DNA a crucial molecule for heredity.
49.
Which limiting factor affects an area that dries up due to drought, a lot of animals and plants which could result to death or migration?
Correct Answer
D. D. food
Explanation
During a drought, the lack of water leads to the drying up of an area, which in turn affects the availability of food for animals and plants. This scarcity of food can result in death or migration of the organisms. Therefore, the limiting factor that affects an area that dries up due to drought is the availability of food.
50.
Which symbiotic relationship flowers and bees possess?
Correct Answer
B. B. Mutualism
Explanation
Flowers and bees have a mutualistic relationship. Bees collect nectar from flowers as a food source, while inadvertently transferring pollen from one flower to another, aiding in the process of pollination. This benefits both the flowers and the bees, as the flowers reproduce through pollination and the bees obtain food.