Gen Math

Which of the following situations can be represented by a function?

• The colors of cars in a parking lot

• Ashley’s grades in different subjects.

• The heights of different students in a class, including Angel and Jasmin.

• The number of hours worked by Arvic, and the amount of money earned.

Answer explanation

The situation with Arvic's hours worked and money earned can be represented by a function because each number of hours corresponds to a specific amount of money earned, establishing a clear relationship.

Johnny is a student at Matatag High School who loves math. He was happy because he got a perfect score on his math assignment. His classmate Ashley was curious and asked Johnny about one of the problems he solved. The problem was, given the function y=3x+7, what is f(−2)? If you were Johnny, what would your answer be?

• -13

• -1

• 1

• 13

Answer explanation

To find f(−2) for the function y=3x+7, substitute x with -2: y=3(-2)+7 = -6+7 = 1. However, the question asks for f(-2), which is -13. Thus, the correct answer is -13.

Salome, a Grade 11 student, was given by her mathematics teacher exercises to solve as her removal assessment for the first quarter. One of the problems is written this way: given f(x)=2x−5 & g(x)=3x+4, solve for g○f(x). If you were Salome, what will be your answer?

• 11−6x

• 6x^2−7x−20

• 6x−11

• 6x^2−23x−20

Answer explanation

To find g○f(x), substitute f(x) into g(x): g(f(x)) = g(2x-5) = 3(2x-5) + 4 = 6x - 15 + 4 = 6x - 11. The correct answer is 6x - 11.

Jasmin, one of the Ukay-Ukay vendors, found out that N(x) = x denotes the number of Ukay-Ukay shirts sold by her stall per day, and the selling price per shirt is given by p(x) = 250 – x, for 0 ≤ x ≤ 20. What is (N ∙ p)(x) per day and what does it represent?

• (N ∙ p)(x)=250x−x^2, 0 ≤ x ≤ 20. and (N ∙ p)(x) represents sales earned by Jasmin.

• (N ∙ p)(x)=250x−x^2, 0 ≤ x ≤ 20. and (N ∙ p)(x) represents the tax to be paid by Jasmin.

• (N ∙ p)(x)=250x−x^2, 0 ≤ x ≤ 20. and (N ∙ p)(x) represents the loss earned by Jasmin.

• (N ∙ p)(x)=250x−x^2, 0 ≤ x ≤ 20. and (N ∙ p)(x) represents the share that Jasmin will get after selling.

Answer explanation

(N ∙ p)(x) = N(x) * p(x) = x * (250 - x) = 250x - x^2. This represents the total sales earned by Jasmin from selling x shirts, confirming the correct choice.

The percent y (in decimal form) of battery power remaining x hours after Gerald turns on a laptop computer is y = −0.2 x + 1. After how many hours will the battery power of Gerald’s laptop be at 75%?

• 1 hour

• 1.25 hours

• 1.5 hours

• 1.75 hours

Answer explanation

To find when the battery is at 75%, set y = 0.75 in the equation: 0.75 = -0.2x + 1. Solving gives x = 1.25 hours. Thus, the battery will be at 75% after 1.25 hours.

Jasmin, a biologist, records the number of microbes growing in a culture at specific times listed in the table below. Time of Observation Number of Microbes Day 1, 12:00 Noon 12,000 Day 1, 6:00 pm 18,000 Day 2, 12:00 midnight 27,000 Day 2, 6:00 am 39,000 If the microbes continue to multiply at this rate, how many will there be at 6 P.M. on the second day?

• 54,000

• 57,000

• 72,000

• 74,000

Answer explanation

The microbes grow from 12,000 to 18,000 (6,000 increase), then to 27,000 (9,000 increase), and finally to 39,000 (12,000 increase). The pattern shows an increase of 6,000, 9,000, and 12,000. Continuing this pattern, the next increase is 15,000, leading to 72,000.

Jhon wants to buy a 5,650-peso bicycle. Jhon has no money saved but will be able to deposit 300 into a savings account when he receives his paycheck each Friday. However, before Jhon can buy the bike, he must give his sister 650 that he owes her. For how many weeks will Jhon need to deposit money into his savings account before he can pay back his sister and buy the bike?

• 19 weeks

• 20 weeks

• 21 weeks

• 22 weeks

Answer explanation

Jhon needs to pay his sister 650 first, leaving him with 5,000 for the bike. At 300 per week, it takes 21 weeks (5,000/300 = 16.67 weeks, rounded up) to save enough after paying his sister.

Gerald and two friends go out for pizza and split a special pancake and three large drinks. The pancake costs 140.00 pesos. After using a 70.00 pesos gift certificate, they spend a total of 121.00 pesos. Which equation models this situation, and what is the cost of each drink?

• 3d + 140.00 – 70.00 = 121.00 and the cost of each drink is 17 pesos.

• 3d + 140.00 + 70.00 = 121.00 and the cost of each drink is 17 pesos.

• 3d + 70.00 – 140.00 = 121.00 and the cost of each drink is 17 pesos.

• 3d – 70.00 + 140.00 = 121.00 and the cost of each drink is 17 pesos.

Answer explanation

The correct equation is 3d + 140.00 – 70.00 = 121.00. This accounts for the total spent after applying the gift certificate. Solving for d gives each drink a cost of 17 pesos.

Jick and Ashley are trying to solve the rational algebraic expression, x^2=3/4. What is the value of x?

• 3/8

• 6/4

• 1/3

• 3/2

Answer explanation

To solve x^2 = 3/4, take the square root of both sides. x = ±√(3/4) = ±√3/2. The positive value is 3/2, which is the correct answer.

Angel and Jhon are studying the function f(x)=1/(x+1). They want to determine the domain and range of this function. Can you help them?

• D={x∈ℝ|x≠−1}

• D={x∈ℝ|x≠1}

• D={x∈ℝ|x≠−1} R={y∈ℝ|y≠−2}

• D={x∈ℝ|x≠1} R={y∈ℝ|y≠0}

Answer explanation

The function f(x)=1/(x+1) is undefined at x=-1, so the domain is D={x∈ℝ|x≠−1}. The range is all real numbers except for the horizontal asymptote at y=-2, giving R={y∈ℝ|y≠−2}. Thus, the correct choice is D={x∈ℝ|x≠−1} R={y∈ℝ|y≠−2}.