GenMath Grade 11 Week 1-10 Exam
AMA OED ANSWERFunction Notation and Applications
Question: Admission price to Enchanted Kingdom park is Php 600 per person. The average patron attending EK spends about Php 500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.
Question: Bananas are sold at Php 50.00 per kilo. Write a function notation that describes this situation.
Question: The cost of joining a gym membership includes a one-time sign-up fee of Php 2000 plus Php 1000 for each month of membership. Which of the following function notations matches this situation?
Question: The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?
Question: Which of the following function notation describes the ordered number pair P(x) = {(1,11), (2,22), (3,33), (4,44)}?
Question: Tickets for a movie costs Php 200.00 each. How would you represent the total cost needed to pay for x number of moviegoers?
Question: Tickets for a movie costs Php 200.00 each. How much is needed to pay for a group of five who wants to watch a movie?
Question: Maya has an internet service that currently has a monthly access fee of Php 999.00 pesos and a connection fee of Php 1.00 per hour. Represent her monthly cost as a function of connection time.
Question: Maya has an internet service that currently has a monthly access fee of Php 999.00 pesos and a connection fee of Php 1.00 per hour. How much will she pay if she was able to use the service for 15 days?
Question: Admission price to Universal Studios park is Php 2600 per person. The average patron attending spends about Php 1500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.
Question: Which of the following function notation describes the ordered number pair P(x) = {(1,6), (2,11), (3,16), (4,21)}?
Function Evaluation
Question: If g(x) = (x+2)/3, find g(-8).
Question: If g(x) = -2x^2 - 3, find g(0).
Question: If g(x) = -8x + 1, find g(-2).
Question: If g(x) = 6/(x-3), find g(5).
Question: If g(x) = x - 5, find g(-1).
Question: If g(x) = -4a + 7, find g(2a).
Question: If g(x) = (-7x + 1)/(x^2 + 1), find g(3).
Question: If g(x) = 3x - 5, find g(4).
Question: If g(x) = 3x^2 + 2x - 1, find g(-1).
Question: If g(x) = 4|x - 3| + 2, find g(1).
Question: Given f(x) = x - 2, find f(0).
Question: Given f(x) = x - 2, find f(3).
Question: Given f(x) = x - 2, find f(-1).
Question: Given f(x) = sqrt(x - 3), what is f(28)?
Question: Given f(x) = sqrt(x - 3), what is f(4)?
Question: Given f(x) = sqrt(x - 3), what is f(12)?
Question: For the function g(x) = 2^x, find g(2).
Question: For the function g(x) = 2^x, find g(4).
Question: For the function g(x) = 2^x, find g(0).
Question: For the function g(x) = 2^x, find g(-2).
Question: For the function g(x) = 2^x, find g(-4).
Question: For the function g(x) = 3^x, find g(2).
Question: For the function g(x) = 3^x, find g(4).
Question: For the function g(x) = 3^x, find g(0).
Question: For the function g(x) = 3^x, find g(-2).
Question: For the function g(x) = 3^x, find g(-4).
Function Operations
Question: Let f(x) = 4x - 5 and g(x) = 3x, find (f + g)(x).
Question: Let f(x) = 4x - 5 and g(x) = 3x, find (f - g)(x).
Question: Let f(x) = 4x - 5 and g(x) = 3x, find (f/g)(x).
Question: Let f(x) = 4x - 5 and g(x) = 3x, find (fg)(x).
Question: Let f(x) = 4x - 5 and g(x) = 3x, find (f o g)(x).
Question: Let f(x) = 2x - 3 and g(x) = 4x, find (f o g)(x).
Question: Let f(x) = -10x - 18 and g(x) = -3x, find (f - g)(x).
Question: Given f(x) = x + 4 and g(x) = 2x + 1, match the expression to its simplification operation: 2x^2 + 9x + 12.
Question: Given f(x) = x + 4 and g(x) = 2x + 1, match the expression to its simplification operation: (x + 4)/(2x + 1).
Question: Given f(x) = x + 4 and g(x) = 2x + 1, match the expression to its simplification operation: -x + 3.
Question: Given f(x) = x + 4 and g(x) = 2x + 1, match the expression to its simplification operation: 3x + 5.
Question: Given f(x) = x + 4 and g(x) = 2x + 1, match the expression to its simplification operation: 2x + 5.
Question: Given f(x) = x + 4 and g(x) = 2x + 1, match the expression to its simplification operation: (2x + 1)/(x + 4).
Question: Given f(x) = x + 2 and g(x) = x^2 - 4, match the expression to its simplification operation: x^2 + x - 2.
Question: Given f(x) = x + 2 and g(x) = x^2 - 4, match the expression to its simplification operation: 1/(x - 2).
Question: Given f(x) = x + 2 and g(x) = x^2 - 4, match the expression to its simplification operation: x^2 - 2.
Question: Given f(x) = x + 2 and g(x) = x^2 - 4, match the expression to its simplification operation: x - 2.
Question: Given f(x) = x + 2 and g(x) = x^2 - 4, match the expression to its simplification operation: -x^2 + x + 6.
Question: Given f(x) = x + 2 and g(x) = x^2 - 4, match the expression to its simplification operation: x^3 + 2x^2 - 4x - 8.
Rational Equations and Functions
Question: Find the solution for the rational equation 3/(x + 1) = 2/(x - 3).
Question: Solve x in the rational equation: (x^2 - 4x)/(x - 2) = (14 - 9x)/(x - 2).
Question: Find the solution for the rational equation: (2/(x + 1) + 5/(2x)) = 2.
Question: Consider the rational function p = (5,125,000V^2 - 449,000V + 19307)/(125V^2(1,000V - 43)), does the function have a V-intercept?
Question: Consider the rational function p = (5,125,000V^2 - 449,000V + 19307)/(125V^2(1,000V - 43)), what value of V is/are the vertical asymptote(s) of the function? (decimal up to third decimal figure)
Question: Consider the rational function p = (5,125,000V^2 - 449,000V + 19307)/(125V^2(1,000V - 43)), does the function have a p-intercept?
Question: Consider the rational function p = (5,125,000V^2 - 449,000V + 19307)/(125V^2(1,000V - 43)), what value of p is the horizontal asymptote of the function?
Question: From the table of values, identify which value of x are the zeroes of the function: x = -6, -5, -4, -3, -2, -1, 0, 1, 2; f(x) = 2.4, undefined, -0.75, 0, 0.22, 0.3, 0.3, 0.22, 0.
Question: After taking a certain antibiotic, the concentration (C) of the drug in the patient's bloodstream is given by C(x) = (0.04t)/(t^2 - 2), where t is the time (in hours) after taking the antibiotic. How many hours after the antibiotic will its concentration be 0.04 units?
Question: The average cost per unit C(x), in dollars, to produce x units of toy cars is given by C(x) = (8000)/(x - 50). What is the approximate cost per unit when 1250 toy cars are produced?
Question: The weekly sale S (in thousands of units) for the t^th week after the introduction of the product in the market is given by S = (120t)/(t^2 + 100). In which week would the sale (S) have been 6?
Question: Train A covers 240 miles in the same time train B covers 180 miles. If the average speed of train A is 20 mph more than that of train B, then what is the average speed of train B?
Question: Two race car drivers Ryan and Philip were taking laps around the race track. It was noted that Ryan drove 52.5 miles in the same time that Philip drove 37.5 miles. If Ryan's average speed was 30 mph more than that of Philip, what was Ryan's average speed?
Question: Consider the rational expression f(x) = (5x - 1)/(x + 2), what is its vertical asymptote?
Question: Consider the rational expression f(x) = (5x - 1)/(x + 2), what is its horizontal asymptote?
Question: What is the zero of the logarithmic function: f(x) = log3(x - 1)?
Question: What is the vertical asymptote of the function f(x) = log3(x - 1)?
One-to-One Functions and Inverses
Question: Is f(x) = 4 - 3x^4 a one-to-one function?
Question: Is f(x) = 3 - 4x a one-to-one function?
Question: Is f(x) = (4 - 3x^4)^(1/2) a one-to-one function?
Question: Is f(x) = 3 - 4y^4 a one-to-one function?
Question: Is f(x) = 10 a one-to-one function?
Question: Is f(x) = 4 - 3x^2 a one-to-one function?
Question: Is f(x) = 4 - 3x a one-to-one function?
Question: Is f(x) = sqrt(4 - 3x^2) a one-to-one function?
Question: Is f(x) = 4 - 3y^2 a one-to-one function?
Question: Is f(x) = 4 a one-to-one function?
Question: Is f(x) = 3 - 8x^2 a one-to-one function?
Question: Is f(x) = 5 - 9x a one-to-one function?
Question: Is f(x) = sqrt(2 - 5x^8) a one-to-one function?
Question: Is f(x) = x a one-to-one function?
Question: Which of the following is the inverse of f(x) = 5x - 4?
Question: Which of the following is the inverse of f(x) = 4x + 12?
Question: Which of the following is the inverse of f(x) = ½(3x + 4)?
Question: A function whose graph is a slanted line has an inverse function.
Question: Some functions have inverse functions.
Question: The absolute value function has an inverse function.
Question: The horizontal line test is used to determine whether a function is one-to-one when its graph is given.
Question: All functions have inverse functions.
Question: The vertical line test is used to determine whether a function is one-to-one when its graph is given.
Question: A function whose graph is a parabola has an inverse function.
Question: The absolute value function for the domain of all positive real numbers has an inverse function.
Question: The graph of a function and its inverse are always reflections of each other in the line y = x.
Question: The relation pairing a real number to its square is a one-to-one function.
Question: The relation pairing an SSS member to his/her SSS number is a one-to-one function.
Exponential Functions
Question: Which of the following represents an exponential function?
Question: Which of the following represents an exponential function?
Question: Which of the following does not represent an exponential function?
Question: Complete the table of values for f(x) = (3)^x: x = -2, -1, 0, 1, 2, 3.
Question: Complete the table of values for f(x) = (1/3)^x: x = -2, -1, 0, 1, 2, 3.
Question: Complete the table of values for f(x) = (5)^x: x = -2, -1, 0, 1, 2, 3.
Question: Given the equation 5^(-2x - 10) = 25^(x + 1), solve for the value of x that will make the equation true.
Question: What is the y-intercept of f(x) = 2^x?
Question: Complete the table of values for y = 2^x: x = -3, -2, -1, 0, 1, 2, 3.
Question: Complete the table of values for y = -2^x: x = -3, -2, -1, 0, 1, 2, 3.
Question: Complete the table of values for y = (3)(2^x): x = -3, -2, -1, 0, 1, 2, 3.
Question: How the graph of y = -2^x relates to y = 2^x.
Question: How the graph of y = (3)(2^x) relates to y = 2^x.
Logarithmic Functions
Question: Find the value of log2 32.
Question: Find the value of log9 729.
Question: Find the value of log5 5.
Question: Find the value of x: 2^4 = x.
Question: Find the value of x: 4^3 = x.
Question: Give the exponential form of log1/2 16 = -4.
Question: Give the exponential form of log7 1 = 0.
Question: Give the exponential form of log5 1/sqrt(5) = -1/2.
Question: Solve for the logarithmic expression: log7 (7^3 * 7^8).
Question: Solve for x in log3 (2x - 1) = 2.
Question: Solve for x in logx 16 = 2.
Simple and Compound Interest
Question: Match the definition: Interest.
Question: Match the definition: Principal.
Question: Match the definition: Maturity Value.
Question: Match the definition: Term.
Question: Match the definition: Interest date.
Question: Find the interest for Principal = 10,000.00, Rate = 8%, Time = 15 years.
Question: Find the principal for Rate = 2%, Time = 5 years, Interest = 10,000.00.
Question: Find the rate for Principal = 360,000.00, Time = 2 years, Interest = 3,600.00.
Question: Find the time for Principal = 500,000.00, Rate = 10.5%, Interest = 175,000.00.
Question: Find the interest for Principal = 880,000.00, Rate = 9.25%, Time = 2.5 years.
Question: Find the maturity value if Php 10,000.00 is deposited in a bank at 2% compounded quarterly for 5 years.
Question: Find the interest if Php 10,000.00 is deposited in a bank at 2% compounded quarterly for 5 years.
Question: When invested at an annual rate of 5%, an amount earned Php 15,000.00 of simple interest in 2 years. How much money was initially invested?
Question: How much money should a student place in a time deposit in a bank that pays 1.1% compounded annually so that he will have Php 200,000.00 after 6 years?
Question: How long will Php 40,000.00 amount to Php 51,200.00 if the simple interest rate is at 12% per annum?
Question: A savings account in a bank yields 0.25% compound interest annually. If you deposited Php 25,000.00 for 4 years, what is the future value of the money invested?
Question: A savings account in a bank yields 0.25% compound interest annually. If you deposited Php 25,000.00 for 4 years, what is the interest paid to you by the bank?
Question: When invested at an annual rate of 7%, an amount earned Php 21,000.00 of simple interest in 3 years. How much money was initially invested?
Question: Find the present value of Php 50,000.00 due in 4 years if money is invested at 12% compounded semi-annually.
Domain and Range
Question: Given the Function: {(5, 10), (6, 12), (7, 14)}, give the domain.
Question: Given the Function: {(5, 10), (6, 12), (7, 14)}, give the range.
Question: Given the Function: {(1, 2), (2, 5), (3, 7)}, give the domain.
Question: Given the Function: {(1, 2), (2, 5), (3, 7)}, give the range.
Question: Given the Function: {(10, 9), (11, 8), (12, 7)}, give the domain.
Question: Given the Function: {(10, 9), (11, 8), (12, 7)}, give the range.
Temperature Conversion
Question: What is the equivalent conversion of 72°F to Celsius? (Note: with two decimal digits)
Question: What is the equivalent conversion of 100°C to Fahrenheit? (Note: with two decimal digits)
Question: What is the equivalent conversion of 70°F to Celsius? (Note: with two decimal digits)
Question: Are the Fahrenheit to Celsius and Celsius to Fahrenheit conversion functions inverse of each other?
Question: What is the equivalent conversion of 68°F to Celsius? (Note: with two decimal digits)
Question: What is the equivalent conversion of 0°C to Fahrenheit? (Note: with two decimal digits)
Exponential Equations
Question: Solve for the value of x: 7^(x+4) = 49^(2x-1).
Question: Solve for the value of x: 4^(x+2) = 8^(2x).
Applications of Functions
Question: When diving in the ocean, you must consider how much pressure you will experience from diving a certain depth. From the atmosphere, we experience about 14.7 psi and for every foot we dive down into the ocean, we experience another 0.44 psi in pressure. How far (in feet) can you dive without experiencing more than 58.7 psi of pressure on your body?
Question: One hundred meters of fencing is available to enclose a rectangular area next to a river. Give a function A that can represent the area that can be enclosed in terms of x.
Question: Given the equation 10x + 3 = 3x - 4, solve for the value of x that will make the equation true.
Frequently Asked Questions
What is a function in mathematics?
A function is a relation between a set of inputs (domain) and a set of outputs (range) where each input is associated with exactly one output. It is often represented as f(x), where x is the input and f(x) is the output.
What is the difference between simple and compound interest?
Simple interest is calculated only on the initial principal amount, using the formula I = PRT. Compound interest is calculated on the principal plus accumulated interest, using the formula A = P(1 + r/n)^(nt), where interest grows over time.
What is a one-to-one function?
A one-to-one function (injective function) is a function where each element of the range corresponds to exactly one element of the domain. It passes the horizontal line test, ensuring no horizontal line intersects the graph more than once.
What are the vertical and horizontal asymptotes of a rational function?
Vertical asymptotes occur where the denominator of a rational function is zero (and the numerator is non-zero), indicating where the function is undefined. Horizontal asymptotes describe the behavior of the function as x approaches infinity, determined by comparing the degrees of the numerator and denominator.
What is the relationship between exponential and logarithmic functions?
Exponential and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y), where a is the base. This relationship allows conversion between exponential and logarithmic forms, useful for solving equations.