GenMath Grade 11 Week 11-20 Exam
AMA OED ANSWERSimple and Compound Interest
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: What interest rate per annum is a fund paying its clients if the third to the last payment of a depositor became Php 510.05 from an initial savings payment of Php 500.00?
Question: When invested at an annual rate of 8%, an amount earned Php 24,000.00 of simple interest in 18 months. How much money was initially invested?
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: Find the present value of Php 50,000.00 due in 4 years if money is invested at 12% compounded semi-annually.
Question: What interest rate per annum is a fund paying its clients if the second to the last payment of a depositor became Php 918.00 from an initial savings payment of Php 900.00?
Question: To what factor should you multiply a principal amount if you wish to compute for the interest earned in 6 months of an investment in a fund that pays 24% per annum?
Question: Suppose Mrs. Reyes would like to save Php 1,000.00 at the end of each month for 9 months in a fund that gives 5% per annum compounded monthly. How much would the value of her savings be after 7 months?
Question: How long will Php 50,000.00 amount to Php 75,000.00 if the simple interest rate is at 15% per annum?
Question: Accumulate Php 15,000.00 for 2 years at 15% compounded monthly.
Question: How much do you need to save per month to have a future value of Php 10,146.00 after 12 months of saving in a fund that gives 12% per annum?
Question: How much should Kaye set aside and invest in a fund earning 2% compounded quarterly if she needs Php 75,000.00 in 15 months?
Question: Your teacher saves Php 5,000.00 every 6 months in a bank that pays 0.25% compounded monthly. How much will be her savings after 10 years?
Question: Your sister recently landed her dream job. As part of planning for future expenses, she started to deposit Php 1,000.00 monthly in a fund that pays 6% compounded quarterly. What is the equivalent interest?
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: Suppose Mrs. Reyes would like to save Php 3,000.00 at the end of each month for six months in a fund that gives 9% per annum compounded monthly. How much would the value of her savings be after 6 months?
Question: A loan of Php 200,000.00 is to be repaid in full after 3 years. If the interest rate is 8% per annum, how much should be paid after 3 years?
Question: Mr. Abad got a Php 700,000.00 loan for the expansion of his business payable monthly in 4 years. How much is the monthly amortization if the interest rate is 12% compounded monthly?
Question: A television set is for sale at Php 13,499.00 in cash or on installment terms, Php 2,500.00 each month for the next 6 months at 9% compounded annually. Which option is better?
Stocks and Bonds
Question: A certain company gave out Php 25.00 dividend per share for its common stock. The market value of the stock is Php 92.00. Determine the stock yield ratio. (Note: Answer should be in percent with two decimal places)
Question: A land developer declared a dividend of Php 10,000,000.00 for its common stock. Suppose there are 600,000 shares of common stock, how much is the dividend per share?
Question: A property holdings declared a dividend of Php 9.00 per share for the common stock. If the stock closes at Php 76.00, how large is the stock yield ratio? (Note: Answer should be in percent with two decimal digits)
Question: Find the amount of the semi-annual coupon for a Php 250,000.00 bond which pays 7% convertible semi-annually for its coupons.
Question: A food corporation declared a dividend of Php 25,000,000.00 for its common stock. Suppose there are 180,000 shares of common stock, how much is the dividend per share? (Note: Answer should have two decimal places.)
Question: Determine the amount of a semi-annual coupon paid for a 3% bond with a face value of Php 80,000.00 which matures after 15 years. (Note: Answer should have two decimal places)
Question: A Php 450,000.00 bond is redeemable at Php 550,000.00 after 5 years. Coupons are given at 5% convertible semi-annually. Find the amount of the semi-annual coupon.
Question: A certain financial institution declared Php 57.00 dividend per share for its common stock. The market value of the stock is Php 198.00. Determine the stock yield ratio. (percentage with 2 decimal places)
Question: Tell whether the following is a characteristic of stocks or bonds: A form of equity financing or raising money by allowing investors to be part owners of the company.
Question: Tell whether the following is a characteristic of stocks or bonds: A form of debt financing, or raising money by borrowing from investors.
Mortgages and Loans
Question: If a condominium is purchased for Php 5,700,000.00 and the bank requires 30% down payment, how much is the mortgaged amount?
Question: For the purchase of a farm worth Php 2,800,000.00, the bank requires 30% down payment, find the mortgaged amount.
Question: A business loan of Php 800,000.00 is to be repaid in full after 2 years. What is the amount to be paid if the effective interest rate is 8%?
Question: A family obtained a Php 1,000,000.00 mortgage. If the monthly payment is Php 38,000.00 for four years, how much is the total interest paid?
Question: Mr. Capan obtained a 10-year mortgage for Php 4,200,000.00. If his monthly payment is Php 39,500.00, how much is the total interest?
Question: For the purchase of a house and lot worth Php 3,800,000.00, the bank requires 20% down payment amount. Find the mortgaged amount.
Question: A car dealer offers a 15% down payment for a purchase of a car. How much is the mortgaged amount if the cash value of the car is Php 1,500,000.00?
Question: Determine what type of loan is needed: Mr. Lau wants to have another branch for his cellphone repair shop. He decided to apply for a loan that can be used to pay for the rentals of the new branch.
Question: Determine what type of loan is needed: Mrs. Alon decided to take her family for a vacation. To cover the expenses, she decided to apply for a loan.
Question: Determine what type of loan is needed: Mr. Agustin plans to have a barbershop. He wants to borrow some money from the bank in order for him to buy the equipment and furniture for the barbershop.
Question: Determine what type of loan is needed: Mr. and Mrs. Craig want to borrow money from the bank to finance the college education of their son.
Question: Determine what type of loan is needed: Mr. Alonzo wants to have some improvements in their 10-year old house. He wants to build a new room for their 13-year-old daughter. He will borrow money from the bank to finance this plan.
Question: Determine what type of loan is needed: Mr. Samson owns a siomai food cart business. He wants to put another cart on a new mall in the other city. He decided to have a loan to establish the new business.
Logarithmic Expressions
Question: Find the value of the logarithmic expression: log2 (2^4/2^10) and log2 2 - log2 2^10.
Question: Find the value of the logarithmic expression: log7 7^5 and 5 · log7 7.
Question: Find the value of the logarithmic expression: log7 (7^3 · 7^8) and log7 7^3 + log7 7^8.
Question: Evaluate the logarithmic expression: 3(log9 x)^2 = 6 log9 x.
Question: Evaluate the logarithmic expression: (log3 2)(log3 4) = log3 6.
Question: Find the value of the logarithmic expression: log2 32.
Question: Find the value of the logarithmic expression: log9 729.
Question: Find the value of the logarithmic expression: log5 5.
Question: Find the value of the logarithmic expression: log7 1.
Question: Find the value of the logarithmic expression: log1/2 16.
Question: Find the value of the logarithmic expression: log3 (27 · 81) and log3 27 + log3 81.
Question: Evaluate the logarithmic expression: log3 2x^2 = log3 2 + 2 log3 x.
Question: Evaluate the logarithmic expression: log 2^2 = (log 2)^2.
Question: Evaluate the logarithmic expression: log3 2x^2 = 2 log3 2x.
Question: Find the value of the logarithmic expression: log7 (49/7) and log7 49 - log7 7.
Question: Without using a calculator, find the value of the following logarithmic expression: log5 (1/sqrt(5)).
Exponential Functions
Question: Which of the following represents an exponential function?
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: Complete the table of values for f(x) = (3)^x: x = -2, -1, 0, 1, 2, 3.
Question: Find the value of x: 2^4 = x.
Question: Find the value of x: 4^3 = x.
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: Which of the following is the inverse of f(x) = 5x - 4?
Question: The horizontal line test is used to determine whether a function is one-to-one when its graph is given.
Question: The absolute value function has an inverse function.
Question: The relation pairing an SSS member to his/her SSS number is a one-to-one function.
Question: Some functions have inverse functions.
Question: The relation pairing a real number to its square is a one-to-one function.
Question: Fill in the table that represents the inverse of the function defined by: x = -4, -3, -2, -1, 0, 1, 2, 3, 4; y = -9, -7, -5, -3, -1, 1, 3, 5, 7.
Question: The set A = {(-4, 4), (-3, 2), (-2, 1), (0, -1), (1, -3), (2, -5)} of ordered pairs form a function. Find the inverse of this function.
Rational Equations
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 + 19,307)/(125V^2(1,000V - 43)), does the function have a p-intercept?
Logical Propositions and Truth Values
Question: Determine the truth value: Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating.
Question: Determine the truth value: Either Jeff is sleeping or Hadji is not eating.
Question: Determine the truth value: Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating.
Question: Determine whether the statement is a proposition and its truth value: Mindanao is an island in the Philippines.
Question: Determine whether the statement is a proposition and its truth value: Find a number which divides your age.
Question: Determine whether the statement is a proposition and its truth value: Help!
Question: Determine whether the statement is a proposition and its truth value: 3 + 2 = 4.
Question: Determine whether the statement is a proposition and its truth value: f(x) = sqrt(x)/(x+1) is a rational function.
Question: Determine whether the statement is a proposition and its truth value: What is the domain of the function?
Question: Determine whether the statement is a proposition and its truth value: I am lying.
Question: Determine whether the statement is a proposition and its truth value: It is not the case that sqrt(2) is a rational number.
Question: Determine the truth value: If Abbey is in Grade 11, then she is a senior high school student.
Question: Determine the truth value: If Abbey is in Grade 11, then she is working as a lawyer.
Question: Determine the truth value: If Abbey has a degree in Computer Science, then she believes in true love.
Rules of Inference
Question: Determine which rule of inference is the basis for the argument: Antonio Luna is a scientist. Therefore, either Antonio Luna or Jose Rizal is a scientist.
Question: Determine which rule of inference is the basis for the argument: Antonio Luna and Jose Rizal like Nelly Boustead. Therefore, Antonio Luna likes Nelly Boustead.
Question: What is the rule of inference that was used in the argument: If p then q. p is true. Therefore, q is true.
Question: Determine whether the argument is valid: If the solution turns blue litmus paper red, then the solution contains acid. The solution does not contain acid. So, the solution does not turn blue litmus paper red.
Question: Determine whether the argument is valid: If the solution turns blue litmus paper red, then the solution contains acid. The solution turns blue litmus paper red, so the solution contains acid.
Question: Determine whether the argument is valid: If you study hard, you refine your communication skills and build up your confidence. If you refine your communication skills and build up your confidence, then your job opportunities increase. Hence, if you study hard, your job opportunities increase.
Question: Determine whether the argument is valid: Kidnapping is wrong if society disapproves of it. Kidnapping is wrong. So society disapproves of kidnapping.
Question: Determine whether the argument is valid: If overeating causes disease, then it is not healthy. Overeating does not cause disease. So overeating is healthy.
Question: Complete the proof of the argument: 1. s (Premise), 2. ~(~s) (Double Negation), 3. (~r) v (~s) (Premise), 4. ~r (2, 3, Disjunctive Syllogism), 5. p v r (Premise), 6. p (4, 5, Disjunctive Syllogism).
Question: Complete the proof of the argument: 1. (p OR r) → (~q) (Premise), 2. (~q) → r (Premise), 3. (p OR r) → r (Law of Syllogism), 4. ~r (Premise), 5. ~(p OR r) (3, 4, Modus Tollens).
Annuities and Payments
Question: How many periods of artificial payments would you make if you are to buy a commodity for quarterly payments of Php 8,000.00 for 8 years starting two years from now?
Question: How many months of artificial payments would you make if you are to buy an appliance for Php 2,000.00 for 1 year starting from the 7th month?
Market Value Comparison
Question: Mr. Santos received two offers on a lot that he wants to sell. Ms. Perez offered Php 50,000.00 down payment and a lump sum of Php 1,000,000.00 after 5 years. Mr. Castro offered Php 50,000.00 down payment and Php 40,000.00 every quarter for 5 years. Compare the market values of the two offers if the money can earn 5% compounded annually.
Simple Interest Computations
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.
Frequently Asked Questions
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), leading to exponential growth over time.
What is a stock yield ratio?
The stock yield ratio is the percentage of the dividend per share relative to the market value of the stock, calculated as (Dividend per Share / Market Value per Share) × 100, indicating the return on investment from dividends.
What is a mortgage, and how is the mortgaged amount calculated?
A mortgage is a loan used to purchase property, where the property serves as collateral. The mortgaged amount is calculated by subtracting the down payment from the total purchase price, often expressed as a percentage of the property’s value.
What is a proposition in logic?
A proposition is a declarative statement that is either true or false, but not both. Examples include "2 + 2 = 4" (true) or "The moon is made of cheese" (false). Non-propositions, like questions or commands, do not have a truth value.
What are rules of inference in logic?
Rules of inference are logical principles used to derive valid conclusions from premises. Examples include Modus Ponens (if p then q, p, therefore q), Addition (p, therefore p or q), and Simplification (p and q, therefore p).