## GMAT111 - General Mathematics

Solve for the value of x:
1. 7x+4 = 492x-1           x =
1. 4x+2 = 82x           x =
Complete the table of values below (answers should be in decimal form):
Find the maturity value and interest if Php 10,000.00 is deposited in a bank at 2% simple interest for 5 years.
Maturity Value: Php
Interest: Php
Find the unknown in the table below:
Principal (P)    Rate (r)    Time (t) (in years)    Interest (I)
10,000.000.0815

0.02510000
360,000.00
236000
500,000.000.105
173250
880,000.000.09252.5
Match the Definition of the terms to the Concept.
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? ( Note: round off your answer to the hundreds and don't use comma and peso sign)
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.
A certain corporation declared a 10% dividend on a stock with a par value of P1000. Ms. Carcamol owns 500 shares of stock with par value of P1000. How much is the dividend she received? (Note: Don't include comma in your answer)
A car dealer offers a 15% down payment for a purchase of a car. How much is the mortgaged amount of the cash value of the car is Php 1,500,000.00?
Determine what type of loan is needed for the following situations:
(a) 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.
(b) Mr. and Mrs. Craig wants to borrow money from the bank to finance the college education of their son.
Determine whether each of the following statements are propositions or not. If the statement is a proposition, determine its truth value. (If it does not have a truth value, put NA)
Statement      Proposition      Truth Value
1   Mindanao is an island in the Philippines.

2   Find a number which divides your age.

3   Help!

4   3 + 2 = 4

Determine the truth value:
Consider the following scenario:
One Friday night, Roman and Malou are busy studying for their Logic exam. Meanwhile, Hadji just tweeted a picture of himself eating crispy pata and sisig. Jeff is sound asleep in his dorm room.
a. Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating.

b. Either Jeff is sleeping or Hadji is not eating.

c. Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating.

Determine which rule of inference is the basis for each of the argument below:
Antonio Luna is a scientist.
Therefore, either Antonio Lune or Jose Rizal is a scientist.
Select one:
What is the rule of inference that was used in the argument below.
Select one:
Determine which rule of inference is the basis for each of the argument below:
Antonio Luna and Jose Rizal like Nelly Boustead.
Therefore, Antonio Lune likes Nelly Boustead.
Select one:
Write the following argument presented in propositional and standard form.
Given the following propositions:
p: There is limited freshwater supply.
q: We should conserve water.
1. If there is limited freshwater supply, then we should conserve water.

2. There is limited water supply.

3. Therefore, we should conserve water.

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks)
1. f(x) = 4-3x4
2. f(x) = 3-4x
3. f(x) = sqrt{4-3x4}
4. f(x) = 3-4y4
5. f(x) = 10
Which of the following represents an exponential function?
Select one:
Complete the table of values below: (Some of the answers are in fraction form)
x                        -2              -1             0              1                2                3
f(x)=(3)x

Some functions have inverse functions.
Select one:
Which of the is the inverse of f(x) = 5x - 4?
Select one:
Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9, the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32.
1. What is the equivalent conversion of 72°F to Celsius?
°F  (Note: with two decimal digits)
2. What is the equivalent conversion of 100°C to Fahrenheit?
°F  (Note: with two decimal digits)

The horizontal line test is used to determine whether a function is one-to-one when its graph is given.
Select one:
For the function g(x) = 2x, find (Some of the answers are in fraction form)
g(2) =
g(4) =
g(0) =
g(-2) =
g(-4) =

A function whose graph is a slanted line has an inverse function.
Select one:
The absolute value function has an inverse function.
Select one:
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?
If Mr. Adel invest P5000 in a financial institution at 6% per annum compounded annually, calculate his interest at the end of three years. (Note: Round off your answer to the nearest hundredth. Don't use peso sign and comma)

Suppose you would like to save P9000 invested at 8% compounded quarterly for 5 years and 6 months.
(a) How much would the value of her savings at the end of the term?
(b) How much is the interest earned by your savings?
How long will Php 50,000.00 amount to Php 75,000.00 if the simple interest rate is at 15% per annum?
years and
months
A deposit of P495 earn 3% interest compounded annually. How much moneyin the banks after for years? (Note: Round off your answer in two decimal places, don't use comma to separate the numbers)
Find the compound interest on P3000 at 5% for 5 years, compounded annually. (Note: Round off your answer to the nearest hundredth. Don't use peso sign and comma)
Accumulate Php 15,000.00 for 2 years at 15% compounded monthly.
A deposit of P3000 earn 2% interest compounded semi-annually. how much money is in the bank after 4 years? (Note: Round off your answer in two decimal places. Don't use comma to separate the numbers)
Company A offers Php 150,000.00 at the end of three years plus Php 300,000.00 at the end of 5 years. Company B offers Php 25,000.00 at the end of each quarter for the next 5 years. Assume that the money is worth 8% compounded annually.
(a) Which offer has a better market value?

(b) What is the market value of Company A’s offer?
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?
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)
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.
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?
Tell whether the following is a characteristic of stocks or bonds:
(a) A form of equity financing or raising money by allowing investors to be part owners of the company.
(a) A form of debt financing, or raising money by borrowing from investors.
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 if 8%?
Determine the type of loan for the following:
(a) 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.
(b) Mrs. Alon decided to take her family for a vacation. To cover the expenses, she decided to apply for a loan.
For the purchase of a farm worth Php 2,800,000.00, the bank requires 30% down payment, find the mortgaged amount.
The vertical line test is used to determine whether a function is one-to-one when its graph is given.
Select one:
Given the Function: {(1, 2), (2, 5), (3, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range:  1 2 3)
1. Domain:
2. Range:
Which of the is the inverse of f(x) = 4x+12?
Select one:
Are the following functions (or functions determined by the equations) one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks)
1. f(x) = 4-3x2
2. f(x) = 4-3x
3. f(x) = squarerootof(4-3x2
4. f(x) = 1-3x4
5. f(x) = 4
All functions have inverse functions.
Select one:
Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9, the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32.
1. What is the equivalent conversion of 70°F to Celsius?
°C  (Note: with two decimal digits)
2. Are the two functions inverse of each other? (Note: "Yes" or "No")

The absolute value function for the domain of all positive real numbers has an inverse function.
Select one:
Which of the following represents an exponential function?
Select one:
A function whose graph is a parabola has an inverse function.
Select one:
For the function g(x) = 3x, find
g(2) =
g(4) =
g(0) =
g(-2) =
(Tip: fraction)
g(-4) =
(Tip: fraction)
Complete the table of values below (Some of the answers are in fraction form) :
x                        -2              -1             0              1                2                3
f(x)=(1/3)x

What is the y-intercept of f(x)=2x?
Given the equation 5(-2x -10) = 25(x + 1), solve for the value of x that will make the equation true.
Find the value of the following logarithmic expressions
(a) log2 32        =
(b) log9 729      =
(c) log5 5          =
Find the value of x
(a) 24 = x             x =
(b) 43 = x             x =
Solve for the following logarithmic functions:
(a) log3 (2x-1) = 2             x =
(b) logx 16 = 2                  x =
and    (Note: enter the answers in increasing numerical value)
What is the zero of the logarithmic function:   f(x) = log(x-1)?
Zero:
What is the vertical asymptote of the function?
x =
When invested at an annual rate of 7%, this amount earned Php 21,000.00 of simple interest in 3 years. How much money was initially invested? (don't use comma to separate your answers)
How long will Php 40,000.00 amount to Php 51,200.00 if the simple interest rate is at 12% per annum?
yrs and
months
Find the interest of Php 50,000.00 due in 4 years if money is invested at 12% simple interest. (Note: Don't use comma)
A savings account in a bank yields 0.25% simple interest. If you deposited Php 25,000.00 for 4 years, compute for the following:
(a) The future value of the money invested.
(b) The interest paid to you by the bank.
A principal of 25000 is placed in a savings account at 9%  compounded semi-annually. How much is in the account after 6 months?
(a) What is the final amount? (nearest ones)

What is the compound amount of P2000 invested for 2 years and 6 months at 5% compounded quarterly? (Note: round off your answer to the nearest hundredths. Don't use comma and peso sign)
Find the compound amount on P1500 at the end of 35 years and 9 months, if the interest rate is 6% compounded quarterly. (Note: Round off your answer to the nearest hundredths. Don't use comma and peso sign.)
At what interest rate will P2,050 amount P3,875 in 4 years and 6 months, if interest is compounded semi - annually? (Note: Round off your answer to the nearest hundredths. Don't include the percentage symbol)
If you deposit P8,000 into an account paying 7% annual interest compounded quarterly, how long  is the approximate time until there is P12,400 in the account? (Note: Round off your answer to the nearest hundreds) )
A P30,000, 10% bond with quarterly coupons is redeemed at 98% at the end of 15 years. Find the redemption value. (Note: Don't use comma in your answer).
XYZ corporation, with a current market value of P50. gave a dividend of P10 per share for its common stocks. ABC corporation, with a current market value of P100, gave a dividend of P15 per share. Use the stock yields ratio to measure how much dividends shareholders are getting in relation to the amount invested of XYZ company. (Note: Don't include the percent sign in your answer)
XYZ corporation, with a current market value of P52. gave a dividend of P10 per share for its common stocks. ABC corporation, with a current market value of P100, gave a dividend of P15 per share. Use the stock yields ratio to measure how much dividends shareholders are getting in relation to the amount invested of ABC company. (Note: Don't include percent sign in your answer)
Determine what type of loan is needed for the following situations:
(a) 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.
(b) 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.
Determine the truth value:

Suppose that Abbey is in Grade 11.
a. If Abbey is in Grade 11, then she is a senior high school student.

b. If Abbey is in Grade 11, then she is working as a lawyer.

c. If Abbey has a degree in Computer Science, then she believes in true love.

Determine whether each of the following statements are propositions or not. If the statement is a proposition, determine its truth value. (If it does not have a truth value, put NA)
Statement      Proposition      Truth Value
1   f(x) = sqrt(x) / ( x+1 ) is a rational function.
2   What is the domain of the function?
3   I am lying.
4   It is not the case that sqrt(2) is a rational number.
Which of the following statements is NOT equivalent to the statement, “There exists either a computer scientist or a mathematician who knows both discrete math and Java.”
Select one:
Determine whether each of the following arguments is valid or not.
a. 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.

b. If the solution turns blue litmus paper red, then the solution contains acid. The solution turns blur litmus paper red, so the solution contains acid.

c. If you study hard, you refine your communication skills and build up your confidence. If you refine your communication skills build up your confidence, then your job opportunities increase. Hence, if you study hard, your job opportunities increase.

d. Kidnapping is wrong if society disapproves of it. Kidnapping is wrong. So society disapproves of kidnapping.

e. If overeating causes disease, then it is not healthy. Overeating does not cause disease. So overeating is healthy.

The propositional form of "If it is not raining and I have the time, then I will go to a movie." given the propositions A: It is raining; B: I have the time; C: I will go to a movie, is:
Select one:
Find the present value of an annuity of P4,800 payable at the end of each quarter for 10 years, if the interest rate rate is 9% compounded annually. (Note. Round off your answer in two decimal places, without using peso sign and comma to separate the numbers)
Complete the proof of the argument below: p V r (~r) V (~s) s
Complete the proof of the argument below:

Proposition              Reason
1.
Premise
2.     ~(~s)1,
3.     (~r) v (~s)
4.
2, 3, Disjunctive Syllogism
5.
Premise
6p4, 5,