## General Math Grade 11 Week 11-20

Learning Activity 4

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?

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 yrs?

Long Quiz 3

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?

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?

How long will Php 40,000.00 amount to Php 51,200.00 if the simple interest rate is at 12% per annum?

Find the present value of Php 50,000.00 due in 4 years if money is invested at 12% compounded semi-annually.

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?

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?

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? (Hint: make sure the units of the interest rate and the term are the same)

How long will Php 50,000.00 amount to Php 75,000.00 if the simple interest rate is at 15% per annum?

Accumulate Php 15,000.00 for 2 years at 15% compounded monthly.

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?

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?

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?

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?

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?

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?

## Learning Activity 6

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)

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?

## Short Quiz 12

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)

Find the amount of the semi-annual coupon for a Php 250,000.00 bond which pays 7% convertible semi-annually for its coupons.

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.)

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)

## Learning Activity 5

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. How much will her funds worth be after 15 years?

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?

## Short Quiz 11

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?

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? (Hint: make sure the units of the interest rate and the term are the same)

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?

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?

How long will Php 40,000.00 amount to Php 51,200.00 if the simple interest rate is at 12% per annum?

-2 years and 4 months

Find the present value of Php 50,000.00 due in 4 years if money is invested at 12% compounded semi-annuall

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?

## Long Quiz 4

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.

A family obtained a Php 1,000,000.00 mortgaged. If the monthly payment is Php 38,000.00 for four years, how much is the total interest paid?

Find the amount of the semi-annual coupon for a Php 250,000.00 bond which pays 7% convertible semi-annually for its coupons.

Tell whether the following is a characteristic of stocks or bonds:

1. # A form of equity financing or raising money by allowing investors to be part owners of the company. Answer (a) A form of debt financing, or raising money by borrowing from investors. Answer

1(a). Stock
2(a). Bond

Determine the type of loan for the following:

If a condominium is purchased for Php 5,700,000.00 and the bank requires 30% down payment, how much is the mortgaged amount?

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)

For the purchase of a farm worth Php 2,800,000.00, the bank requires 30% down payment, find the mortgaged amount.

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 what type of loan is needed for the following situations:

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.)

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?

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)

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?

If a condominium is purchased for Php 5,700,000.00 and the bank requires 30% down payment, how much is the mortgaged amount?

A family obtained a Php 1,000,000.00 mortgaged. If the monthly payment is Php 38,000.00 for four years, how much is the total interest paid?

Determine what type of loan is needed for the following situations

-Consumer loan

## Learning Activity 8

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.
-True
b. Either Jeff is sleeping or Hadji is not eating.
-True
c. Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating.
-False

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.            Y                TRUE
2.Find a number which divides your age.                N                NA
3.Help!                                                N                NA
4.3 + 2 = 4                                         Y                FALSE

## Short Quiz 14

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.            Y                FALSE
2 What is the domain of the function?                         N                NA
3 I am lying.                                                N                NA
4 It is not the case that sqrt(2) is a rational number.     Y                TRUE

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.
-True
b. If Abbey is in Grade 11, then she is working as a lawyer.
-False
c. If Abbey has a degree in Computer Science, then she believes in true love.
-True

## Learning Activity 9

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.

What is the rule of inference that was used in the argument in #1
-Modus Ponens

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.
-Simplification

## Short Quiz 15

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.
-Valid

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.
-Valid

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.
-Valid

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

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

## Learning Activity 10

Complete the proof of the argument below:

Proposition                      Reason
1.    s                            Premise
2. ~(~s)                    Double Negation
3. (~r) v (~s)                    Premise
4. ~r                    2, 3, Disjunctive Syllogism
5.  p      OR                        remise
6    p                    4, 5, Disjunctive Syllogism

## Short Quiz 16

Complete the proof of the argument below:

Proposition                Reason
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

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?
-12

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.)

log2 (2^4/2^10)and log2 2^- log2 2^10
-5

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?
-12

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.)

log7 75 and 5 · log7 7
-5

3(log9 x)2 = 6 log9 x
-False

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.)

log7 (73 · 78) and log7 73 + log7 78
-11

(log3 2)(log3 4) = log3 6
-False

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.
-11250

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?
-800

The horizontal line test is used to determine whether a function is one-to-one when its graph is given.
-True

Consider the rational function p=(5,125,000V2−449,000V+19307)/(125V2(1,000V−43))p=(5,125,000V2−449,000V+19307)/(125V2(1,000V−43)), does the function have a p-intercept?
-

The relation pairing an SSS member to his/her SSS number is a one-to-one function.
-True

The absolute value function has an inverse function.
-False

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)
-28.79

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%?
-933120

Which of the is the inverse of (\f(x) = 5x - 4\)?
-(\f(x) = (x + 4)/5\)

(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.
-Consumer Loan

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?
-73152.8

For the purchase of a farm worth Php 2,800,000.00, the bank requires 30% down payment, find the mortgaged amount.
-1960000

Fill in the table that represents the inverse of the function defined by:
-*Look at the pic in this folder*

Find the solution for the rational equation: ((2/(x+1)+5/2x)=2\).
-

How long will Php 50,000.00 amount to Php 75,000.00 if the simple interest rate is at 15% per annum?
-3 years and 4 months

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.
-*Look at the pic in this folder* Complete the table of values below:

f(x)=(3)^x=   -2              -1             0              1                2                3

 -4              -2 0 2 4 6

Some functions have inverse functions.

-True

# 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? (Hint: make sure the units of the interest rate and the term are the same)

-426225

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 offer if the money can earn 5% compounded annually.

A.1,050,000.00
B.9,000.00
C.The Php1,050,000.00

ind the unknown in the table below:Use Simple Interest Computation for your answers.

Principal (P)    Rate (r)    Time (t) (in years)    Interest (I)  10,000.008%15Answer Answer 2%510,000.00360,000.00Answer 23,600.00500,000.0010.5%Answer 175,000.00880,000.009.25%2.5Answer 1. 12,000
2.35.29

or the function g(x) = 2x, find

g(2) = Answer g(4) = Answer g(0) = Answer g(-2) = Answer g(-4) = Answer 18433.68

# Which of the following represents an exponential function? Select one: a. The number of trees in a rainforest b. population growth of microorganisms c. The conversion of fahrenheit to celsius d. The amount billed to a girl who bought a basket of flowers

Without using a calculator, find the value of the following logarithmic expression.

-3

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks)

1. f(x)=4−3x4f(x)=4−3x4 Answer 2. f(x)=3−4xf(x)=3−4x Answer 3. f(x)=4−3x4−−−−−−√2f(x)=4−3x42 Answer 4. f(x)=3−4y4f(x)=3−4y4 Answer 5. f(x)=10f(x)=10 Answer Without using a calculator, find the value of the following logarithmic expression.

log5 5

-1

Without using a calculator, find the value of the following logarithmic expression.

log7 1

-0

# (log3 2)(log3 4) = log3 8 Select one: True False

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?

-251942.4

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. Answer (b) Mrs. Alon decided to take her family for a vacation. To cover the expenses, she decided to apply for a loan. Answer

b. Personal loan

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.

# Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.) log7 (73 · 78) and log7 73 + log7 78

-11

4= x

-64

log1/2 16

-4

log2 32

=5

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.)

log3 (27 · 81) and log3 27 + log3 81

-7

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.

-3040000

log3 2x2 = log3 2 + 2 log3 x

-false

# log9 729

=3

log 22 = (log 2)2

=false

The relation pairing a real number to its square is a one-to-one function.

Select one: True

log3 2x2 = 2 log3 2x

-false

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

(Pagpaliten mo lang value ng x at y )

(log3 2)(log4) = log

Select one: True False

2= x

=16

log7 (49/7) and log7 49 - log7 7

=1

3 log9 x2 = 6 log9 x

=true

GMAT-111
Learning Activity 4

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 yrs?

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?

GMAT-111 / ► Week 12: Key Concepts of Simple and Compound Inter... / ► Learning Activity 5

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. How much will her funds worth be after 15 years?
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?

GMAT-111 / ► Week 12: Key Concepts of Simple and Compound Inter... / ► Short Quiz 11

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?
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?
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? (Hint: make sure the units of the interest rate and the term are the same)
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?

=A. 14628.79
b. cash

=1275000

# 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. Answer (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. Answer

=Consumer Loan

(a) A form of equity financing or raising money by allowing investors to be part owners of the company. Answer (a) A form of debt financing, or raising money by borrowing from investors. Answer 