**Third Quarter Project in Advanced Algebra**

**Following Thy**

Footsteps

Footsteps

Table of Contents

**LINEAR**

FUNCTIONS

FUNCTIONS

“It is not once nor twice but times without number that the same ideas make their appearance in the world” – Aristotle.

To know how to make a palace, we must first learn how to make a simple house. We must first understand the thin roots before we deal with the thick trunk. In other words, we must learn the basics.

Good day Mathemagicians! The Mathematical/Logical group of III-Helium, proudly challenges you a brain-squeezing Math Quiz of simple yet tricky Advanced Algebra math problems that involve linear, quadratic, polynomial, and rational functions.

We wish you all the best! Keep those neurons working!

May God bless you and enjoy!

Polynomial Functions

(Word Problems)

Rational Functions

(Word Problems)

Linear Functions

(Word Problems)

Quadratic Functions

(Word Problems)

Introduction

**QUADRATIC**

FUNCTIONS

FUNCTIONS

**POLYNOMIAL**

FUNCTIONS

FUNCTIONS

**RATIONAL**

FUNCTIONS

FUNCTIONS

1.) 8 years from now Peter will be 26 years old. The current sum of the ages of Peter and Paul is 53. How old is Paul right now?

2.) Suppose Johnny can paint an entire house in twelve hours. It takes Marvin eight hours to finish painting the same house. How long would it take them finish painting the house together?

3.) If six men can do a job in fourteen days, how many would it take to do the job in twenty-one days?

4.) How many liters of a 70% alcohol solution should a scientist mix with 50 liters of a 40% alcohol solution so he could obtain a 50% alcohol solution?

5.) Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. Find the smaller number?

6.) Gino has a 500-foot roll of palisade and a large field. He wants to construct a rectangular horse stable area. What will be the dimensions of the field in which will have the largest horse stable area?

7.) A very random picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?

8.) An enchanted garden measuring 12 meters by 16 meters is to have a pathway with colorful ornaments around it, increasing the total area to 285 square meters. What will be the width of the pathway?

9.) The hypotenuse of a right triangle is 6 more than the shorter leg. The longer leg is

three more than the shorter leg. Find the length of the shorter leg.

10.) Mickey and his friends ride his boat up and down a river. The water in the river flows at 6 miles per hour. They took 5 hours longer to travel 360 miles against the current than they did to travel 360 miles with the current. What is the speed of Mickey's boat in still water?

11.) If an arrow is shot upward on the moon with a velocity of 50m/s, its height in meters after t seconds is given by: h(t)= 50(t)-0.83(t)(squared). After how many seconds will the arrow hit the moon's surface?

7.) A cubic polynomial function has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)?

5.) Four girls are making bracelets with their beads. Two girls have the same number of bead sets and they both have 1 more bead set than the 3rd girl. The 4th girl has 1 bead set less than the 3rd girl. If all the number of bead sets of each girl is multiplied, the product would be 18. How many bead sets does each girl have?

14.) A two digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their place. Through formulating the quadratic equation whose root(s) is (are) digit(s) of the number, find the number.

16.) Bugs Bunny was sunbathing while Daffy Duck was mowing the lawn in their backyard. Daffy can mow the lawn in 4 hours while Bugs can mow the same lawn in 5 hours. How long would it take both of them, working together, to mow the lawn?

17.) The Road Runner runs 15 km per hr faster than Wile Coyote. By the time it takes the Road Runner to reach 80 km, Wile Coyote B has gone 50 km. Find the speed of The Road Runner and Wile Coyote.

18.) A plane flies 450 miles with the wind and 300

miles against the wind in the same length of time. If the speed of the wind is 20 mph, what is the speed of the plane in still air?

19.) Taylor bought a closet of floral Victoria's Secret blouses for $450. She kept two for herself and sold the rest for $560, making a profit of $10 on each shirt. How many blouses were in the closet?

20.) A loaded moving truck is traveling 20 mph faster than the Japanese train. In the time it takes the train to travel 160 miles, the truck travels 240 miles. Find the speed of the truck.

CONGRATULATIONS!

You have successfully followed your footsteps for discovering the Wonders of the Wonderland of Mathematics and Mathemagicians!

Live your dreams and follow your heart!

Remember to keep your 2013 BLESSED!

CREDITS:

Group 1 III-Helium

(Logical Group)

Angelica Louisse

A. Aluben

Neil Joseph

Jayo

Ed Carlo

G. Maglasang

Jemar Jude

A. Maranga

Elsa

Trinidad

Edited, Layout-ed

& Animated by:

Alyssa Camille

D. Malig-on

SHINE

BRIGHT!

Be the LIGHT!

15.) In the Disney movie The Little Mermaid, according to rumors, Ariel had sisters who were sextuplets. Aquata, Andrina, Arista, Attina, Adella & Alana, Ariel's sisters are 26 years older than her. The product of the sextuplet's and Ariel's ages 3 years from now will be 360. Through formulating a quadratic equation, find their present ages.