reviewer for mathematics part 2
TRANSCRIPT
![Page 1: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/1.jpg)
NATIONAL ACHIEVEMENT TEST
REVIEW 2015
(MATHEMATICS)
Prepared by:
Ms. Ma. Irene G. Gonzales
![Page 2: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/2.jpg)
OTHER TYPES OF FUNCTIONS
1. SQUARE ROOT FUNCTIONS
Form:
Domain:
Range: (if the form is )
(if the form is )
xxf )(
0xx |
0yy |
0yy |
xxf )(
xxf )(
(Gonzales, 2015)
![Page 3: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/3.jpg)
(Gonzales, 2015)
![Page 4: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/4.jpg)
(Gonzales, 2015)
![Page 5: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/5.jpg)
OTHER TYPES OF FUNCTIONS
2. RATIONAL FUNCTIONS
Form:
Domain: Values of x that are real except the value that
makes the denominator equal to 0.
)(
)()(
xD
xNxf
(Gonzales, 2015)
![Page 6: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/6.jpg)
OTHER TYPES OF FUNCTIONS
2. RATIONAL FUNCTIONS
Form:
Range: If the highest degree of the numerator and the
denominator are equal, divide the coefficient of the
highest degree of the numerator to the coefficient of
the highest degree of the denominator.
)(
)()(
xD
xNxf
(Gonzales, 2015)
![Page 7: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/7.jpg)
OTHER TYPES OF FUNCTIONS
2. RATIONAL FUNCTIONS
Form:
Range: If the highest degree of the numerator is less than
the highest degree of the denominator, then the range
is .
)(
)()(
xD
xNxf
0yy |
(Gonzales, 2015)
![Page 8: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/8.jpg)
OTHER TYPES OF FUNCTIONS
3. LOGARITHMIC FUNCTIONS
Form:
Domain:
Range:
xxfalog)(
0xx |
Ryy |
(Gonzales, 2015)
![Page 9: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/9.jpg)
(Gonzales, 2015)
![Page 10: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/10.jpg)
(Gonzales, 2015)
![Page 11: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/11.jpg)
OTHER TYPES OF FUNCTIONS
4. IDENTITY FUNCTIONS
Form:
Domain:
Range:
xxf )(
Rxx |
Ryy |
(Gonzales, 2015)
![Page 12: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/12.jpg)
OTHER TYPES OF FUNCTIONS
5. CONSTANT FUNCTIONS
Form: Graph: horizontal line
Domain:
Range:
cxf )(
Rxx |
cy
(Gonzales, 2015)
![Page 13: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/13.jpg)
(Gonzales, 2015)
![Page 14: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/14.jpg)
OTHER TYPES OF FUNCTIONS
6. ABSOLUTE VALUE FUNCTIONS
Form: Graph: v - shaped
Domain:
Range:
xxf )(
Rxx |
0yy |
(Gonzales, 2015)
![Page 15: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/15.jpg)
INEQUALITIES
INEQUALITY SYMBOLS
☺less than
☺greater than
☺not equal to
☺less than or equal to
☺greater than or equal to
(Gonzales, 2015)
![Page 16: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/16.jpg)
Examples
1. In how many ways can you arrange the
letters in the word “heptagon”?
2. In how many ways can you arrange the
letters of the word “happy”?
(Gonzales, 2015)
![Page 17: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/17.jpg)
Examples
3. In how many ways can a committee of
three be formed from a group of 10
members?
(Gonzales, 2015)
![Page 18: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/18.jpg)
Circular Permutation
1. How many ways can you sit 5 people in
a round table with 5 seats?
(Gonzales, 2015)
![Page 19: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/19.jpg)
PROBABILITY
- field of mathematics that deals with chance.
P(event) = n(Event)
n(Sample Space)
(Gonzales, 2015)
![Page 20: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/20.jpg)
Example
1. A coin is tossed. Find:
a. the sample space
b. the probability of getting a head
(Gonzales, 2015)
![Page 21: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/21.jpg)
Example
2. If a card is drawn from a well-shuffled
deck of 52 cards, what is the probability
that it is a king of diamonds?
(Gonzales, 2015)
![Page 22: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/22.jpg)
Example
3. A box contains five red, two white, and
three green balls. If a ball is selected at
random, find the probability that it is
a. red c. not red
b. green d. black
(Gonzales, 2015)
![Page 23: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/23.jpg)
Example
4. A card is selected at random from an
ordinary deck of playing cards. Find the
probability that the card is
a. a heart c. a 4 or an 8
b. is black d. a red queen
(Gonzales, 2015)
![Page 24: Reviewer for Mathematics Part 2](https://reader031.vdocuments.site/reader031/viewer/2022013122/55ce65b6bb61eb321d8b469d/html5/thumbnails/24.jpg)
Example5. A large box contains 365 tickets, one for
each day of a common year. Suppose one
ticket is selected at random.
a.) Find the probability that the selected
day is in December.
b.) Find the probability that the selected
day is your birthday.
(Gonzales, 2015)