NATIONAL ACHIEVEMENT TEST

REVIEW 2015

(MATHEMATICS)

Prepared by:

Ms. Ma. Irene G. Gonzales

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)

(Gonzales, 2015)

(Gonzales, 2015)

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)

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)

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)

OTHER TYPES OF FUNCTIONS

3. LOGARITHMIC FUNCTIONS

Form:

Domain:

Range:

xxfalog)(

0xx |

Ryy |

(Gonzales, 2015)

(Gonzales, 2015)

(Gonzales, 2015)

OTHER TYPES OF FUNCTIONS

4. IDENTITY FUNCTIONS

Form:

Domain:

Range:

xxf )(

Rxx |

Ryy |

(Gonzales, 2015)

OTHER TYPES OF FUNCTIONS

5. CONSTANT FUNCTIONS

Form: Graph: horizontal line

Domain:

Range:

cxf )(

Rxx |

cy

(Gonzales, 2015)

(Gonzales, 2015)

OTHER TYPES OF FUNCTIONS

6. ABSOLUTE VALUE FUNCTIONS

Form: Graph: v - shaped

Domain:

Range:

xxf )(

Rxx |

0yy |

(Gonzales, 2015)

INEQUALITIES

INEQUALITY SYMBOLS

☺less than

☺greater than

☺not equal to

☺less than or equal to

☺greater than or equal to

(Gonzales, 2015)

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)

Examples

3. In how many ways can a committee of

three be formed from a group of 10

members?

(Gonzales, 2015)

Circular Permutation

1. How many ways can you sit 5 people in

a round table with 5 seats?

(Gonzales, 2015)

PROBABILITY

- field of mathematics that deals with chance.

P(event) = n(Event)

n(Sample Space)

(Gonzales, 2015)

Example

1. A coin is tossed. Find:

a. the sample space

b. the probability of getting a head

(Gonzales, 2015)

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)

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)

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)

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)