MATH 4TH QUARTER

If m∠8=125°, what must m∠3 be so that AB∥CD?

55

If mm∠1=43∘, what is m∠6∘?

137∘

In the figure below, there are two pairs of parallel lines and each pair is cut by the same transversal. What is m∠C?

120

The Math Club adviser wishes to choose two students from a set of 6 qualified students: four boys and two girls. This pair will represent the club in a Math Olympiad. How many possible pairs are there?

15

In the blank template for a tree diagram below, how many possible outcomes are there?

16

How many possible outcomes can you get from rolling a die and tossing two coins?

24

How many three-letter words (disregard the meaning) are may be formed from the word QUIZ when repetition of a letter is not allowed?

24

A coin is tossed five times. How many possible outcomes are there?

32

For questions 4 to 5, refer to the following situation: Mary is undecided on what to wear. For her upper garment, she may choose between shirt or a blouse. For her lower garment, she may choose between pants or shorts. After some time, she finally went out in shorts and shirt. How many possible outcomes are there considering she has to choose one lower garment and one upper garment?

4

In the blank template for tree diagram in the previous item (also shown below), how many possible results are there in the second level of the experiment?

4

What does the sample space contain?

all the possible outcomes of an experiment

To find the experimental probability of an event, what must be conducted?

an experiment

Analyze the table of outcomes below. What are the outcomes in A and B?

(4,3) and (5,6)

In tossing a coin and a die once, which of the following can be an outcome.

(H,5)

Patrick has a bag with 7 blue marbles and 3 red marbles. He picks a marble at random from the bag, puts it back into the bag and then picks another marble at random. How many possible outcomes are there?

100

After 300 trials, Nicole realized that the queen of hearts has come out 25 times already. What is the experimental probability of the queen of hearts NOT being chosen?

11/12

How many choices are there if a Basketball uniform comes in white, yellow, blue or green and in small, medium, or large sizes?

12

Four dice are rolled. What is the total number of outcomes?

1296

Margarette rolled a die 200 times. The results are as follows: What is the experimental probability of the result being an even number?

13/25

Margarette rolled a die 200 times. The results are as follows: What is the experimental probability of the result being a prime number?

21/40

In a group of 5 boys, one is short, and the other four are taller and are almost of the same height. In how many ways can these boys form a single file if the shortest needs to be in front?

24

If m∠2=60∘, what is m∠3? In the figure, l1,l2 and l3 are parallel lines cut by transversals t1 and t2.

30∘

In the figure below, there are two pairs of parallel lines and each pair is cut by the same transversal. Find the value of y.

35

An unknown number of ping pong balls have been numbered 1, 2, 3, and so on. The probability of randomly selecting a prime number when drawing a ping pong ball is 3/10. If the highest prime number used was 37, how many balls are there?

40

In the figure below, l1, l2, If m∠1=43∘, what is m∠3∘?

43∘

How many one-digit, two-digit, and three-digit whole numbers may be formed from the digits 1, 2, and 3 if repetition of digits is allowed.

45

The process of repeating an activity whose outcomes are limited to well-defined choices is called what?

Experiment

In the previous question, which is not an event?

HT

In the table of all possible outcomes shown below for tossing a coin 2 times, what event is missing? (2nd row blank)

HT

Your best friend asked you to accompany him to buy a lotto ticket. According to him, his horoscope states he will be lucky that day so he wants to buy a ticket with his savings. How will you use the concept of probability to convince him not to spend too much on tickets?

I will give him instances wherein he could see the real picture of having a very little chance of winning so that he will not be wasting his money and time.

What do you call angles that are on opposite sides of the transversal and are found inside the two parallel lines?

alternate interior angles

If m∠3=m∠6m, is AB parallel to CD?

always

Given: m∠1=m∠4, ∠3, and ∠4 are supplementary. Prove: l∥m

consecutive interior angles are supplementary

Refer to the figure below. A two-column proof will be constructed step by step. You are to give the reason for the given statement in the current step. Given: m∠1=m∠4, ∠3, and ∠4 are supplementary. Prove: l∥m m∠3 + m∠4 = 180

definition of Supplementary Angles

In tossing a coin, a head shows up. What do we call the tossing of the coin?

experiment

In what forms can probabilities be expressed?

fraction, percent, decimal

Which of the following is not a reason for using a tree diagram in getting all possible outcomes on an experiment?

it is the easiest and fastest way to get all possible outcomes in an experiment

Which of the following statements is correct about the experimental probability of an event?

it my vary from one experiment to another

If m∠3+m∠5=178°, is AB parallel to CD?

never

What is the formula for finding the experimental probability of an event?

no. of times an event actually appears / no. of times the activity is repeated

he formula for finding the probability of an event is:

no. of times an event can occur / no. of all possible outcomes

The likelihood of the occurrence of an event is called its

probability

Study the tree diagram below. What experiment can you deduce from it?

spinning a three-colored spinner and then flipping a coin

What must be true of alternate exterior angles formed by two lines and a transversal that cuts the lines for the lines to be parallel?

the alternate exterior angles must be congruent

What must be true of consecutive interior angles formed by two lines and a transversal that cuts the lines for the lines to be parallel?

the consecutive interior angles must be supplementary

What must be true of corresponding angles formed by two lines and a transversal that cuts the lines for the lines to be parallel?

the corresponding angles must be congruent

A single die is rolled once. Which of the following cannot be considered an event?

the die shows a number greater than 6

Which of the following is true about consecutive interior angles formed by parallel lines cut by a transversal?

they are supplementary

A ------------------_is an illustration that originates from a starting point, and has vertical or horizontal "levels" for each trial displaying the possible outcomes for that level originating at each of the possible outcomes from the previous trial.

tree diagram

The Supreme Pupil Government president conducted a survey whether they want to have a referendum. The survey form consisted of two possible answers: yes and no. What is the outcome in this situation?

voting for a yes or a no

What is the probability of getting a 7 when rolling a regular die?

0

In the figure below, there are two pairs of parallel lines and each pair is cut by the same transversal. What is m∠A?

120

What is the probability of a tail showing up when a coin is tossed?

1/2

Find the probability of getting a number that is divisible by 3 when tossing a regular die?

1/3

Christine rolled a die 50 times. The results are as follows: What is the experimental probability of the result being 4?

1/5

Clocks come in two types: wall or desk. They come in five colors: red, yellow, green, blue and white. How many possible choices are there?

10

How many possible outcomes may result from spinning the two spinners below?

12

Two spinners are spun once. The first spinner has the outcomes A or B, and the second one has the outcomes 1, 2, 3, 4, 5, 6, 7, or 8. What is the total number of outcomes of the experiment?

16

Janine tossed a coin 15 times. The head turned up 6 times in all her trials. What is the experimental probability of getting a head?

2/5

There are 10 questions on a True or False test. In how many ways can the test be completed?

20

In the figure, there are two pairs of parallel lines and each pair is cut by the same transversal. Find the measure of x.

25

What is the probability of choosing a vowel when randomly selecting a letter in the English alphabet?

5/26

When you pick a card from a standard deck of cards, how many total outcomes are possible?

52

A bag contains 2 red, 3 green, and 2 blue balls. Two balls are drawn at simultaneously. How many possible outcomes are there?

6

How many elements does the sample space for rolling a die have?

6

How many possible outcomes are there if you have a choice of muffins or toast with coffee, milk or juice?

6

To increase sales, a car manufacturer offers a limited edition of cars with a choice of any of the following colors and any of the following engine sizes: How many different combinations can a customer choose from?

6

Using the digits 4, 5, and 6, how many 2-digit numbers can you make without repeating any of the digits?

6

If m∠2=60∘, what is m∠9?

60

How many five-digit numbers can be formed from the set {5,6,7,8,9,0} if zero cannot be the first digit and the numbers cannot be repeated.

600

If randomly choosing a month of the year, what is the probability that the chosen month will have 31 days in it?

7/12

In the school canteen, you have a choice of one main dish, one vegetable, and one beverage. The choices for main dish are pork and chicken meat. The vegetable choices are broccoli and cabbage. The drink choices are juice and water. How many choices consisting of a main dish, a vegetable, and a drink are possible?

8

Suppose you are offered to choose for breakfast between rice or wheat bread with either hotdog or egg and a drink of either coffee or hot chocolate. Your initial tree diagram would look like the figure below. If you continue the tree, how many possible outcomes can you make?

8

Study the two statements that follow: A. The sample space is the set of all possible outcomes in an experiment. B. An event is a subset of the sample space.

Both statements A and B are true

If m∠5=m∠8°, can one say that AB∥CD?

No

A card is chosen from a regular deck. Which has the highest probability, getting a heart, getting a king, or getting the king of hearts?

The probability of getting a heart

Given: m∠1=m∠4, ∠3, and ∠4 are supplementary. Prove: l∥m m∠2 = m∠3

Vertical angle theorem

For questions 4 to 5, refer to the following situation: Mary is undecided on what to wear. For her upper garment, she may choose between shirt or a blouse. For her lower garment, she may choose between pants or shorts. After some time, she finally went out in shorts and shirt. What is the experiment in the given situation?

choosing what to wear for her upper and lower garments.

What is the possible experiment that could generate a sample space of the given table below?

rolling two dice at once

What do you call the set of all possible results of an experiment?

sample space