Quiz about PNZ Review

Question 1

Which of the following represent the dimension of a rectangular picture frame with an area of $$\left(x^2-21x+104\right)\ in^2$$ ?

Accepted Answer

8 in and 13 in

Answer

7 in and 12 in

Answer

6 in and 11 in

Answer

9 in and 14 in

Question 2

In a school rectangular garden, the number of plants in each row is one less than the number of rows. If the total number of plants is 42, what is the number of rows and the number of plants per rows?

Accepted Answer

7 rows and 6 plants

Answer

6 rows and 7 plants

Answer

14 rows and 3 plants

Answer

3 rows and 14 plants

Question 3

Which of the following expressions is rational expression?

Accepted Answer

$$\frac{x^3-\frac{1}{2}}{x+1}$$

Answer

$$\frac{2x}{3y^{-2}}$$

Answer

$$\frac{x^{\frac{1}{2}}-1}{5y}$$

Answer

$$\frac{2\sqrt[]{x}+3}{\sqrt[]{x}}$$

Question 4

The student is working on the equation $$\frac{x}{3}+\frac{1}{2}=1$$ . His steps are shown as follows:

Step 1: $$2x+3=6$$

Step 2: $$2x=6-3$$

Step 3: $$2x=-3$$

Step 4: $$x=\frac{3}{2}$$

Accepted Answer

Step 3

Answer

Step 1

Answer

Step 2

Answer

Step 4

Question 5

Michelle is 10 years older than her brother, Tony. In five years, her brother will be two-thirds of her age. How old is Tony now?

Accepted Answer

15

Answer

25

Answer

45

Answer

55

Question 6

Which of the following Cartesian planes show the points that is 5 units to the left of the origin and 3 units below x-axis?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 7

Cagsawa Pili Donuts charges Php 24 each for a special doughnut plus a fixed charge of Php 5 for the box. Which equation represents the relationship between the number of doughnuts $$x$$ and the total cost $$y$$ in pesos.

Accepted Answer

24x + 5 = y

Answer

24y + x = 5

Answer

5y + x = 24

Answer

5x + y =24

Question 8

Solong Hill is one of the famous attractions in Bicol found in Camalig, Albay. Suppose the hill was illustrated as shown, the following choices have the same slope with the figure EXCEPT:

Accepted Answer

$$(3,3)\ and\ (5,8)$$

Answer

$$y=\frac{2}{5}x+1$$

Answer

$$5y=2x+5$$

Answer

$$\left(3,3\right)\ and\ \left(8,5\right)$$

Question 9

Rewrite the equation $$3x+5y=-20$$ in slope-intercept form.

Accepted Answer

$$y=-\frac{3}{5}x-4$$

Answer

$$y=\frac{3}{5}x-4$$

Answer

$$y=-\frac{3}{5}x+4$$

Answer

$$y=\frac{3}{5}x+4$$

Question 10

Which of the following lines contain the points $$\left(-2,0\right)\ and\ \left(0,1\right)$$ , what is the graph of a line?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 11

A student is driving a motorcycle from school to his home then he stops at a gasoline station to refill his motor's gasoline tank. If the gasoline is Php 55.10 per liter, how much will it cost if he purchases 4 liters?

Accepted Answer

Php 220.40

Answer

Php 220.50

Answer

Php 220.42

Answer

None of the choices

Question 12

Rony and Ryan bought vegetables in the market. Rony bought a total of Php 600 worth of vegetables which includes eggplant that costs Php 55 per kilo and string beans that cost Php 65 per kilo. While Ryan bought a total of php 700 worth of vegetables which includes eggplant that cost Php 60 per kilo and string beans that cost Php 50 per kilo. Which of the following systems of equations best represent the situation?

Accepted Answer

$$55x+65y=600$$

$$60x+50y=700$$

Answer

$$65x+55y=700$$

$$60x-50y=600$$

Answer

$$55x-65y=600$$

$$60x-50y=700$$

Answer

$$55x-65y=600$$

$$60x+50y=700$$

Question 13

Which system of linear equations represent the graph?

Accepted Answer

$$3x+5y=15;\ $$

$$6x+10y=30$$

Answer

$$3x-5y=15;\ $$

$$6x+5y=-30$$

Answer

$$3x+5y=-15;\ $$

$$6x-10y=30$$

Answer

$$3x+5y=-15;\ $$

$$6x+10y=30$$

Question 14

Which of the following symbols should be used to make the mathematical sentence $$3x+7y\ $$ _ $$10$$ a linear inequality in two variables wherein the first expression is greater than the second?

Accepted Answer

$$>$$

Answer

$$
e$$

Answer

$$<$$

Answer

$$=$$

Question 15

Among the given mathematical sentences, which are considered linear equations in two variables?

A. $$2x=8y-9$$

B. $$5y-3>7x$$

C. $$10y-2x=-4$$

D. $$6x+4y e12$$

Accepted Answer

A and C

Answer

B and D

Answer

C and D

Answer

A and B

Question 16

Lebron is taller than Curry and Curry's height is 6 feet. Suppose Lebron's height and Curry's height has a difference of not more than 0.5 feet, which of the following is true?

i. Lebron's height is $$\le$$ 6.5 feet

ii. Lebron's height is $$\ge$$ 6.5 feet

iii. If $$x$$ = Lebron's height and $$y$$ =Curry's height then $$x+y\le12$$ feet and 6 inches

iv. If $$x$$ = Lebron's height and $$y$$ =Curry's height then $$x+y\ge12$$ feet and 6 inches

Accepted Answer

ii and iii

Answer

i and iii

Answer

ii and iv

Answer

i and iv

Question 17

Ambo was asked by his brother to buy some quality face masks and face shields. A face mask costs Php 10.25 each while a face shield costs Php 29.50 each. His brother gave him Php 1000 and said he can spend no more than Php 500 and the total number of items should not exceed to 30. In order to maximize the number of items and his expenses, Ambo thought of buying...

i. equal quantity of face masks and face shields

ii. more face masks and less face shields

iii. less face masks and more face shields

iv. the number of face masks is twice the number of face shields

Which of Ambo's though is true?

Accepted Answer

iv only

Answer

i only

Answer

ii only

Answer

iii only

Question 18

Which of the following relations is a function?

Accepted Answer

Option B is correct

Answer

$$\left\{\left(1,-2\right),\ \left(-2,3\right),\left(-3,4\right),\ \left(-3,5\right)\right\}$$

Answer

C.

Answer

D.

Question 19

Ana asserted that the relations (Apple, Narra), (Banana, Coconut), (Orange, acacia), (Grapes, Mahogany) and { ( 3,4) , ( 4,5 ) , ( 5 ,6 ) , ( 6,7 ) , ( 7 , 8 ) } are both functions. Which statement/s can be used to support and prove her claim?

I. It is one-to-many correspondence.

II. It is one-to-one correspondence.

III. It is many-to-one correspondence.

IV. It is many-to-many correspondence.

Accepted Answer

II only

Answer

I, II, and III

Answer

I, II, III, and IV

Answer

I only

Question 20

Emma noticed that the more food she eats, the bigger her abdomen. What is the dependent variable in this situation?

Accepted Answer

amount of food

Answer

Anna's weight

Answer

type of food

Answer

abdomen's circumference

Question 21

What is the domain of the function

$$\left\{\left(-2,5\right),\ \left(-1,-10\right),\ \left(4,5\right),\left(2,6\right)\right\}$$ ?

Accepted Answer

$$D=\left\{-2,-1,4,2\right\}$$

Answer

$$D=\left\{5,6,10\right\}$$

Answer

$$D=\left\{-1,2,4\right\}$$

Answer

$$D=\left\{-2,-1,-4,2\right\}$$

Question 22

Which graph shows a linear function whose slope and $$y$$ -intercept are $$\frac{-2}{3}$$ and 3 respectively?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 23

Jessa opened a bicycle rental shop near Ligao City Park. Suppose her sister wanted to rent a bike at Php 25 per hour and an additional Php 10 for the bike helmet. How much will her sister have to pay if she would rent a bike for 5 hours with bike helmet? Use the table to answer the given question.

Accepted Answer

Php 135

Answer

Php 120

Answer

Php 175

Answer

Php 125

Question 24

It has been observed that a particular plant's growth is directly proportional to time. It is measured 3 cm when it arrived at the nursery and 3.5 cm exactly one week later. If the plant continues to grow at this rate, what would be the height of the plant after 5 weeks?

Accepted Answer

The height of the plant will be 5.5 cm.

Answer

The height of the plant will be 4 cm.

Answer

The height of the plant will be 4.5 cm.

Answer

The height of the plant will be 5 cm.

Question 25

What is the inverse of a conditional statement:

"If P, then Q"?

Accepted Answer

If not P, then not Q.

Answer

If not Q, then not P.

Answer

If not P, then Q.

Answer

If P, then Q.

Question 26

Given the conditional statement,"An even number is divisible by 2."

Which is not true about its truth table?

i. The converse and inverse statement are true.

ii. The inverse statement is false.

iii. The contrapositive statement is false.

Accepted Answer

ii only

Answer

i and ii

Answer

i only

Answer

ii and iii

Question 27

Consider the following statements:

Statement 1: If the measure of an angle is greater than 90, then it is an obtuse angle.

Statement 2: The measure of $$\angle FIT$$ is $$125\degree$$ .

What could be the next statement?

Accepted Answer

$$\angle FIT$$ is an obtuse angle.

Answer

The measure of $$\angle FIT>90\degree$$ .

Answer

The measure of $$\angle FIT\ is\ 130\degree.$$

Answer

$$\angle FIT$$ is a right angle.

Question 28

Which of the following terms best describe the locations of Iriga City and Tabaco City on the Philippine map?

Accepted Answer

point

Answer

line

Answer

plane

Answer

space

Question 29

In $$\Delta CEF$$ , $$\overline{ED}$$ bisects $$\overline{CF}$$ . If $$CF=30\ cm$$ , what definition would explain why $$CD=15\ cm$$ ?

Accepted Answer

Definition of midpoint

Answer

Definition of ray

Answer

Definition of segment

Answer

Definition of congruent

Question 30

Mrs. Locsin asked Nesty to illustrate: $$\Delta TRY\cong\Delta CAN$$ with $$\overline{TR}\cong\overline{CA},\ \overline{RY}\cong\overline{AN},\ and\ \overline{YT}\cong\overline{NC}$$ . If you were Nesty how can you create, visualize and model the triangle.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 31

Which of the triangle congruence can be used to say that these triangles are congruent?

Accepted Answer

Side-Angle-Side (SAS) Congruence Postulate

Answer

Side-Side-Side (SSS) Congruence Postulate

Answer

Side-Angle-Angle (SAA) Theorem

Answer

Angle-Side-Angle (ASA) Congruence Postulate

Question 32

If $$\Delta CAN\ \cong\Delta LYT$$ , find the measure of $$\angle A$$ and $$\angle T$$ respectively.

Accepted Answer

$$51\degree,\ 82\degree$$

Answer

$$47\degree,\ 82\degree$$

Answer

$$82\degree,\ 51\degree$$

Answer

$$82\degree,\ 47\degree$$

Question 33

If $$\Delta MNO\ \cong\Delta RST$$ and $$MN=12\ cm,\ ST=24\ cm$$ and $$RT=6\ cm$$ . What are the respective lengths of $$MO$$ and $$RS$$ in cm?

Accepted Answer

$$6,\ 12$$

Answer

$$24,\ 12$$

Answer

$$6,\ 24$$

Answer

$$12,\ 6$$

Question 34

Refer to the diagram, which of the following congruence statement proves that $$\Delta NOP\cong\Delta DES$$ ?

Accepted Answer

$$\overline{NO}\cong\overline{DE}$$

$$\overline{OP}\cong\overline{ES}$$

$$\overline{PN}\cong\overline{S}D$$

Answer

$$\angle S\cong\angle P$$

$$\overline{NO}\cong\overline{DE}$$

$$\angle O\cong\angle E$$

Answer

$$\overline{NO}\cong\overline{DE}$$

$$\angle O\cong\angle E$$

$$\overline{OP}\cong\overline{ES}$$

Answer

$$\overline{NO}\cong\overline{DE}$$

$$\angle O\cong\angle E$$

$$\angle S\cong\angle P$$

Question 35

Given that $$\angle L\cong\angle K$$ and $$\overline{EK}\cong\overline{OL}$$ , what is the third congruence needed to prove that $$\Delta LOW\cong\Delta KEY$$ by ASA Congruence Postulate?

Accepted Answer

$$\angle E\cong\angle O$$

Answer

$$\angle LWO\cong\angle KYE$$

Answer

$$\overline{EY}\cong\overline{OW}$$

Answer

$$\angle W\cong\angle Y$$

Question 36

Using the figure, name the postulate that will make the triangle congruent.

Accepted Answer

SAS Congruence Postulate

Answer

ASA Congruence Postulate

Answer

AAS Congruence Postulate

Answer

SSS Congruence Postulate

Question 37

Given that $$\angle E\cong\angle R$$ , and $$EF\cong RQ$$ , what is the third congruence needed to prove that $$\Delta EFG\cong\Delta RQP$$ by ASA?

Accepted Answer

$$\angle F\cong\angle Q$$

Answer

$$\angle F\cong\angle P$$

Answer

$$\angle G\cong\angle P$$

Answer

$$\angle F\cong\angle G$$

Question 38

During Math Camp, campers need to construct their tent. They fixed a tent in a shape of a triangle. The illustration shows the structure of the tent. Given that in $$\Delta LOV,\ \overline{OE}$$ is the perpendicular bisector of $$\overline{LV}$$ . If $$LE=40\ cm\ $$ and $$EV=8x\ cm$$ , then what is $$x$$ ?

Accepted Answer

$$5\ cm$$

Answer

$$8\ cm$$

Answer

$$10\ cm$$

Answer

$$40\ cm$$

Question 39

Which of the figures illustrate the Hinge Theorem?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 40

Which of the following set of lengths does not form a triangle?

Accepted Answer

$$10\ cm,\ 10\ cm,\ 20\ cm$$

Answer

$$9\ cm,\ 9\ cm,\ 16\ cm$$

Answer

$$10\ cm,\ 10\ cm,\ 19\ cm$$

Answer

$$9\ cm,\ 9\ cm,\ 17\ cm$$

Question 41

Given the figure, which angles measure greater than the measure of $$\angle6$$ ?

Accepted Answer

$$\angle8,\ \angle4,\ and\ \angle9$$

Answer

$$\angle3,\ \angle8,\ and\ \angle1$$

Answer

$$\angle2,\ \angle1,\ and\ \angle9$$

Answer

$$\angle7,\ \angle5,\ and\ \angle4$$

Question 42

Given $$\Delta ABC$$ with exterior angle $$\angle BCD$$ , find the measure of $$\angle B$$ , if $$m\angle A=58\degree$$ and $$m\angle BCD=135\degree$$ .

Accepted Answer

$$77\degree$$

Answer

$$87\degree$$

Answer

$$193\degree$$

Answer

$$188\degree$$

Question 43

Nicko and Duane are playing a five-peso coin and an octahedron, a special die with eight congruent faces marked 1 to 8. If they toss the coin and roll the octahedron simultaneously, how many possible outcomes are there?

Accepted Answer

$$16$$

Answer

$$8$$

Answer

$$12$$

Answer

$$20$$

Question 44

You were invited by your cousin to attend her birthday party. You only have four pairs of pants, two shirts and three pairs of shoes left in the cabinet. By applying the fundamental counting principle, how many different outfits can you choose?

Accepted Answer

$$36$$

Answer

$$48$$

Answer

$$24$$

Answer

$$64$$

Question 45

In a raffle draw, the grand prize is a 10.4-inch android tablet. Joy hopes to win the android tablet for her online class. She joins the raffle draw and wrote her name on five tickets. If there is a total of 155 tickets in the raffle draw, what is the probability that she will win the grand prize?

Accepted Answer

$$\frac{1}{31}$$

Answer

$$\frac{3}{50}$$

Answer

$$\frac{5}{15}$$

Answer

$$\frac{2}{25}$$

Question 46

A teacher prepared a prize box for her students during a quiz bee. If a student answers a question correctly, he will pick a prize inside the box. The prize box contains different colors of pens. Nine of the pens are blue, three of the pens are green, and twelve of the pens are red. What is the probability that a student selects a green pen?

Accepted Answer

$$\frac{1}{8}$$

Answer

$$\frac{9}{24}$$

Answer

$$\frac{3}{12}$$

Answer

$$\frac{12}{30}$$

Question 47

Which of the following situations illustrate theoretical probability and experimental probability?

I. John tossed a coin 10 times and recorded the results. He came up with the table on the left. Then he computed the probability: $$\frac{6}{10}=0.6=60\%$$

II. In tossing a coin, Siena would expect 50% of the time it might land on heads. So, for 10 times of tossing a coin, she would expect it to land on heads 5 times.

Accepted Answer

Situation I illustrates experimental probability and situation II illustrates theoretical probability.

Answer

Situation I and II both illustrate experimental probability.

Answer

Situation I and II both illustrate theoretical probability.

Answer

Situation I illustrates theoretical probability and situation II illustrates experimental probability.

Question 48

There are 12 colored candies in a jar consisting of pink, red, blue and orange . Five of the candies are pink. The probability of getting a red candy is $$\frac{2}{12}$$ or $$\frac{1}{6}$$ , which is twice the probability of getting blue candies. Construct a table for the probability of selecting a colored candy?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

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