Question 1

The standard form of the equation of the hyperbola centered at $\left(h,k\right)$ is given by which of the following equations.

Accepted Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Question 2

The perimeter and the diagonal of a rectangle are 40 cm and 16 cm, respectively. What are the dimensions of the rectangle?

Accepted Answer

4.71 cm and 15.29 cm

Answer

9.42 cm and 30.58 cm

Answer

14.9 cm and 10.1 cm

Answer

42.1 cm and 3.8 cm

Question 3

Which sigma notation expresses the series 1+4+7+10+13?

Accepted Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Question 4

Which of the following represents a finite sequence?

Accepted Answer

5,9,13,21.

Answer

1,5,9,13,17, ...

Answer

3, 6,9,12,15, . . .

Answer

2,4,6,8,10, . . .

Question 5

What is true about asymptotes of the hyperbola?

i. A hyperbola has two asymptotes.

ii. the asymptotes of hyperbola intersects at the origin.

iii. The asymptotes of hyperbola contain the diagonals of the central box.

Accepted Answer

i and iii

Answer

i only

Answer

i, ii, and iii

Answer

i and ii

Question 6

The graphs of the following equations are non-degenerate conics sections. Identify the hyperbola.

i. $3x^2-2y^2=12$

ii. $9y^2+16x^2=144$

iii. $y^2+x^2-2x+4y-20=0$

iv. $4x^2-9y^2-16x+18y+10=0$

Accepted Answer

i and iv

Answer

i only

Answer

iii only

Answer

i, iii, iv

Question 7

From the circular piece of metal steel with diameter of 20 cm, a rectangular piece with perimeter of 56 cm is to cut as shown. Find the dimensions of the rectangular piece.

Accepted Answer

12 cm by 16 cm

Answer

8 cm by 20 cm

Answer

4 cm by 24 cm

Answer

2cm by 26 cm

Question 8

What are the first 5 terms of the sequence $\left(h,k\right)$

Accepted Answer

3,5,7,911

Answer

1,3,5,7,9

Answer

4,5,6,7,8

Answer

1,2,3,4,5

Question 9

Which of the following is the general term of the sequence whose first 5 terms are 3,1,-1,-3,-5?

Accepted Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Question 10

An arch in the form of a semi-ellipse is 50 feet wide at the base and has a height of 16 feet. How wide is the arch at the height of 8 feet above the base? Evaluate Rico's solution, from which part of the solution is incorrect?

Accepted Answer

ii

Answer

iii

Answer

iv

Answer

i

Question 11

Given the system of nonlinear equations below,

$\left\{4x^2+25y^2=41\right\}$

$\left\{36x^2+25y^2=169\right\}$ , what are the conic sections involved?

Accepted Answer

ellipses

Answer

hyperbolas

Answer

circle, hyperbola

Answer

circle, ellipse

Question 12

Given the system of nonlinear equations below,

$\left\{4x^2+25y^2=41\right\}$

$\left\{36x^2+25y^2=169\right\}$ , how many solution/s or point/s of intersection are there?

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 13

Given the system of nonlinear equations below,

$\left\{4x^2+25y^2=41\right\}$

$\left\{36x^2+25y^2=169\right\}$ , what is/are the solution/s of the given system of nonlinear equations?

i. $\left(2,1\right)$

ii. (-2,1)

iii. (-2,-1)

iv. (2,-1)

Accepted Answer

i, ii, iii, iv

Answer

i, ii, and iv

Answer

i only

Answer

iii only

Question 14

Every year, the Philippines get hit by approximately 20 typhoons. Accurate forecast is therefore needed for the people to be ready when the typhoon strikes. Suppose typhoon X is in the country and is predicted to have 350-km radius. Further, it was reported that town A located 260 km south and 255 km west from its eye is at the periphery or circumference of the typhoon. The town folks want to verify the news. (Assume that the eye of the typhoon is at the origin of the coordinate plane). What is the equation of the circular periphery of the typhoon X?

Accepted Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Question 15

Every year, the Philippines get hit by approximately 20 typhoons. Accurate forecast is therefore needed for the people to be ready when the typhoon strikes. Suppose typhoon X is in the country and is predicted to have 350-km radius. Further, it was reported that town A located 260 km south and 255 km west from its eye is at the periphery or circumference of the typhoon. The town folks want to verify the news. (Assume that the eye of the typhoon is at the origin of the coordinate plane). At what point is town A located?

Accepted Answer

(255, 260)

Answer

(350,20)

Answer

(260,3500

Answer

(255, 350)

Question 16

Every year, the Philippines get hit by approximately 20 typhoons. Accurate forecast is therefore needed for the people to be ready when the typhoon strikes. Suppose typhoon X is in the country and is predicted to have 350-km radius. Further, it was reported that town A located 260 km south and 255 km west from its eye is at the periphery or circumference of the typhoon. The town folks want to verify the news. (Assume that the eye of the typhoon is at the origin of the coordinate plane). Was the report that town A is at the periphery or circumference of the typhoon accurate?

Accepted Answer

No, because town A is $\left(h,k\right)$ is farther than 350 km.

Answer

No, because town A is $\left(h,k\right)$ is nearer than 255 km .

Answer

Yes, because town A is $\left(h,k\right)$ is farther than 350 km.

Answer

Yes, because town A is $\left(h,k\right)$ is nearer than 255 km.

Question 17

The increasing enrollment at Dulo High School can be modeled by the equation $\left(h,k\right)$ , where t represents the number of years after 2010. The increasing enrollment at Gitna High School can be modeled by the equation $G\left(t\right)=\ 24t+570$ .What equation is obtained after applying the concept of the last statement?

Accepted Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Answer

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Question 18

The increasing enrollment at Dulo High School can be modeled by the equation $\left(h,k\right)$ , where t represents the number of years after 2010. The increasing enrollment at Gitna High School can be modeled by the equation $G\left(t\right)=\ 24t+570$ . After how many years will the enrollments of the two schools be equal?

Accepted Answer

6 years

Answer

5 years

Answer

3 years

Answer

4 years

Question 19

The increasing enrollment at Dulo High School can be modeled by the equation $\left(h,k\right)$ , where t represents the number of years after 2010. The increasing enrollment at Gitna High School can be modeled by the equation $G\left(t\right)=\ 24t+570$ . In what year will the enrollments of the two schools are equal?

Accepted Answer

2016

Answer

2015

Answer

2014

Answer

2013

Question 20

Find the value/s of $\left(h,k\right)$ so that the graph of $G\left(t\right)=\ 24t+570$ is a circle for $9y^2+16x^2=144$

Accepted Answer

11

Answer

1

Answer

16

Answer

5

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