math quiz to g8

2016 DIVISION FESTIVAL OF TALENTS

Category B:

MATH QUIZ (Team-Orals) (Judges’ Copy)

GRADE 8

15-second Questions [2 points each]

15.1. Factor out completely the polynomial, 5𝑥 3 + 20𝑥 2 + 20𝑥.

𝟓𝒙(𝒙 + 𝟐)(𝒙 + 𝟐)

15.2. What is the expanded form of the expression, 2(𝑥 + 𝑦)3?

𝟐𝒙𝟑 + 𝟔𝒙𝟐 𝒚 + 𝟔𝒙𝒚𝟐 + 𝟐𝒚𝟑

or 𝟓𝒙(𝒙 + 𝟐)𝟐

15.3. If 9𝑚2 + 𝑘 + 49 is a perfect square trinomial, what expression should replace 𝑘? 15.4. What is the product when the expression

12𝑥 𝑦2

is multiplied to

𝑥𝑦 3 12

42m

?

𝒙𝟐 𝒚

15.5. For which values of 𝑥 is the relation, 𝑓(𝑥 ) = √𝑥 + 1 defined?

𝒙 ≥ −𝟏

15.6. What is the slope of line of the equation 7𝑥 − 3𝑦 = 5?

𝟕 𝟑

15.7. Given 𝑦 = 3𝑥 − 2, what is the value of 𝑥 if 𝑦 = −5?

-1

15.8. What is the slope of the line perpendicular to the graph of 𝑥 + 5𝑦 = −12

5

15.9. Divide 6𝑥 5 𝑦 + 3𝑥 3 𝑦 + 9𝑥𝑦 by 3𝑥𝑦.

𝟐𝒙𝟒 + 𝒙𝟐 + 𝟑

15.10. A system of equation is composed of two linear equations whose graphs are parallel. How many solutions does the system of equations have?

None, zero, no solution

30-second Questions, [3 points each]

30.1. If the x-intercept of 3𝑥 − 2𝑦 = 12 is 𝑎 and its y-intercept is 𝑏, what is 3𝑎 − 2𝑏 equal to? 30.2. Solve the system of linear equations, 3𝑥 + 2𝑦 = −4 { 2𝑥 − 𝑦 = −12

24 (-4, 4) or 𝒙 = −𝟒; 𝒚 = 𝟒

30.3. Find the area of the figure below. 𝟐𝒙 + 𝟔 𝟓𝒙𝟐 + 𝟐𝟎𝒙

𝟐𝒙

𝒙+𝟖

30.4. Eighteen 1 𝑐𝑚 × 1 𝑐𝑚 square tiles are arranged to form a rectangle with no overlaps and without leaving gaps in the interior. Find the three possible perimeters of the rectangle 2

18 cm, 22 cm, and 38 cm

𝑥 2

30.5. If 𝑥 6 = 64 and(𝑥 − 2) = 𝑏, what is 𝑏2 + 𝑥?

3 or -2

60-second Questions, [5 points each]

60.1. Simplify: (𝑥 + 3)2 + (𝑥 + 2)3 − (𝑥 2 + 1)2 60.2. The area of a rectangle is the rectangle?

−𝒙𝟒 + 𝒙𝟑 + 𝟓𝒙𝟐 + 𝟏𝟖𝒙 + 𝟏𝟔

𝑥 2 −100

2𝑥+20

8

20

. If its length is

, what is the height of

𝟓𝒙−𝟓𝟎 𝟓 𝟒

𝟒

or

(𝒙 − 𝟏𝟎)

2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL) GRADE

8

4

60.3. Simplify the complex rational expression:

4− 2 𝑦 2

2+𝑦

60.4. Two vehicles travelled 𝑥 + 4 kilometers. The first vehicle travelled for 𝑥−4 𝑥 2 − 16 hours while the second travelled for 2 hours. How much greater is the second vehicle’s speed than the first? 60.5. If 𝑥 + 𝑦 = 4 and 𝑥 2 + 𝑦 2 = 10, what is the value of 𝑥 4 + 𝑦 4 ?

𝟐𝒚 − 𝟐 𝒚

𝟐𝒙 + 𝟑 𝒙−𝟒

82

Clincher Questions

C1. Give the factors of the trinomial 𝑥 2 + 9𝑥 − 22. C2. The area of a rectangle is 2𝑥 2 + 𝑥 − 3 while its width 𝑥 − 1. How much longer is its length than its width? 3−2 +2−3

−1

(𝒙 + 𝟏𝟏)(𝒙 − 𝟐)

𝒙+𝟒 𝟏 𝟏𝟕

C3. Evaluate the expression: (2−3 −3−2 ) . Do-or-Die Question

DOD1. One of the factors of 2𝑎2 + 5𝑎 − 12 is 𝑎 + 4. What is the other factor?

𝟐𝒂 − 𝟑

2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL) GRADE

8

2016 DIVISION FESTIVAL OF TALENTS

Category B:

MATH QUIZ (Team-Orals) (Quizmaster’s Copy)

GRADE 8

15-second Questions [2 points each] 15.1. Factor out completely the polynomial, 5𝑥 3 + 20𝑥 2 + 20𝑥. 15.2. What is the expanded form of the expression, 2(𝑥 + 𝑦)3 ? 15.3. If 9𝑚2 + 𝑘 + 49 is a perfect square trinomial, what expression should replace 𝑘? 15.4. What is the product when the expression

12𝑥 𝑦2

is multiplied to

𝑥𝑦 3 12

?

15.5. For which values of 𝑥 is the relation, 𝑓(𝑥) = √𝑥 + 1 defined? 15.6. What is the slope of line of the equation 7𝑥 − 3𝑦 = 5? 15.7. Given 𝑦 = 3𝑥 − 2, what is the value of 𝑥 if 𝑦 = −5? 15.8. What is the slope of the line perpendicular to the graph of 𝑥 + 5𝑦 = −12 15.9. Divide 6𝑥 5 𝑦 + 3𝑥 3 𝑦 + 9𝑥𝑦 by 3𝑥𝑦. 15.10. A system of equation is composed of two linear equations whose graphs are parallel. How many solutions does the system of equations have? 30-second Questions, [3 points each] 30.1. If the x-intercept of 3𝑥 − 2𝑦 = 12 is 𝑎 and its y-intercept is 𝑏, what is 3𝑎 − 2𝑏 equal to? 30.2. Solve the system of linear equations, 3𝑥 + 2𝑦 = −4 { 2𝑥 − 𝑦 = −12 30.3. Find the area of the figure.

𝟐𝒙 + 𝟔 𝟐𝒙

𝒙+𝟖

2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL) GRADE

8

30.4. Eighteen 1 𝑐𝑚 × 1 𝑐𝑚 square tiles are arranged to form a rectangle with no overlaps and without leaving gaps in the interior. Find the three possible perimeters of the rectangle 2

𝑥 2

30.5. If 𝑥 6 = 64 and(𝑥 − 2) = 𝑏, what is 𝑏 2 + 𝑥? 60-second Questions, [5 points each] 60.1. Simplify: (𝑥 + 3)2 + (𝑥 + 2)3 − (𝑥 2 + 1)2 60.2. The area of a rectangle is rectangle?

𝑥 2 −100 8

. If its length is

2𝑥+20 20

, what is the height of the

4

60.3. Simplify the complex rational expression:

4− 2 𝑦 2 𝑦

2+

.

4 2 Re: The quantity of 4 minus 2 all over the quantity of 2 plus 𝑦 𝑦 60.4. Two vehicles travelled 𝑥 + 4 kilometers. The first vehicle travelled for 𝑥−4 𝑥 2 − 16 hours while the second travelled for 2 hours. How much greater is the second vehicle’s speed than the first? 60.5. If 𝑥 + 𝑦 = 4 and 𝑥 2 + 𝑦 2 = 10, what is the value of 𝑥 4 + 𝑦 4 ?

Clincher Questions C1. Give the factors of the trinomial 𝑥 2 + 9𝑥 − 22. C2. The area of a rectangle is 2𝑥 2 + 𝑥 − 3 while its width 𝑥 − 1. How much longer is its length than its width? C3. Evaluate the expression: (

3−2 +2−3 2−3 −3−2

−1

)

.

Do-or-Die Question DOD1. One of the factors of 2𝑎2 + 5𝑎 − 12 is 𝑎 + 4. What is the other factor?

2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL) GRADE

8