332955715 math quiz to g8

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

GRADE 8

2016 DIVISION FESTIVAL OF TALENTS

MATH QUIZ (Team-Orals) (Judges’ Copy)

15-second Questions [2 points each]

15.1. Factor out completely the polynomial, 5𝑥³+ 20𝑥²+ 20𝑥. 𝟓𝒙(𝒙 + 𝟐)(𝒙 + 𝟐)

or 𝟓𝒙(𝒙 + 𝟐)^𝟐

15.2. What is the expanded form of the expression, 2(𝑥 + 𝑦)³? _{+ 𝟐𝒚}^𝟐𝒙^𝟑^{+ 𝟔𝒙}𝟑 ^𝟐^{𝒚 + 𝟔𝒙𝒚}^𝟐

15.3. If 9𝑚²+ 𝑘 + 49 is a perfect square trinomial, what expression should

replace 𝑘? 42m

15.4. What is the product when the expression ^12𝑥

𝑦² is multiplied to ^𝑥𝑦³

12? 𝒙^𝟐𝒚

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 6𝑥⁵𝑦 + 3𝑥³𝑦 + 9𝑥𝑦 by 3𝑥𝑦. ^𝟐𝒙^𝟒^{+ 𝒙}^𝟐^{+ 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? 24

30.2. Solve the system of linear equations,

{3𝑥 + 2𝑦 = −4 2𝑥 − 𝑦 = −12

(-4, 4) or 𝒙 = −𝟒; 𝒚 = 𝟒 30.3. Find the area of the figure below.

𝟓𝒙^𝟐+ 𝟐𝟎𝒙

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 18 cm, 22 cm, and

38 cm

30.5. If 𝑥⁶ = 64 and(²

𝑥−^𝑥

2)² = 𝑏, what is 𝑏² + 𝑥? 3 or -2

60.1. Simplify: (𝑥 + 3)²+ (𝑥 + 2)³− (𝑥²+ 1)² −𝒙^𝟒+ 𝒙^𝟑+ 𝟓𝒙^𝟐 + 𝟏𝟖𝒙 + 𝟏𝟔

60.2. The area of a rectangle is ^𝑥²⁻¹⁰⁰

8 . If its length is ^2𝑥+20

20 , what is the height of the rectangle?

𝟓𝒙−𝟓𝟎 𝟒 or

𝟓

𝟒(𝒙 − 𝟏𝟎) Category B:

GRADE 8

𝟐𝒙 + 𝟔

𝟐𝒙 𝒙 + 𝟖

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GRADE 8

60.3. Simplify the complex rational expression:

4−⁴

𝑦2

2+²

𝑦

𝟐𝒚 − 𝟐 𝒚

60.4. Two vehicles travelled 𝑥 + 4 kilometers. The first vehicle travelled for 𝑥²− 16 hours while the second travelled for ^𝑥−4

2 hours. How much greater is the second vehicle’s speed than the first?

𝟐𝒙 + 𝟑 𝒙 − 𝟒

60.5. If 𝑥 + 𝑦 = 4 and 𝑥²+ 𝑦² = 10, what is the value of 𝑥⁴+ 𝑦⁴? 82 Clincher Questions

C1. Give the factors of the trinomial 𝑥²+ 9𝑥 − 22.

(𝒙 + 𝟏𝟏)(𝒙 − 𝟐)

C2. The area of a rectangle is 2𝑥²+ 𝑥 − 3 while its width 𝑥 − 1. How much

longer is its length than its width? 𝒙 + 𝟒

C3. Evaluate the expression: (³⁻²⁺²⁻³

2⁻³−3⁻²)⁻¹. 𝟏

𝟏𝟕 Do-or-Die Question

DOD1. One of the factors of 2𝑎²+ 5𝑎 − 12 is 𝑎 + 4. What is the other factor? ^{𝟐𝒂 − 𝟑}

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GRADE 8

2016 DIVISION FESTIVAL OF TALENTS

MATH QUIZ (Team-Orals) (Quizmaster’s Copy) 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 9𝑚

²

+ 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

^𝑥𝑦³

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?

30.1. 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.

Category B:

GRADE 8

𝟐𝒙 + 𝟔

𝟐𝒙 𝒙 + 𝟖

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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

30.5. If 𝑥

⁶

= 64 and(

²

𝑥

−

^𝑥

2

)

²

= 𝑏, what is 𝑏

²

+ 𝑥?

60.1. Simplify: (𝑥 + 3)

²

+ (𝑥 + 2)

³

− (𝑥

²

+ 1)

²

60.2. The area of a rectangle is

^𝑥²⁻¹⁰⁰

8

. If its length is

^2𝑥+20

20

, what is the height of the rectangle?

60.3. Simplify the complex rational expression:

4−

⁴

𝑦2

2+

²

𝑦

.

Re: The quantity of 4 minus 4

𝑦

²

all over the quantity of 2 plus 2 𝑦

60.4. Two vehicles travelled 𝑥 + 4 kilometers. The first vehicle travelled for 𝑥

²

− 16 hours while the second travelled for

^𝑥−4

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 2𝑎

²

+ 5𝑎 − 12 is 𝑎 + 4. What is the other factor?