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
