Grade 9 Math Quiz for Team Oral Presentations

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1 | P a g e o f 2 2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL) GRADE 9

2016 DIVISION FESTIVAL OF TALENTS

MATH QUIZ (Team-Orals) (Judges’ Copy)

15-second Questions [2 points each]

15.1. What is the sum of the roots of 𝑥²− 2015𝑥 − 2016 = 0? 2015 15.2. Transform the equation ^𝑥

2− ¹

5𝑥 = 1 into its corresponding quadratic

equation of the form 𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0 ^𝟓𝒙

𝟐− 𝟏𝟎𝒙 − 𝟐 = 𝟎

15.3. What are the roots of the quadratic equation, 𝑥²+ 𝑥 − 56 = 0? -8, and 7 15.4. In parallelogram QRST, the measurement of ∠𝑄 is twice the measurement

of ∠𝑅. What is the difference between the measurements of ∠𝑆 and ∠𝑇? 60 degrees 15.5. The legs of a right triangle measure 5 and 12 inches. What is its

perimeter? 30 inches

15.6. The solutions of a quadratic equation are the first two prime numbers.

Give the quadratic equation in standard form. ^𝒙^𝟐− 𝟓𝒙 + 𝟔 = 𝟎

15.7. If 𝑎 varies directly as 𝑏 and 𝑎 = 3 when 𝑏 = 14, find 𝑎 when 𝑏 = 42. 𝒂 = 𝟗 15.8. If 𝑦 varies directly as the square of 𝑥, by how many percent will y increase

if 𝑥 is increased by 50 percent? 125%

15.9. What constant must be added to 𝑥²+ 7𝑥 to make it a perfect square trinomial?

𝟒𝟗

15.10. What is the range of 𝑦 = −2(𝑥 − 2)²+ 5? 𝒚 ≤ 𝟓 𝟒

30-second Questions, [3 points each]

30.1. Simplify (²⁻¹⁺³⁻¹

2⁻¹−3⁻¹)⁻¹. 𝟏

𝟓 30.2. When the function 𝑓(𝑥) = 2𝑥²− 𝑘𝑥 + 3 is evaluated at 𝑓(−2), the value

obtained is 15. What is the value of k? 𝒌 = 𝟐

30.3. What are the coordinates of the turning point of the graph of 𝑦 = 2𝑥²−

4𝑥 + 1? (𝟏, −𝟏)

30.4. The quotient of two numbers is ⁵

3 and their product is 240. What are the

numbers? 12 and 20

30.5. A tank can be filled by one pipe in 10 hours, by another in 12 hours, and by a third in 15 hours. How many hours will it take the three pipes all open together to fill the tank?

4 hours

60.1. Matthew can finish a job 3 hours more than it takes Kevin. If they work together, they can finish the same job in 2 hours. How long would it take

Matthew to finish the job alone? 6 hours

60.2. Solve the radical equation: 2√𝑥 + 5³ = 4√2𝑥 − 15³ . 𝟐𝟓 60.3. How many factors of 2⁹⁹⁹ are greater than 2 016? 989 𝟑

Category B:

GRADE 9

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60.4. A plastic storage box in the shape of a rectangular prism has a length of 𝑥 + 3, a width of 𝑥 − 4 and a height of 5. Represent the surface area of the

box as a trinomial in terms of 𝑥. ^𝟐𝒙^𝟐^{+ 𝟏𝟖𝒙 − 𝟑𝟒}

60.5. The sum of the areas of two similar polygons is 65 square units. If their perimeters are 12 units and 18 units, respectively, find the area of the

larger polygon. 45 sq units

Clincher Questions

C1. A certain number when divided by 19 gives 18 as a quotient and a

remainder of 16. What is the number? 358

C2. The sum of two numbers is 22 and the sum of their squares is 250. What is

the product of the two numbers? 117

C3. What is the equation of the parabola that passes through the points (1,-1),

(0,-3), and (2,-3)? ^−𝟐𝒙^𝟐+ 𝟒𝒙 − 𝟑 = 𝟎

Do-or-Die Question

DOD1. Solve the quadratic inequality 2𝑥²+ 7𝑥 ≤ −6 _{−𝟐 ≤ 𝒙 ≤}^−𝟑

𝟐

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2016 DIVISION FESTIVAL OF TALENTS

MATH QUIZ (Team-Orals) (Quizmaster’s Copy) 15-second Questions [2 points each]

15.1. What is the sum of the roots of 𝑥²− 2015𝑥 − 2016 = 0?

15.2. Transform the equation ^𝑥₂− ¹

5𝑥= 1 into its corresponding quadratic equation of the form 𝑎𝑥²+ 𝑏𝑥 + 𝑐 = 0

15.3. What are the roots of the quadratic equation, 𝑥²+ 𝑥 − 56 = 0?

15.4. In parallelogram QRST, the measurement of ∠𝑄 is twice the measurement of

∠𝑅. What is the difference between the measurements of ∠𝑆 and ∠𝑇?

15.5. The legs of a right triangle measure 5 and 12 inches. What is its perimeter?

15.6. The solutions of a quadratic equation are the first two prime numbers. Give the quadratic equation in standard form.

15.7. If 𝑎 varies directly as 𝑏 and 𝑎 = 3 when 𝑏 = 14, find 𝑎 when 𝑏 = 42.

15.8. If 𝑦 varies directly as the square of 𝑥, by how many percent will y increase if 𝑥 is increased by 50 percent?

15.9. What constant must be added to 𝑥²+ 7𝑥 to make it a perfect square trinomial?

15.10. What is the range of 𝑦 = −2(𝑥 − 2)²+ 5?

30.1. Simplify

(

²⁻¹⁺³⁻¹

2⁻¹−3⁻¹

)

−1

.

30.2. When the function 𝑓(𝑥) = 2𝑥²− 𝑘𝑥 + 3 is evaluated at 𝑓(−2), the value obtained is 15. What is the value of k?

30.3. What are the coordinates of the turning point of the graph of 𝑦 = 2𝑥²− 4𝑥 + 1?

Category B:

GRADE 9

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4 | P a g e o f 2 2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL) GRADE 9 30.4. The quotient of two numbers is ⁵

3 and their product is 240. What are the numbers?

30.5. A pipe can be filled by one pipe in 10 hours, by another in 12 hours, and by a third in 15 hours. How many hours will it take the three pipes all open

together to fill the tank?

60.1. Matthew can finish a job 3 hours more than it takes Kevin. If they work together, they can finish the same job in 2 hours. How long would it take Matthew to finish the job alone?

60.2. Solve the radical equation: 2 √𝑥 + 5³ = 4 √2𝑥 − 15³ . 60.3. How many factors of 2⁹⁹⁹ are greater than 2 016?

60.4. A plastic storage box in the shape of a rectangular prism has a length of 𝑥 + 3, a width of 𝑥 − 4 and a height of 5. Represent the surface area of the box as a trinomial in terms of 𝑥.

60.5. The sum of the areas of two similar polygons is 65 square units. If their perimeters are 12 units and 18 units, respectively, find the area of the larger polygon.

Clincher Questions

C1. A certain number when divided by 19 gives 18 as a quotient and a remainder of 16. What is the number?

C2. The sum of two numbers is 22 and the sum of their squares is 250. What is the product of the two numbers?

C3. What is the equation of the parabola that passes through the points (1,-1), (0,- 3), and (2,-3)?

Do-or-Die Question

DOD1. Solve the quadratic inequality 2𝑥² + 7𝑥 ≤ −6