math quiz to g9

2016 DIVISION FESTIVAL OF TALENTS

Category B:

MATH QUIZ (Team-Orals) (Judges’ Copy)

GRADE 9

15-second Questions [2 points each]

15.1. What is the sum of the roots of 𝑥 2 − 2015𝑥 − 2016 = 0? 𝑥

2015

1

15.2. Transform the equation 2 − 5𝑥 = 1 into its corresponding quadratic equation of the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 15.3. What are the roots of the quadratic equation, 𝑥 2 + 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 𝑥 2 + 7𝑥 to make it a perfect square trinomial? 15.10. What is the range of 𝑦 = −2(𝑥 − 2)2 + 5?

𝟓𝒙𝟐 − 𝟏𝟎𝒙 − 𝟐 = 𝟎

-8, and 7 60 degrees 30 inches 𝒙𝟐 − 𝟓𝒙 + 𝟔 = 𝟎

𝒂=𝟗 125% 𝟒𝟗 𝟒 𝒚≤𝟓

30-second Questions, [3 points each] 2−1 +3−1

𝟏 𝟓

−1

30.1. Simplify (2−1 −3−1 ) . 30.2. When the function 𝑓 (𝑥 ) = 2𝑥 2 − 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 = 2𝑥 2 − 4𝑥 + 1?

(𝟏, −𝟏)

5

30.4. The quotient of two numbers is 3 and their product is 240. What are the numbers? 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?

12 and 20 4 hours

60-second Questions, [5 points each]

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? 3

3

60.2. Solve the radical equation: 2 √𝑥 + 5 = 4√2𝑥 − 15. 60.3. How many factors of 2999 are greater than 2 016?

1|P age of 2

6 hours 𝟐𝟓 𝟑 989

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

9

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.

𝟐𝒙𝟐 + 𝟏𝟖𝒙 − 𝟑𝟒

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)?

−𝟐𝒙𝟐 + 𝟒𝒙 − 𝟑 = 𝟎

Do-or-Die Question

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

2|P age of 2

−𝟐 ≤ 𝒙 ≤

−𝟑 𝟐

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

9

2016 DIVISION FESTIVAL OF TALENTS

Category B:

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

GRADE 9

15-second Questions [2 points each] 15.1. What is the sum of the roots of 𝑥 2 − 2015𝑥 − 2016 = 0? 𝑥

1

15.2. Transform the equation 2 − 5𝑥 = 1 into its corresponding quadratic equation of the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 15.3. What are the roots of the quadratic equation, 𝑥 2 + 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 𝑥 2 + 7𝑥 to make it a perfect square trinomial? 15.10. What is the range of 𝑦 = −2(𝑥 − 2)2 + 5?

30-second Questions, [3 points each] 30.1.

−1 2−1+3−1 Simplify ( −1 −1) . 2 −3

30.2. When the function 𝑓 (𝑥) = 2𝑥 2 − 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 = 2𝑥 2 − 4𝑥 + 1?

3|P age of 2

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

9

5

30.4. The quotient of two numbers is 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-second Questions, [5 points each] 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? 3

3

60.2. Solve the radical equation: 2 √𝑥 + 5 = 4 √2𝑥 − 15. 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 2𝑥 2 + 7𝑥 ≤ −6

4|P age of 2

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

9