Romania · Grade 12 · Practice Sheet 29

1. 1.

   A wave has frequency 183 Hz and wavelength 4.87 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the momentum of a 59 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A wave has frequency 31 Hz and wavelength 1.08 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   An object with initial velocity 9 m/s accelerates at 2.7 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   A population of 3,000 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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6. 6.

   A 21 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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7. 7.

   Solve using the quadratic formula: x² + 0x − 4 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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8. 8.

   Find the force needed to accelerate a 20 kg mass at 7.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the population standard deviation of: 9, 2, 7, 12, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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10. 10.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 10 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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11. 11.

    Find the sum of the first 6 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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12. 12.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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13. 13.

    Find the gravitational potential energy of a 7 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A 9 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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15. 15.

    Find the gravitational potential energy of a 5 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A wave has frequency 568 Hz and wavelength 4.26 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A current of 2.3 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A 11 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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19. 19.

    A wave has frequency 409 Hz and wavelength 4.91 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Solve using the quadratic formula: x² − 5x − 6 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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