South Korea · Grade 11 · Practice Sheet 7

1. 1.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A wave has frequency 103 Hz and wavelength 1.24 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the force needed to accelerate a 55 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Two masses 3,900 kg and 470 kg are 14 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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5. 5.

   A wave has frequency 647 Hz and wavelength 3.72 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the force needed to accelerate a 40 kg mass at 3.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A 6 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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8. 8.

   Find the population standard deviation of: 7, 18, 18, 9, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A population of 8,200 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    Find the population standard deviation of: 18, 6, 18, 4, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Find the force needed to accelerate a 3 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A current of 5.4 A flows through a 12 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    In a triangle, a = 9, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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14. 14.

    A wave has frequency 108 Hz and wavelength 0.63 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A 2 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    An object with initial velocity 13 m/s accelerates at 5 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A force of 28 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A wave has frequency 297 Hz and wavelength 1.11 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A 30 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Find the population standard deviation of: 12, 20, 16, 3, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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