France · Classe 12 · Practice Sheet 17

1. 1.

   Find the population standard deviation of: 2, 15, 8, 4, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A cone has base radius 9 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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3. 3.

   Find the gravitational potential energy of a 14 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 251 Hz and wavelength 2.98 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Two masses 1,000 kg and 410 kg are 2 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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6. 6.

   A wave has frequency 197 Hz and wavelength 3.4 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A force of 268 N acts on an area of 1.7 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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8. 8.

   In a triangle, a = 18, b = 17 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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9. 9.

   Find the momentum of a 22 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A cone has base radius 6 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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11. 11.

    A triangle has sides a = 10 cm and b = 18 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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12. 12.

    A force of 50 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A current of 7.5 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A force of 211 N acts on an area of 3.6 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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15. 15.

    Find the momentum of a 13 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    An object with initial velocity 9 m/s accelerates at 3 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the momentum of a 12 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Two masses 8,800 kg and 790 kg are 10 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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19. 19.

    A cone has base radius 7 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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20. 20.

    Find the population standard deviation of: 4, 14, 17, 12, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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