Germany · Klasse 12 · Practice Sheet 6

1. 1.

   Two masses 1,600 kg and 590 kg are 20 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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2. 2.

   A population of 5,200 grows 8% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A force of 272 N acts on an area of 4.7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A triangle has sides a = 8 cm and b = 15 cm with an included angle C = 45°. 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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5. 5.

   A 39 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Find the population standard deviation of: 15, 10, 4, 5, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A force of 444 N acts on an area of 4.6 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   In a triangle, a = 12, b = 5 and the included angle C = 110°. 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.

   A wave has frequency 39 Hz and wavelength 0.57 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the momentum of a 57 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A force of 368 N acts on an area of 1.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A body starts at 9 m/s and accelerates at 1.5 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A device runs at 228 V drawing 5.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A wave has frequency 171 Hz and wavelength 3.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A body starts at 9 m/s and accelerates at 2.4 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    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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17. 17.

    Find the momentum of a 24 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the population standard deviation of: 7, 3, 4, 7, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    Find the gravitational potential energy of a 9 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A current of 0.9 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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