Hungary · Grade 11 · Practice Sheet 8

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A population of 9,000 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Two masses 3,700 kg and 380 kg are 7 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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4. 4.

   Find the momentum of a 27 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the force needed to accelerate a 17 kg mass at 4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A 27 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.

   Find the force needed to accelerate a 35 kg mass at 6.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the gravitational potential energy of a 23 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A force of 87 N acts on an area of 1.2 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A wave has frequency 607 Hz and wavelength 1.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the force needed to accelerate a 51 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A device runs at 228 V drawing 3.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A 8 kg object moves at 14 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the population standard deviation of: 2, 19, 4, 19, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the gravitational potential energy of a 22 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the sum of the first 8 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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18. 18.

    Find the momentum of a 1 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 307 N acts on an area of 8.4 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A cylinder has radius 2 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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