Czechia · Grade 11 · Practice Sheet 27

1. 1.

   Find the gravitational potential energy of a 48 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A force of 78 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A wave has frequency 317 Hz and wavelength 1.98 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A cylinder has radius 2 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   Two masses 7,400 kg and 120 kg are 19 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 force of 27 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Two masses 8,100 kg and 150 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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8. 8.

   Find the force needed to accelerate a 29 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 126 N acts on an area of 1.5 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the force needed to accelerate a 18 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 6 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    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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13. 13.

    A cone has base radius 4 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    Find the population standard deviation of: 11, 8, 14, 17, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A cylinder has radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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18. 18.

    A force of 71 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A current of 6.2 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the gravitational potential energy of a 5 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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