Spain · Grado 11 · Practice Sheet 27

1. 1.

   A wave has frequency 100 Hz and wavelength 1.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Find the momentum of a 33 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A right-angled triangle has legs of 12 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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5. 5.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 8 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A population of 3,600 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   Find the force needed to accelerate a 32 kg mass at 7.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A population of 3,300 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   An object has mass 161.2 g and volume 31 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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10. 10.

    A force of 54 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the population standard deviation of: 12, 17, 8, 19, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A force of 16 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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13. 13.

    A 37 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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14. 14.

    A cylinder has radius 12 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    An object has mass 310.8 g and volume 37 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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16. 16.

    A current of 6.5 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the momentum of a 24 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the gravitational potential energy of a 39 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A force of 106 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the gravitational potential energy of a 50 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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