Italy · Classe 12 · Practice Sheet 8

1. 1.

   Find the population standard deviation of: 16, 6, 6, 3, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Find the gravitational potential energy of a 22 kg object raised 8 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A current of 4.1 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A population of 2,600 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   A current of 2.6 A flows through a 30 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A force of 358 N acts on an area of 1.9 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   An object with initial velocity 0 m/s accelerates at 4.3 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A force of 73 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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10. 10.

    Find the gravitational potential energy of a 42 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the force needed to accelerate a 15 kg mass at 4.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A device runs at 63 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the sum of the first 3 terms of a geometric series with first term a = 2 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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15. 15.

    A wave has frequency 728 Hz and wavelength 3.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A 28 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A population of 7,900 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A wave has frequency 491 Hz and wavelength 3.07 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    A body starts at 11 m/s and accelerates at 5.8 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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