New Zealand · Year 12 · Practice Sheet 27

1. 1.

   Find the population standard deviation of: 4, 7, 17, 4, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A current of 3.3 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A device runs at 58 V drawing 7.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the gravitational potential energy of a 24 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the population standard deviation of: 17, 12, 6, 2, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A device runs at 135 V drawing 8.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Solve using the quadratic formula: x² + 3x − 10 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   Find the population standard deviation of: 10, 20, 6, 9, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Find the gravitational potential energy of a 38 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A triangle has sides a = 19 cm and b = 15 cm with an included angle C = 90°. 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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11. 11.

    Two masses 1,900 kg and 160 kg are 16 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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12. 12.

    Find the force needed to accelerate a 32 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    An object with initial velocity 11 m/s accelerates at 4.9 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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14. 14.

    A 6 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A device runs at 221 V drawing 9.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A force of 199 N acts on an area of 1.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A 25 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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18. 18.

    Find the force needed to accelerate a 39 kg mass at 2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A device runs at 48 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    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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