Australia · Year 12 · Practice Sheet 5

1. 1.

   A cone has base radius 5 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Solve using the quadratic formula: x² − 5x + 4 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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4. 4.

   A device runs at 17 V drawing 4.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Two masses 8,300 kg and 110 kg are 15 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 triangle has sides a = 10 cm and b = 13 cm with an included angle C = 45°. 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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7. 7.

   Find the momentum of a 1 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 236 N acts on an area of 4.1 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   An object with initial velocity 12 m/s accelerates at 2.3 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    A current of 8 A flows through a 6 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    Solve using the quadratic formula: x² − 5x + 4 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A current of 6 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    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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15. 15.

    A device runs at 11 V drawing 9.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the momentum of a 33 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A force of 107 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    An object with initial velocity 5 m/s accelerates at 1.7 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    Find the momentum of a 51 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the population standard deviation of: 10, 2, 7, 2, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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