New Zealand · Year 12 · Practice Sheet 16

1. 1.

   Find the gravitational potential energy of a 46 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A wave has frequency 400 Hz and wavelength 1.09 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Two masses 6,100 kg and 150 kg are 4 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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4. 4.

   Find the force needed to accelerate a 30 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the population standard deviation of: 9, 12, 11, 5, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   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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7. 7.

   A cone has base radius 5 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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8. 8.

   A device runs at 9 V drawing 2.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A force of 372 N acts on an area of 4.1 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A cone has base radius 2 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Solve using the quadratic formula: x² − 6x + 5 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    $4,000 is invested at 8% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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13. 13.

    A device runs at 58 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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15. 15.

    A current of 5.4 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A force of 80 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Solve using the quadratic formula: x² − 2x + 0 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A force of 95 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A body starts at 3 m/s and accelerates at 4.7 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A cone has base radius 5 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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