Denmark · Grade 12 · Practice Sheet 31

1. 1.

   Find the gravitational potential energy of a 43 kg object raised 40 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A wave has frequency 620 Hz and wavelength 3.25 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A force of 252 N acts on an area of 8.9 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A cone has base radius 5 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   A current of 3.2 A flows through a 19 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Two masses 3,900 kg and 830 kg are 19 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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7. 7.

   Find the momentum of a 41 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Two masses 5,600 kg and 650 kg are 12 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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9. 9.

   A force of 34 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the population standard deviation of: 5, 3, 17, 4, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    kr 700 is invested at 3% compound interest per annum for 5 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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12. 12.

    A device runs at 73 V drawing 7.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A cone has base radius 11 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A body starts at 19 m/s and accelerates at 4.6 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A device runs at 125 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A body starts at 2 m/s and accelerates at 5.4 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    kr 2,800 is invested at 3% compound interest per annum for 5 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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18. 18.

    A current of 1.1 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A device runs at 153 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Solve using the quadratic formula: x² + 3x − 4 = 0.

    Formula:Quadratic Formula

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

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