Sweden · Grade 12 · Practice Sheet 6

1. 1.

   Two masses 8,300 kg and 160 kg are 18 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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2. 2.

   Find the force needed to accelerate a 19 kg mass at 1.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the gravitational potential energy of a 40 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A body starts at 18 m/s and accelerates at 4.9 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   In a triangle, a = 14, b = 12 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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6. 6.

   Find the population standard deviation of: 17, 9, 4, 8, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the momentum of a 22 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A 38 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Two masses 7,500 kg and 300 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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10. 10.

    A force of 11 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    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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12. 12.

    A device runs at 154 V drawing 6.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

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

    Formula:Quadratic Formula

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

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14. 14.

    kr 2,900 is invested at 6% compound interest per annum for 4 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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15. 15.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 10 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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16. 16.

    A force of 120 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A wave has frequency 492 Hz and wavelength 4.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A force of 271 N acts on an area of 0.7 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 878 Hz and wavelength 3.89 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A current of 0.7 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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