Ukraine · Grade 12 · Practice Sheet 27

1. 1.

   A wave has frequency 807 Hz and wavelength 3.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the force needed to accelerate a 22 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   An object with initial velocity 8 m/s accelerates at 4.5 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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4. 4.

   A device runs at 165 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A body starts at 19 m/s and accelerates at 1.5 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the population standard deviation of: 14, 17, 18, 4, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A wave has frequency 387 Hz and wavelength 2.68 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Solve using the quadratic formula: x² − 9x + 20 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the sum of the first 4 terms of a geometric series with first term a = 7 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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10. 10.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 7 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

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

    Formula:Quadratic Formula

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

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12. 12.

    Find the momentum of a 30 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Two masses 6,400 kg and 470 kg are 8 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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14. 14.

    A force of 11 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the momentum of a 16 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the population standard deviation of: 10, 20, 5, 9, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    In a triangle, a = 12, b = 18 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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18. 18.

    A body starts at 16 m/s and accelerates at 5.2 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A wave has frequency 342 Hz and wavelength 1.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A 37 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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