Norway · Grade 12 · Practice Sheet 38

1. 1.

   A wave has frequency 454 Hz and wavelength 4.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   An object with initial velocity 9 m/s accelerates at 3.4 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   Find the population standard deviation of: 15, 20, 7, 9, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the gravitational potential energy of a 14 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A wave has frequency 385 Hz and wavelength 0.73 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the gravitational potential energy of a 21 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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8. 8.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 8 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A current of 6 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    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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11. 11.

    A body starts at 8 m/s and accelerates at 5.6 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A force of 15 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the force needed to accelerate a 15 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A body starts at 18 m/s and accelerates at 5.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the force needed to accelerate a 51 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    In a triangle, a = 16, b = 10 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    Two masses 4,600 kg and 320 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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18. 18.

    Find the population standard deviation of: 19, 10, 3, 20, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 12 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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20. 20.

    Find the population standard deviation of: 19, 11, 12, 2, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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