Spain · Grado 12 · Practice Sheet 18

1. 1.

   A wave has frequency 583 Hz and wavelength 3.03 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A force of 114 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A wave has frequency 643 Hz and wavelength 2.44 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 5 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   Find the force needed to accelerate a 21 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A wave has frequency 390 Hz and wavelength 4.42 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A force of 112 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   An object with initial velocity 0 m/s accelerates at 1.6 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 4 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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10. 10.

    A body starts at 17 m/s and accelerates at 3.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the population standard deviation of: 4, 6, 19, 16, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    In a triangle, a = 14, b = 10 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A body starts at 18 m/s and accelerates at 4.5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    An object with initial velocity 2 m/s accelerates at 4.1 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the momentum of a 26 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A cone has base radius 5 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    Find the momentum of a 38 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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