Poland · Klasa 12 · Practice Sheet 20

1. 1.

   A wave has frequency 864 Hz and wavelength 2.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the sum of the first 6 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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3. 3.

   Find the momentum of a 45 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the population standard deviation of: 20, 4, 14, 14, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A triangle has sides a = 13 cm and b = 19 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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6. 6.

   A device runs at 42 V drawing 9.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Solve using the quadratic formula: x² − 7x + 12 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A body starts at 13 m/s and accelerates at 3 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   An object with initial velocity 4 m/s accelerates at 3.2 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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10. 10.

    A cone has base radius 4 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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11. 11.

    Find the gravitational potential energy of a 19 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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13. 13.

    Find the momentum of a 45 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    In a triangle, a = 5, b = 12 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    An object with initial velocity 9 m/s accelerates at 4.1 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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16. 16.

    A device runs at 174 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the force needed to accelerate a 2 kg mass at 4.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the momentum of a 8 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 332 N acts on an area of 7.9 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

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

    Formula:Momentum

    $p = mv$

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