Norway · Grade 12 · Practice Sheet 10

1. 1.

   Find the gravitational potential energy of a 7 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   An object with initial velocity 11 m/s accelerates at 3.8 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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3. 3.

   Find the sum of the first 7 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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4. 4.

   Find the gravitational potential energy of a 9 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A cone has base radius 6 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

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

   Formula:Sum of a Geometric Series

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

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7. 7.

   A body starts at 15 m/s and accelerates at 3.8 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the gravitational potential energy of a 41 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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10. 10.

    Find the population standard deviation of: 15, 15, 14, 12, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A wave has frequency 283 Hz and wavelength 3.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the momentum of a 31 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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14. 14.

    A device runs at 8 V drawing 4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A wave has frequency 156 Hz and wavelength 1.12 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A device runs at 17 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A current of 0.7 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the force needed to accelerate a 19 kg mass at 7.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A triangle has sides a = 16 cm and b = 7 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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20. 20.

    A body starts at 0 m/s and accelerates at 4.3 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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