Norway · Grade 12 · Practice Sheet 24

1. 1.

   Find the force needed to accelerate a 48 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A body starts at 9 m/s and accelerates at 1.9 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A triangle has sides a = 14 cm and b = 14 cm with an included angle C = 45°. 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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4. 4.

   An object with initial velocity 14 m/s accelerates at 1.5 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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5. 5.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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6. 6.

   Find the force needed to accelerate a 16 kg mass at 0.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 108 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A 37 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A force of 22 N moves an object 4 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A body starts at 3 m/s and accelerates at 3.7 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A triangle has sides a = 5 cm and b = 20 cm with an included angle C = 120°. 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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12. 12.

    Find the population standard deviation of: 20, 13, 5, 8, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    Find the gravitational potential energy of a 46 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A device runs at 233 V drawing 6.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A wave has frequency 191 Hz and wavelength 3.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A body starts at 14 m/s and accelerates at 4.2 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 261 N acts on an area of 2.3 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Find the gravitational potential energy of a 9 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 6 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A triangle has sides a = 5 cm and b = 14 cm with an included angle C = 45°. 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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