Egypt · Grade 12 · Practice Sheet 30

1. 1.

   Find the force needed to accelerate a 31 kg mass at 7.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   An object with initial velocity 9 m/s accelerates at 4.4 m/s² for 3 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: 14, 2, 5, 19, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A body starts at 18 m/s and accelerates at 1 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A device runs at 36 V drawing 2.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A triangle has sides a = 12 cm and b = 13 cm with an included angle C = 60°. 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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7. 7.

   Find the momentum of a 33 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A cone has base radius 4 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   Two masses 8,000 kg and 440 kg are 5 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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10. 10.

    In a triangle, a = 8, b = 7 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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11. 11.

    A wave has frequency 35 Hz and wavelength 4.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A cone has base radius 3 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    A triangle has sides a = 17 cm and b = 20 cm with an included angle C = 60°. 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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14. 14.

    A device runs at 67 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the momentum of a 51 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the population standard deviation of: 14, 17, 10, 4, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    Find the force needed to accelerate a 9 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A force of 59 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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20. 20.

    A body starts at 15 m/s and accelerates at 5.1 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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