Morocco · Grade 12 · Practice Sheet 1

1. 1.

   Find the momentum of a 56 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   In a triangle, a = 9, b = 16 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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3. 3.

   Find the force needed to accelerate a 48 kg mass at 1.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   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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5. 5.

   Find the force needed to accelerate a 43 kg mass at 7.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 6 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A force of 101 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A force of 39 N acts on an area of 8.1 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    An object with initial velocity 3 m/s accelerates at 1.4 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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11. 11.

    Find the gravitational potential energy of a 17 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A device runs at 44 V drawing 6.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 20 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A cone has base radius 5 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    Solve using the quadratic formula: x² − 1x − 6 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Two masses 4,300 kg and 290 kg are 10 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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17. 17.

    An object with initial velocity 4 m/s accelerates at 1.2 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A wave has frequency 425 Hz and wavelength 0.36 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the momentum of a 54 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the gravitational potential energy of a 12 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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