Morocco · Grade 12 · Practice Sheet 17

1. 1.

   Find the sum of the first 5 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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2. 2.

   In a triangle, a = 8, b = 5 and the included angle C = 110°. 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.

   A 25 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A device runs at 188 V drawing 3.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A force of 49 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A force of 333 N acts on an area of 7.6 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 112 Hz and wavelength 4.24 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A current of 7 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A body starts at 7 m/s and accelerates at 4.5 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Two masses 6,300 kg and 250 kg are 3 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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11. 11.

    A body starts at 13 m/s and accelerates at 5.3 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A force of 281 N acts on an area of 2.7 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    An object with initial velocity 13 m/s accelerates at 3.3 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A cone has base radius 6 cm and height 18 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.

    Find the population standard deviation of: 4, 6, 8, 4, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A force of 39 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Two masses 6,500 kg and 110 kg are 16 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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18. 18.

    A force of 153 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Two masses 3,600 kg and 650 kg are 14 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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20. 20.

    A 21 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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