Lebanon · Grade 12 · Practice Sheet 13

1. 1.

   Two masses 7,100 kg and 230 kg are 11 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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2. 2.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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3. 3.

   A device runs at 7 V drawing 8.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A force of 212 N acts on an area of 3.7 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A wave has frequency 273 Hz and wavelength 4.31 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Two masses 6,200 kg and 270 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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7. 7.

   Find the momentum of a 16 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 305 N acts on an area of 5.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A triangle has sides a = 5 cm and b = 14 cm with an included angle C = 90°. 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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10. 10.

    A 37 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Solve using the quadratic formula: x² + 4x + 3 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    Find the population standard deviation of: 20, 17, 2, 13, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A force of 82 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    An object with initial velocity 3 m/s accelerates at 3.4 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    Find the force needed to accelerate a 41 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the momentum of a 16 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    LL 2,200 is invested at 4% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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18. 18.

    In a triangle, a = 7, b = 16 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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19. 19.

    Find the momentum of a 17 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

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

    Formula:Sum of an Arithmetic Series

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

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