Chile · Grado 12 · Practice Sheet 11

1. 1.

   Find the momentum of a 25 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A wave has frequency 431 Hz and wavelength 3.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Two masses 8,300 kg and 570 kg are 20 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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4. 4.

   A triangle has sides a = 18 cm and b = 7 cm with an included angle C = 30°. 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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5. 5.

   A wave has frequency 172 Hz and wavelength 4.29 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A population of 3,800 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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7. 7.

   A triangle has sides a = 15 cm and b = 8 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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8. 8.

   Two masses 8,400 kg and 850 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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9. 9.

   A device runs at 157 V drawing 4.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the population standard deviation of: 11, 2, 16, 2, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Solve using the quadratic formula: x² + 0x − 25 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A wave has frequency 123 Hz and wavelength 2.98 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A body starts at 14 m/s and accelerates at 5.4 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    A force of 7 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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15. 15.

    Two masses 6,400 kg and 550 kg are 17 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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16. 16.

    A force of 49 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A population of 6,300 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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18. 18.

    In a triangle, a = 14, b = 15 and the included angle C = 40°. 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.

    A triangle has sides a = 17 cm and b = 16 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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20. 20.

    Find the momentum of a 18 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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