Ukraine · Grade 12 · Practice Sheet 45

1. 1.

   Find the force needed to accelerate a 14 kg mass at 5.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A population of 4,000 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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3. 3.

   Find the gravitational potential energy of a 12 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A device runs at 121 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the momentum of a 4 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the population standard deviation of: 8, 3, 11, 14, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A body starts at 12 m/s and accelerates at 2.8 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A wave has frequency 343 Hz and wavelength 2.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Two masses 8,100 kg and 330 kg are 2 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.

    An object with initial velocity 5 m/s accelerates at 2.9 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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11. 11.

    In a triangle, a = 9, b = 7 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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12. 12.

    A current of 1.1 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A cone has base radius 9 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

    A current of 6 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A force of 434 N acts on an area of 9.6 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Solve using the quadratic formula: x² + 6x + 8 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A device runs at 162 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    In a triangle, a = 5, b = 18 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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20. 20.

    Find the momentum of a 55 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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