Russia · Grade 12 · Practice Sheet 37

1. 1.

   Find the momentum of a 23 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Two masses 7,500 kg and 780 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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3. 3.

   In a triangle, a = 15, b = 14 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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4. 4.

   A current of 4.7 A flows through a 5 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the population standard deviation of: 15, 17, 2, 2, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A body starts at 12 m/s and accelerates at 3.6 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   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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8. 8.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A population of 2,800 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    Find the momentum of a 59 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A device runs at 222 V drawing 5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A wave has frequency 815 Hz and wavelength 1.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    ₽2,200 is invested at 8% compound interest per annum for 3 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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14. 14.

    Two masses 6,000 kg and 600 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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15. 15.

    Find the momentum of a 35 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A triangle has sides a = 12 cm and b = 8 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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17. 17.

    A device runs at 125 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the force needed to accelerate a 31 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A force of 10 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the gravitational potential energy of a 13 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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