Russia · Grade 11 · Practice Sheet 38

1. 1.

   A force of 273 N acts on an area of 0.6 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 1 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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3. 3.

   Two masses 5,600 kg and 470 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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4. 4.

   Find the force needed to accelerate a 7 kg mass at 3.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   An object with initial velocity 15 m/s accelerates at 3.7 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A wave has frequency 463 Hz and wavelength 0.47 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the momentum of a 24 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A triangle has sides a = 7 cm and b = 14 cm with an included angle C = 60°. 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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9. 9.

   A current of 0.8 A flows through a 40 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the gravitational potential energy of a 27 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A population of 5,600 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A force of 159 N acts on an area of 6.7 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A cone has base radius 4 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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14. 14.

    A device runs at 217 V drawing 9.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A population of 1,800 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the force needed to accelerate a 49 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    An object has mass 77.4 g and volume 18 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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18. 18.

    A force of 388 N acts on an area of 6.8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 158 Hz and wavelength 4.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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