Greece · Grade 11 · Practice Sheet 42

1. 1.

   Two masses 7,400 kg and 270 kg are 19 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.

   A cylinder has radius 11 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A wave has frequency 118 Hz and wavelength 4.88 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A force of 76 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   An object has mass 42.9 g and volume 11 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the momentum of a 42 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the sum of the first 5 terms of a geometric series with first term a = 4 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 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   Find the population standard deviation of: 16, 16, 12, 2, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 2 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    A body starts at 1 m/s and accelerates at 3.8 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A wave has frequency 666 Hz and wavelength 3.92 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the sum of the first 5 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A force of 484 N acts on an area of 4.5 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the sum of the first 4 terms of a geometric series with first term a = 7 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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17. 17.

    A population of 8,000 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A current of 1.4 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    An object has mass 48 g and volume 15 cm³. Find its density.

    Formula:Density

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

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20. 20.

    An object with initial velocity 0 m/s accelerates at 4.4 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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