Czechia · Grade 11 · Practice Sheet 22

1. 1.

   Two masses 4,000 kg and 740 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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2. 2.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 12 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   Solve using the quadratic formula: x² + 2x + 0 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   An object with initial velocity 0 m/s accelerates at 2.3 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   Kč 1,700 is invested at 6% compound interest per annum for 5 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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6. 6.

   An object with initial velocity 3 m/s accelerates at 4.3 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   In a triangle, a = 10, b = 15 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   Find the population standard deviation of: 10, 9, 4, 11, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Solve using the quadratic formula: x² − 9x + 20 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    Find the force needed to accelerate a 53 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 33 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A wave has frequency 866 Hz and wavelength 1.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    An object has mass 104 g and volume 20 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A cylinder has radius 2 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A current of 4 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the momentum of a 3 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A wave has frequency 595 Hz and wavelength 0.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A device runs at 124 V drawing 5.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

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

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A device runs at 125 V drawing 3.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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