Germany · Klasse 11 · Practice Sheet 22

1. 1.

   Find the population standard deviation of: 16, 20, 3, 12, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Solve using the quadratic formula: x² + 11x + 30 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A triangle has sides a = 14 cm and b = 10 cm with an included angle C = 120°. 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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4. 4.

   Find the momentum of a 37 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the population standard deviation of: 9, 4, 19, 6, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

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

   Formula:Quadratic Formula

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

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7. 7.

   A cylinder has radius 11 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the population standard deviation of: 10, 6, 17, 11, 8 (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 − 3x − 4 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A wave has frequency 782 Hz and wavelength 1.24 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A right-angled triangle has legs of 7 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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12. 12.

    Two masses 8,900 kg and 590 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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13. 13.

    Find the force needed to accelerate a 31 kg mass at 3.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the sum of the first 5 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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15. 15.

    Find the gravitational potential energy of a 11 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A 27 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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17. 17.

    Two masses 3,600 kg and 220 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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18. 18.

    A wave has frequency 636 Hz and wavelength 3.87 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    €1,600 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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20. 20.

    Find the momentum of a 4 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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