Germany · Klasse 11 · Practice Sheet 8

1. 1.

   Solve using the quadratic formula: x² − 1x − 20 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 9 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   €1,400 is invested at 3% compound interest per annum for 2 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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4. 4.

   An object has mass 48.6 g and volume 27 cm³. Find its density.

   Formula:Density

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

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5. 5.

   Find the momentum of a 48 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A triangle has sides a = 17 cm and b = 15 cm with an included angle C = 45°. 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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7. 7.

   Find the population standard deviation of: 9, 5, 13, 3, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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9. 9.

   A body starts at 4 m/s and accelerates at 1.3 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    €1,200 is invested at 5% 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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11. 11.

    An object has mass 51.7 g and volume 11 cm³. Find its density.

    Formula:Density

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

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12. 12.

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

    Formula:Sum of a Geometric Series

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

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13. 13.

    Two masses 2,500 kg and 390 kg are 17 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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14. 14.

    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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15. 15.

    A wave has frequency 204 Hz and wavelength 1.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Two masses 4,200 kg and 530 kg are 11 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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17. 17.

    An object has mass 187 g and volume 34 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A force of 234 N acts on an area of 4.3 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 448 Hz and wavelength 1.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    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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