Germany · Klasse 11 · Practice Sheet 50

1. 1.

   An object has mass 87.4 g and volume 38 cm³. Find its density.

   Formula:Density

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

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2. 2.

   An object with initial velocity 0 m/s accelerates at 4.7 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A force of 416 N acts on an area of 6.5 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   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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5. 5.

   A triangle has sides a = 13 cm and b = 19 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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6. 6.

   A wave has frequency 62 Hz and wavelength 2.61 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   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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8. 8.

   In a triangle, a = 5, b = 10 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Find the population standard deviation of: 16, 4, 6, 5, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A force of 495 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A right-angled triangle has legs of 6 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Find the force needed to accelerate a 43 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A force of 59 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Solve using the quadratic formula: x² + 4x − 5 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A triangle has sides a = 5 cm and b = 13 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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16. 16.

    A cylinder has radius 13 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A wave has frequency 736 Hz and wavelength 1.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A device runs at 132 V drawing 1.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    In a triangle, a = 7, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    An object has mass 166.4 g and volume 26 cm³. Find its density.

    Formula:Density

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

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