Germany · Klasse 9 · Practice Sheet 15

1. 1.

   A right-angled triangle has legs of 16 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A wave has frequency 571 Hz and wavelength 1.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the momentum of a 53 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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5. 5.

   Solve for x: 7x + 13 = 62.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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6. 6.

   A train moves at 97 km/h for 3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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7. 7.

   A device runs at 235 V drawing 2.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the gravitational potential energy of a 47 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A cone has base radius 8 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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10. 10.

    Solve for x: 5x + 16 = 61.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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11. 11.

    €4,300 is invested at 5% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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12. 12.

    An object has mass 176.9 g and volume 29 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A current of 4 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the force needed to accelerate a 30 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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16. 16.

    €270 is shared in the ratio 4 : 5. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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17. 17.

    A car travels 434 km in 7 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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18. 18.

    A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    Find the force needed to accelerate a 58 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A train moves at 67 km/h for 2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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