Germany · Klasse 10 · Practice Sheet 19

1. 1.

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

   Formula:Quadratic Formula

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

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2. 2.

   A triangle has sides a = 8 cm and b = 11 cm with an included angle C = 30°. 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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3. 3.

   A 39 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the force needed to accelerate a 29 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A 21 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Find the momentum of a 12 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A cylinder has radius 6 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   A device runs at 38 V drawing 0.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the momentum of a 5 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A right-angled triangle has legs of 14 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    An object has mass 277.3 g and volume 47 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A right-angled triangle has legs of 10 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    €1,500 is invested at 5% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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14. 14.

    A right-angled triangle has legs of 16 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A wave has frequency 294 Hz and wavelength 3.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Solve for x: 2x + 6 = 28.

    Formula:Solving a Linear Equation

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

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17. 17.

    €1,100 is invested at 5% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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18. 18.

    Find the gravitational potential energy of a 50 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the force needed to accelerate a 19 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A right-angled triangle has legs of 10 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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