Austria · Klasse 10 · Practice Sheet 41

1. 1.

   A cylinder has radius 12 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Find the momentum of a 17 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A force of 84 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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4. 4.

   Solve for x: 6x + 15 = 33.

   Formula:Solving a Linear Equation

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

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5. 5.

   An object with initial velocity 11 m/s accelerates at 1 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   Find the force needed to accelerate a 9 kg mass at 5.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   An object with initial velocity 13 m/s accelerates at 2.5 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   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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9. 9.

   A force of 38 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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11. 11.

    Solve using the quadratic formula: x² − 2x − 15 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A wave has frequency 584 Hz and wavelength 0.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Solve for x: 6x + 4 = 34.

    Formula:Solving a Linear Equation

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

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14. 14.

    Find the gravitational potential energy of a 20 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A body starts at 16 m/s and accelerates at 5.7 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    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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17. 17.

    Find the force needed to accelerate a 14 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A 32 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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20. 20.

    A triangle has sides a = 15 cm and b = 17 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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