France · Classe 10 · Practice Sheet 27

1. 1.

   A cylinder has radius 7 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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2. 2.

   A 10 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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3. 3.

   An object has mass 81 g and volume 45 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Solve for x: 4x + 7 = 19.

   Formula:Solving a Linear Equation

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

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5. 5.

   A cylinder has radius 14 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   An object with initial velocity 6 m/s accelerates at 3.4 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   €500 is invested at 6% 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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8. 8.

   Find the momentum of a 59 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A force of 67 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A 33 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A wave has frequency 512 Hz and wavelength 4.18 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A 28 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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13. 13.

    Find the force needed to accelerate a 36 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A 15 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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15. 15.

    A triangle has sides a = 11 cm and b = 11 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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16. 16.

    In a triangle, a = 10, b = 5 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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17. 17.

    Find the momentum of a 15 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    €4,000 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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20. 20.

    Find the force needed to accelerate a 51 kg mass at 5.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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