Italy · Classe 11 · Practice Sheet 19

1. 1.

   A right-angled triangle has legs of 20 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.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   An object has mass 53.2 g and volume 7 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A 3 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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5. 5.

   An object has mass 87.4 g and volume 23 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A right-angled triangle has legs of 19 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A cone has base radius 10 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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8. 8.

   Find the gravitational potential energy of a 34 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A 18 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A force of 38 N moves an object 8 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    In a triangle, a = 16, b = 18 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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12. 12.

    Find the momentum of a 12 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    An object with initial velocity 3 m/s accelerates at 1.4 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    An object has mass 218.4 g and volume 28 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A triangle has sides a = 7 cm and b = 10 cm with an included angle C = 90°. 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 body starts at 5 m/s and accelerates at 3 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A current of 6.6 A flows through a 5 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A force of 31 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    €900 is invested at 5% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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20. 20.

    Find the population standard deviation of: 7, 10, 13, 14, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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