Brazil · Ano 11 · Practice Sheet 2

1. 1.

   An object has mass 14 g and volume 14 cm³. Find its density.

   Formula:Density

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

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2. 2.

   Find the population standard deviation of: 13, 15, 7, 10, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   An object with initial velocity 10 m/s accelerates at 2.6 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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4. 4.

   A force of 358 N acts on an area of 3.7 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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5. 5.

   Find the gravitational potential energy of a 42 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the momentum of a 2 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A force of 16 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A triangle has sides a = 20 cm and b = 8 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.

   Find the population standard deviation of: 11, 14, 14, 13, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A cylinder has radius 3 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    Solve using the quadratic formula: x² + 5x − 6 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    Find the population standard deviation of: 5, 9, 10, 5, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A population of 1,600 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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14. 14.

    A right-angled triangle has legs of 20 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the momentum of a 13 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the gravitational potential energy of a 14 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    An object with initial velocity 0 m/s accelerates at 4.5 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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18. 18.

    A wave has frequency 546 Hz and wavelength 2.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A current of 3.4 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the population standard deviation of: 11, 11, 20, 9, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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