Hong Kong · Grade 11 · Practice Sheet 50

1. 1.

   A triangle has sides a = 5 cm and b = 16 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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2. 2.

   A wave has frequency 574 Hz and wavelength 2.4 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   An object with initial velocity 5 m/s accelerates at 3.7 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Find the force needed to accelerate a 13 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A triangle has sides a = 19 cm and b = 18 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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6. 6.

   A force of 68 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 519 Hz and wavelength 1.78 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A 25 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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9. 9.

   A current of 2.9 A flows through a 45 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the gravitational potential energy of a 38 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    HK$ 1,600 is invested at 3% 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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12. 12.

    Find the population standard deviation of: 9, 20, 19, 17, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A right-angled triangle has legs of 14 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    An object has mass 114 g and volume 30 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A 15 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    A device runs at 240 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Solve using the quadratic formula: x² + 9x + 18 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A device runs at 218 V drawing 8.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 444 N acts on an area of 1.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A wave has frequency 533 Hz and wavelength 0.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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