Hungary · Grade 11 · Practice Sheet 6

1. 1.

   A triangle has sides a = 5 cm and b = 12 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 48 Hz and wavelength 4.88 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A body starts at 9 m/s and accelerates at 4.6 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A current of 2.8 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A right-angled triangle has legs of 4 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A cylinder has radius 11 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   A current of 2.8 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   An object has mass 60 g and volume 10 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A current of 1.6 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.

    An object has mass 210.6 g and volume 27 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A body starts at 4 m/s and accelerates at 4.3 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A population of 1,600 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the force needed to accelerate a 57 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A force of 57 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A 32 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 gravitational potential energy of a 38 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    An object with initial velocity 10 m/s accelerates at 3.9 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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19. 19.

    Find the population standard deviation of: 7, 9, 5, 12, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    Find the momentum of a 36 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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