Norway · Grade 11 · Practice Sheet 39

1. 1.

   Two masses 3,100 kg and 100 kg are 3 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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2. 2.

   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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3. 3.

   Solve using the quadratic formula: x² + 1x + 0 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   An object has mass 203 g and volume 35 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A force of 118 N acts on an area of 4 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the force needed to accelerate a 34 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the momentum of a 40 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A triangle has sides a = 10 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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9. 9.

   A force of 59 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A wave has frequency 664 Hz and wavelength 2.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    An object has mass 47.3 g and volume 11 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A force of 31 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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13. 13.

    Find the force needed to accelerate a 14 kg mass at 8.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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15. 15.

    A force of 90 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A current of 2 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A device runs at 87 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the momentum of a 12 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A device runs at 157 V drawing 3.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the population standard deviation of: 7, 9, 11, 10, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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