Austria · Klasse 12 · Practice Sheet 45

1. 1.

   A triangle has sides a = 12 cm and b = 11 cm with an included angle C = 60°. 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 force of 100 N moves an object 19 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   In a triangle, a = 9, b = 14 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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4. 4.

   Two masses 1,600 kg and 660 kg are 17 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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5. 5.

   Find the population standard deviation of: 6, 12, 20, 7, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the force needed to accelerate a 28 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 52 N moves an object 12 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   €1,000 is invested at 6% 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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9. 9.

   A force of 26 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the gravitational potential energy of a 20 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A wave has frequency 495 Hz and wavelength 3.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A body starts at 16 m/s and accelerates at 3 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A force of 43 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Two masses 5,700 kg and 570 kg are 4 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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15. 15.

    An object with initial velocity 13 m/s accelerates at 1 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the momentum of a 49 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A 38 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    Find the gravitational potential energy of a 48 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    An object with initial velocity 2 m/s accelerates at 4.7 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    €3,100 is invested at 4% compound interest per annum for 2 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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