Australia · Year 12 · Practice Sheet 42

1. 1.

   A force of 33 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A triangle has sides a = 6 cm and b = 14 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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3. 3.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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4. 4.

   Find the gravitational potential energy of a 27 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A current of 0.9 A flows through a 21 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A body starts at 12 m/s and accelerates at 2.6 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A 22 kg object moves at 25 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the force needed to accelerate a 53 kg mass at 5.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 49 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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11. 11.

    A wave has frequency 530 Hz and wavelength 3.93 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A force of 71 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    $3,000 is invested at 5% compound interest per annum for 4 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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14. 14.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

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

    Formula:Sum of a Geometric Series

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

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16. 16.

    A force of 254 N acts on an area of 1.7 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    An object with initial velocity 4 m/s accelerates at 2.5 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.

    Find the force needed to accelerate a 60 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the momentum of a 20 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Solve using the quadratic formula: x² − 2x − 8 = 0.

    Formula:Quadratic Formula

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

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