Ireland · Year 12 · Practice Sheet 1

1. 1.

   A force of 113 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   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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3. 3.

   Find the momentum of a 32 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   An object with initial velocity 7 m/s accelerates at 2.3 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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5. 5.

   In a triangle, a = 18, b = 9 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   Find the population standard deviation of: 3, 10, 7, 12, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A device runs at 37 V drawing 8.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the gravitational potential energy of a 45 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A body starts at 13 m/s and accelerates at 2 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A wave has frequency 475 Hz and wavelength 2.02 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A current of 5.9 A flows through a 32 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Find the force needed to accelerate a 28 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A cone has base radius 8 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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14. 14.

    A force of 97 N acts on an area of 4.5 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A device runs at 103 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A body starts at 12 m/s and accelerates at 5.5 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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18. 18.

    Find the momentum of a 24 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    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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20. 20.

    A device runs at 152 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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