Greece · Grade 12 · Practice Sheet 31

1. 1.

   Find the momentum of a 19 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A force of 140 N acts on an area of 4.4 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A cone has base radius 12 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A wave has frequency 831 Hz and wavelength 2.7 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the force needed to accelerate a 50 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A device runs at 25 V drawing 0.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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8. 8.

   Find the population standard deviation of: 12, 16, 2, 19, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   In a triangle, a = 6, b = 9 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A triangle has sides a = 6 cm and b = 13 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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11. 11.

    A 16 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Find the gravitational potential energy of a 20 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the force needed to accelerate a 22 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the momentum of a 40 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    In a triangle, a = 8, b = 10 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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17. 17.

    Solve using the quadratic formula: x² + 11x + 30 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A device runs at 195 V drawing 8.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 334 N acts on an area of 4.4 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A force of 45 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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