Brazil · Ano 11 · Practice Sheet 39

1. 1.

   A wave has frequency 413 Hz and wavelength 0.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the momentum of a 41 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Find the population standard deviation of: 20, 12, 2, 3, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the force needed to accelerate a 3 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A cone has base radius 5 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A device runs at 196 V drawing 6.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A cylinder has radius 2 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 1 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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9. 9.

   A cylinder has radius 6 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A device runs at 233 V drawing 7.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A cone has base radius 7 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Find the gravitational potential energy of a 28 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the momentum of a 41 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A triangle has sides a = 13 cm and b = 20 cm with an included angle C = 120°. 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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15. 15.

    A force of 328 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Solve using the quadratic formula: x² + 4x − 12 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A cone has base radius 2 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A force of 56 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the population standard deviation of: 5, 8, 6, 18, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    Find the force needed to accelerate a 46 kg mass at 4.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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