Peru · Grado 11 · Practice Sheet 12

1. 1.

   Find the population standard deviation of: 16, 19, 4, 12, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   In a triangle, a = 11, b = 10 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A device runs at 197 V drawing 7.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A 31 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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5. 5.

   Find the force needed to accelerate a 60 kg mass at 5.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A current of 4.5 A flows through a 32 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the momentum of a 2 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 275 N acts on an area of 0.7 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A current of 3.4 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    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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11. 11.

    A 7 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A wave has frequency 773 Hz and wavelength 2.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the force needed to accelerate a 27 kg mass at 8.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 5 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A body starts at 5 m/s and accelerates at 4.2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    An object with initial velocity 13 m/s accelerates at 1.3 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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17. 17.

    A force of 9 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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18. 18.

    A cylinder has radius 4 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Find the momentum of a 38 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the force needed to accelerate a 13 kg mass at 1.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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