Finland · Grade 11 · Practice Sheet 3

1. 1.

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

   Formula:Standard Deviation (Population)

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

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2. 2.

   An object has mass 78.4 g and volume 28 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   Solve using the quadratic formula: x² + 5x + 4 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the momentum of a 21 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A cylinder has radius 2 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   Solve using the quadratic formula: x² − 4x − 5 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A cylinder has radius 6 cm and height 10 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 momentum of a 4 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the sum of the first 6 terms of a geometric series with first term a = 7 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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10. 10.

    A body starts at 20 m/s and accelerates at 4.8 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A cylinder has radius 5 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 7 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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13. 13.

    A cylinder has radius 13 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A device runs at 133 V drawing 6.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A current of 6.8 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the gravitational potential energy of a 25 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    Find the force needed to accelerate a 27 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A body starts at 16 m/s and accelerates at 1.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A device runs at 69 V drawing 6.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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