Greece · Grade 12 · Practice Sheet 48

1. 1.

   A cone has base radius 12 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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2. 2.

   A body starts at 11 m/s and accelerates at 3.9 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A force of 115 N acts on an area of 8.3 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A wave has frequency 502 Hz and wavelength 3.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 6 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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6. 6.

   Find the sum of the first 5 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Find the population standard deviation of: 13, 11, 3, 6, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Find the force needed to accelerate a 36 kg mass at 7.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Solve using the quadratic formula: x² − 3x + 0 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A device runs at 91 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A force of 30 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Find the momentum of a 43 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Two masses 3,400 kg and 120 kg are 3 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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14. 14.

    A body starts at 8 m/s and accelerates at 2.5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Two masses 8,800 kg and 240 kg are 11 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    A device runs at 90 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A cone has base radius 3 cm and height 23 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 body starts at 5 m/s and accelerates at 2.2 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A device runs at 147 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the population standard deviation of: 16, 4, 20, 18, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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