Sweden · Grade 12 · Practice Sheet 29

1. 1.

   A cone has base radius 8 cm and height 20 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.

   Find the momentum of a 53 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A force of 199 N acts on an area of 7.1 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Find the gravitational potential energy of a 11 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A device runs at 195 V drawing 8.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 4 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   In a triangle, a = 9, b = 9 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   A device runs at 176 V drawing 9.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the momentum of a 26 kg object moving at 17 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Two masses 8,500 kg and 180 kg are 9 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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11. 11.

    A force of 140 N acts on an area of 0.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Find the force needed to accelerate a 32 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A current of 3.9 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A wave has frequency 333 Hz and wavelength 1.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A population of 4,300 grows 8% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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16. 16.

    A 31 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Solve using the quadratic formula: x² + 1x − 30 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A current of 1.6 A flows through a 43 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the population standard deviation of: 5, 17, 3, 16, 14 (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 sum of the first 4 terms of a geometric series with first term a = 4 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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